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#2301714 - 07/13/14 01:01 AM Theoretical tuning sequence
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
I came up with an interesting tuning sequence, which I've tested in simulations. It is of no practical use, but since I find it interesting, perhaps others will also.

First tune A3 from A4 (from fork) and leave it there. The temperament octave is F3-E4.

Select a random note (excluding A3) from the temperament octave. Now play a P4 and a P5 from that note within the temperament octave, except when you selected A#3 or B3, then play two P4s. Now tune the note you randomly selected to make both intervals equal beating.

Repeat.

Eventually all notes will end up in ET with less than 1 cent error. If all notes were randomly detuned by as much as 50 cents you will need to do this about 600-1500 times.

Continuing beyond this will not improve matters substantially, as in true ET they are of course not equal beating. (You can get the error down to about 0.6 cents if your persist, but not less than that.)

If you refine the sequence by making the intervals beat in the correct proportion (by 4/3 or 3/2) you can continue and will end up with an error below 0.2 cents if you persist for 1000-2000 repeats.

Kees

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#2301745 - 07/13/14 03:00 AM Re: Theoretical tuning sequence [Re: DoelKees]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Ah, funny you should come up with this. I was toying with something similar last year and thought of it as an iterative convergence. My thought was to start with an untuned span of a 5th, then tune the next span of a 5th above by tuning each note with an equal beating lower 4th and 5th chromatically up to the top of the span. Then do the same in reverse down the lower span. Then up the upper span again, down the lower etc etc. My fuzzy logic tells me it should eventually converge towards equal spaced semitones i.e. ET.

The thought came to me because of the fact that tuning up the treble with equal beating extended 5ths and 8ths in theory smoothes out an unequal temperament towards the extremity. So why not use this property to tune an equal tempered middle section.

Edit - I tried it on a client's piano and it did not work very well grin


Edited by Chris Leslie (07/13/14 03:02 AM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2301778 - 07/13/14 06:39 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Ah! Interesting!

Equal beating intervals. I guess Bill Bremmer has designed his EBVT III in such a way.

Here is another exercise on tuning ET, not by using equal beating intervals, but by just intonation fifths, fourths, major thirds and octaves.

Tuning equal temperament by using just intonation techniques was discovered/invented in 1807 by John Farey.

He discovered that five just fourths, minus two just fifths, minus one just major third create a fifth that is almost identical to an equal temperament fifth. Today this type of fifth is known as a "schisma fifth".

schisma fifth ratio = 4/3*4/3*4/3*4/3*4/3*2/3*2/3*4/5 = 16384/10935 = 1.498308185

ET fifth ratio = 2^(7/12) = 1.498307077

The error is = 1200*log2(1.498308185/1.498307077) = 0.00128 cents!



And he designed a bearing plan (tuning sequence) to tune equal temperament by tuning only pure, beatless, intervals.



Tune each note from the previous one, everything without exception is to be tuned in just intonation (characters in bold indicate ET tuned notes):

C4, Ab3, Db4, Gb3/F#3, B3, E4, A3, D4, G3
G3, Eb3, Ab3, Db4, Gb3/F#3, B3,E3, A3, D4
D4, Bb3, Eb4, Ab3, Db4, Gb4/F#4, B3, E4, A3
A3, F3, Bb3, Eb4, Ab3, Db4, Gb3/F#3, B3, E4
E4, E3, C3, F3, Bb3, Eb4, Ab3, Db4, Gb3/F#3, B3
B3, B2, G2, C3, F3, Bb3, Eb3, Ab3, Db3, Gb3/F#3
F#3, D3, G2, C3, F3, Bb2, Eb3, Ab3, Db4/C#4
C#4, C#3, A2, D3, G2, C3, F3, Bb3, Eb3, Ab3/G#3
G#3, E3, A2, D3, G2, C3, F3, Bb2, Eb3, Eb4/D#4
D#4, D#3, B2, E3, A2, D3, G2, C3, F3, Bb3/A#3
A#3, A#2, F#2, B2, E3, A2, D3, G2, C3, F3, F4

Of course, this is only a theoretical exercise as the errors involved in tuning such a long sequence, 97 notes to tune, are far greater than is acceptable for a correct ET setting.

But it is interesting to know he has discovered a just intonation technique to temper an ET fifth.




Edited by Gadzar (07/13/14 06:53 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2301834 - 07/13/14 11:56 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
I am intrigued that other tuners are still experimenting with these ideas. It seems to imply that the current sequences available today are still considered inefficient by some technicians. I believe this to be so.

That is why I am working on a sequence and method that I will soon publish as a book. In my opinion, a highly accurate and efficient sequence/method would have to have the following elements:

1. The sequence should require as little iteration as possible. I.e. each step should place each note as accurately as possible. (My sequence has one iteration, using the upper skeleton to iterate F4)

2. The sequence should use windows as much as possible, instead of equalities. (My sequence uses windows for every note except one, which uses an equality.)

3. The method should emphasize and encourage clean unisons and good stability.

4. Obviously, the sequence should use as many checks as possible to ensure accuracy from P4/P5 and m3/M3/M6 relationships.

The real beauty of this approach is a mating of method with sequence. I've tried to explain some of the elements of this method, but without the big picture, the benefits of each element are not clear. That's why I'm not being specific regarding the details.

The book is almost half done and I'll probably post the introduction when I'm finished.

If anyone would like to proof read it before it's published, let me know.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2301926 - 07/13/14 05:44 PM Re: Theoretical tuning sequence [Re: Gadzar]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Originally Posted By: Gadzar
...Here is another exercise on tuning ET, not by using equal beating intervals, but by just intonation fifths, fourths, major thirds and octaves...

...Tuning equal temperament by using just intonation techniques was discovered/invented in 1807 by John Farey.
But it is interesting to know he has discovered a just intonation technique to temper an ET fifth.


This may be slightly off-topic, but there is also a similar method to get an absolute beat rate of a RBI by tuning perfect just intervals. It is simple:

If you tune the beginning of a 5th/4th sequence from A3 (A3-E4-B3-F#4) using perfect intervals, then the beat rate of the A3-F#4 6th is very close to the M3 beat rate of F4-A4. This could be used as a seed to begin a Contiguous M3rd sequence using something absolute to start with.

With no iH, the beat rate of the M6th is 13.8, and the M3rd is also 13.8.
With strong inharmonicity, the beat rate of the M6th is about 13.5, and the M3rd is about 13.0. The difference with strong iH makes an error of only about 0.5 cents.


Edited by Chris Leslie (07/13/14 05:46 PM)
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Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2301964 - 07/13/14 07:39 PM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
This is amazing. There are several combinations of pure, equal beating and/or proportional beating intervals which give the correct tempering of ET intervals.

The sequence of Bill Bremmer, ET via Marpurg is a good example, it combines proportional tuning (for the setting of CM3s), pure tuning of P4s and P5s and equal beating P4s and P5s to get an almost perfect ET.

Also, if you are good to judge the tempering of M3s then you can try this: tune an octave, say for example A3A4, now tune pure P4s from A3 up to D4 and G4 and from A4 down to E4 and B3. Then you tune D#4 by equally tempering both M3s B3D#4 and D#4G4 (proportional tuning). The resulting D#4 is quasi perfect ET, the theoretical error is 0.000000000000384 cents.

From there, you can tune two chains of CM3s: F3, A3, C#4, F4, A4 and G3,B3, D#4, G4 just by proportional tuning of M3s. And you have tuned every other note between F3 and A4.



Edited by Gadzar (07/13/14 07:53 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302082 - 07/14/14 04:07 AM Re: Theoretical tuning sequence [Re: DoelKees]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Rafael, I have done my math on the D#4 method and I get something different. If I make equal beating M3rds either side of D#4 (if that is what you mean) the D#4 ends up sharp by 1 cent. If the D#4 is at proper ET pitch then the two M3rds have a 4/5 beat speed ratio, just like in a CM3rd progression but at wrong pitch.


Edited by Chris Leslie (07/14/14 04:16 AM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2302091 - 07/14/14 05:01 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2069
Loc: Pretoria, South Africa
Rafael,

Very interesting shortcut to D#4.

I'm trying to figure out how one would then proceed to tune the ladder of CM3s: G3-B3-D#4-G4.

The other CM3 ladder is different, because both A3 and A4 are fixed. But with this ladder on G3, the only reference is D#4, and there is no outside M3 for verification. I suppose the logical way is to tune D#3 as an auxiliary note?
_________________________
Autodidact interested in piano technology.
LinkedIn profile
1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2302097 - 07/14/14 05:43 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Chris, here are the maths. I hope I'm not wrong.

From A3=220 we tune up a pure fourth D4=4/3×220=293.33 and up a pure fourth to G4=4/3×293.33=391.11

From A4 we tune down a pure fourth to E4=3/4×440=330 and down a pure fourth to B3= 3/4×330=247.5

Now to proportionally tune D#4 to B3 and G4 we must have D#4/B3=G4/D#4 so D#4=(B3×G4)^(1/2)=(247.5×391.11)^(1/2)=311.13

Wich compared to ET theoretical frequence of D#4=440×2^(-6/12)=311.13

results in no error at all.


Edited by Gadzar (07/14/14 05:44 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302103 - 07/14/14 06:14 AM Re: Theoretical tuning sequence [Re: Mark R.]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Mark,

If you are good at tempering proportional M3s, all you need is one note of a CM3s chain.

Here we tune

A4 to fork
A3 to A4, the octave size you like.
D4 to A3, as a pure fourth
G4 to D4, as a pure fourth
E4 to A4, as a pure fourth
B3 to E4, as a pure fourth
D#4 to B3/G4, as a proportional M3. That means D#4/B3 = G4/D#4.

to aurally tune such M3s you must be good on tempering M3s, and place D#4 at the spot where B3D#4 sounds as tempered as D#4G4. For this, G4D#4 should beat faster than D#4B3, in a approximate ratio of 5 to 4, but I usually do not count beats, nor estimate beat rates by themselves, but I estimate the amount of tempering (harshness or roughness) in the major thirds.

Now you have A and D# accurately tuned, you can tune the rest of the CM3s involved with your usual techniques, for example tuning:

-F3 to A3 at about 7 bps
-F4 to F3 as a clean octave, the same size A3A4 or slightly wider.
-C#4 to A3/F4, as a proportional M3, exactly the same as for D#4, from here refine the tuning of F3, C#4 and F4 to have a nice progression of the beat rates of the CM3s.

From there you have several ways to continue, one is what you said tuning

-D#3 to D#4 as a clean octave, the same size of F3F4 or slightly wider.

and then tune G3, B3 between D#3 and D#4 to have a nice progression of CM3s.

Another would be to directly tune B3 to have A3C#4 < B3D#4 < C#4F4.

And then tune G3 to have F3A3 < G3B3 < A3C#4.

Now you can refine the tuning of D#3, G3, B3 by checking the progression of the CM3s.

By using the same proportional technique you can now tune the remaining two chains of CM3s.

For example tune A#3 inbetween F3 and D#4. The fourths F3A#3 and A#3D#4 must have the same amount of tempering.

And C4 can be tuned inbetween G3 and F4 the same way, using the fourths G3C4 and C4F4.

This is a sequence that is very accurate and self correcting.

Some may not like it because it doesn't use P5s. But it can be modified to include P5s.




Edited by Gadzar (07/14/14 06:44 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302113 - 07/14/14 07:07 AM Re: Theoretical tuning sequence [Re: Gadzar]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Originally Posted By: Gadzar
Chris, here are the maths. I hope I'm not wrong.

From A3=220 we tune up a pure fourth D4=4/3×220=293.33 and up a pure fourth to G4=4/3×293.33=391.11

From A4 we tune down a pure fourth to E4=3/4×440=330 and down a pure fourth to B3= 3/4×330=247.5

Now to proportionally tune D#4 to B3 and G4 we must have D#4/B3=G4/D#4 so D#4=(B3×G4)^(1/2)=(247.5×391.11)^(1/2)=311.13

Wich compared to ET theoretical frequence of D#4=440×2^(-6/12)=311.13

results in no error at all.

I confused equal beating and proportional M3rds. But as you explained to Mark, to tune proportional M3rds either side of D#4 I don't think you can do it without expanding out to a whole chain of CM3rds.


Edited by Chris Leslie (07/14/14 07:07 AM)
_________________________
Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2302118 - 07/14/14 07:27 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2069
Loc: Pretoria, South Africa
Thanks for this, Rafael.

I've been using ET via Marpurg, and I see some possible shortcuts here, to get more quickly to the F3-F4 whole-tone scale, having to correct fewer notes afterwards.
_________________________
Autodidact interested in piano technology.
LinkedIn profile
1922 49" Zimmermann, project piano.
1970 44" Ibach, daily music maker.

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#2302125 - 07/14/14 07:55 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.

For my dayly work I tune:

A4, A3, F3, F4, C#4 (CM3s), A#3/F#3/B3, G#3/C4/G3 (setting the P4s tempering with G3B3, Sanderson/Baldassin), then expanding the mini temperament F3-C#4 to D4, D#4, E4.

I tune this as quick as I can, leaving imperfections untouched.

In the fine tuning, I retune every note with all tests I judge necessary. Kent Swafford has a very nice essay on correcting a temperament.

For me it is useless to pursue perfection in the first pass, you are going to move everything in the fine tuning, so why bother?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2302130 - 07/14/14 08:16 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Great work, Doel and others! I got the idea of equal beating intervals from Owen Jorgensen's little known and little used second publication, The Handbook of Equal Beating Temperaments. The usefulness at fist seemed only to be that one was not guessing at anything. Whatever the piano's scaling and inharmonicity may be, it is incorporated automatically.

In the EBVT, I was looking for a way to provide a sequence that I could reproduce reliably more than anything else and that perhaps others who may take an interest could also. But I discovered something else that was far more profound: When two intervals, either slowly or rapidly beating, have the very same beat rate, those beats tend to cancel each other.

This is what makes the EBVT (or EBVT III) sound so much purer than it is when music is played in the simple keys. It often sounds like a much stronger temperament that would have too much harshness in the remote keys to be useful. Yet the acoustic trick allows for moderated harshness in the remote keys that is not only tolerable but often just enough to actually be titillating. Who said that width of Rapidly Beating Intervals (RBI) has no effect on emotions? I certainly know that it does!

For more than 20 years, I refused to tune ET for anyone for any reason. Yet, what I found as a pleasant surprise from the ET via Marpurg was that same canceling effect due to the equally beating intervals. Now, if I choose to tune a temperament with no key color or someone insists upon ET because of ultra sensitivity to RBI's any wider than what ET would provide for, I have a solution that provides for a much "cleaner" sound overall than a true ET could provide.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#2302139 - 07/14/14 09:05 AM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Kees:

Just some general comments, because you know what you are doing and what you are talking about. That is, what I am going to mention, I am sure you have already thought about.

You have described an algorithm. It favors the 2nd, 3rd and 4th partials when iH exists. I expect that in the case of a jump in iH, the RBIs would not be progressive.

I will often use the relationship of the SBI beatrates to smooth out a tuning, or when touching up a tuning. It is the same idea.

I had been toying with the idea of a sequence that is based on the M3/M6 test. Of course this requires a temperament span of greater than an octave. It may also work well as an algorithm, I think... Something like:

A3 = 220hz
A3-C#3 = 9bps
A3-E4 = -0.5bps
G3-E4 = 9bps
G3-D4/A3-D4 = -1/2 ratio

Of course, so far these are just rule-of thumb numbers. As the algorithm progresses, any errors would be corrected only part way. I would think three times thru the sequence would be sufficient. I'll have to play with it on my simulator.

This would continue with something like:

B3-E4/E4-A4 = 2/3 ratio AND
G3-B3/A3-C#3 = 7/8 ratio (both won't happen, so the error is averaged between the two)
F3-D4 = G3-B3

Then next M3/M6 test can produce a A3-D#4-A4 contiguous tritone, but the m3/M3 inversion of the M3/M6 test would probably be used.

Then three more M3/M6 tests should complete the temperament. Of course then the errors are checked and corrected by averaging. I suppose the averaging could be weighted according to a preference...

I'll see if I can find the time to play with this. Not as an aural tuning sequence, but as an algorithm.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2302153 - 07/14/14 10:10 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 219
Loc: Germany
Originally Posted By: Bill Bremmer RPT
...But I discovered something else that was far more profound: When two intervals, either slowly or rapidly beating, have the very same beat rate, those beats tend to cancel each other.

This is what makes the EBVT (or EBVT III) sound so much purer than it is when music is played in the simple keys. It often sounds like a much stronger temperament that would have too much harshness in the remote keys to be useful. Yet the acoustic trick allows for moderated harshness in the remote keys that is not only tolerable but often just enough to actually be titillating. Who said that width of Rapidly Beating Intervals (RBI) has no effect on emotions? I certainly know that it does!

For more than 20 years, I refused to tune ET for anyone for any reason. Yet, what I found as a pleasant surprise from the ET via Marpurg was that same canceling effect due to the equally beating intervals. Now, if I choose to tune a temperament with no key color or someone insists upon ET because of ultra sensitivity to RBI's any wider than what ET would provide for, I have a solution that provides for a much "cleaner" sound overall than a true ET could provide.


With my research i found the opposite to be true:
Equal beating increases (worsens) beat intensities and does not cancel them.





Edited by Bernhard Stopper (07/14/14 10:13 AM)
_________________________
Bernhard Stopper
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(Amadeus, the movie)

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#2302192 - 07/14/14 11:56 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Mark,

If you are good at tempering proportional M3s, all you need is one note of a CM3s chain.

Here we tune

A4 to fork
A3 to A4, the octave size you like.
D4 to A3, as a pure fourth
G4 to D4, as a pure fourth
E4 to A4, as a pure fourth
B3 to E4, as a pure fourth
D#4 to B3/G4, as a proportional M3. That means D#4/B3 = G4/D#4.

to aurally tune such M3s you must be good on tempering M3s, and place D#4 at the spot where B3D#4 sounds as tempered as D#4G4. For this, G4D#4 should beat faster than D#4B3, in a approximate ratio of 5 to 4, but I usually do not count beats, nor estimate beat rates by themselves, but I estimate the amount of tempering (harshness or roughness) in the major thirds.

Now you have A and D# accurately tuned, you can tune the rest of the CM3s involved with your usual techniques, for example tuning:

-F3 to A3 at about 7 bps
-F4 to F3 as a clean octave, the same size A3A4 or slightly wider.
-C#4 to A3/F4, as a proportional M3, exactly the same as for D#4, from here refine the tuning of F3, C#4 and F4 to have a nice progression of the beat rates of the CM3s.

From there you have several ways to continue, one is what you said tuning

-D#3 to D#4 as a clean octave, the same size of F3F4 or slightly wider.

and then tune G3, B3 between D#3 and D#4 to have a nice progression of CM3s.

Another would be to directly tune B3 to have A3C#4 < B3D#4 < C#4F4.

And then tune G3 to have F3A3 < G3B3 < A3C#4.

Now you can refine the tuning of D#3, G3, B3 by checking the progression of the CM3s.

By using the same proportional technique you can now tune the remaining two chains of CM3s.

For example tune A#3 inbetween F3 and D#4. The fourths F3A#3 and A#3D#4 must have the same amount of tempering.

And C4 can be tuned inbetween G3 and F4 the same way, using the fourths G3C4 and C4F4.

This is a sequence that is very accurate and self correcting.

Some may not like it because it doesn't use P5s. But it can be modified to include P5s.




But, tuning a pure interval in ET is a waste of time, because you will have to correct it later on.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2302198 - 07/14/14 12:20 PM Re: Theoretical tuning sequence [Re: Gadzar]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
But, tuning a pure interval in ET is a waste of time, because you will have to correct it later on.


I guess you have not read my earlier post:


Originally Posted By: Gadzar
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.

For my dayly work I tune:

A4, A3, F3, F4, C#4 (CM3s), A#3/F#3/B3, G#3/C4/G3 (setting the P4s tempering with G3B3, Sanderson/Baldassin), then expanding the mini temperament F3-C#4 to D4, D#4, E4.

I tune this as quick as I can, leaving imperfections untouched.

In the fine tuning, I retune every note with all tests I judge necessary. Kent Swafford has a very nice essay on correcting a temperament.

For me it is useless to pursue perfection in the first pass, you are going to move everything in the fine tuning, so why bother?


And if you did read this post, then you have to understand the objective of the exercise is to precisely locate the tuning of D#4, nothing more. I am not tuning the piano.

And about what you say of waste of time, let me tell you that I never tune a piano in a single pass. never!


I always do at least two passes, even if the piano is at pitch. So, all what I do in the first pass is to be moved in the fine tuning. It is in this second pass, the fine tuning pass, where I strive for stability. In this pass, more than tuning I am setting the pins and rendering the strings.

Maybe you'll say it's a waste of time, but it's the way I do it.
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#2302199 - 07/14/14 12:30 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
Mark Cerisano, RPT Online   content
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Originally Posted By: Bernhard Stopper
Originally Posted By: Bill Bremmer RPT
...But I discovered something else that was far more profound: When two intervals, either slowly or rapidly beating, have the very same beat rate, those beats tend to cancel each other.

This is what makes the EBVT (or EBVT III) sound so much purer than it is when music is played in the simple keys. It often sounds like a much stronger temperament that would have too much harshness in the remote keys to be useful. Yet the acoustic trick allows for moderated harshness in the remote keys that is not only tolerable but often just enough to actually be titillating. Who said that width of Rapidly Beating Intervals (RBI) has no effect on emotions? I certainly know that it does!

For more than 20 years, I refused to tune ET for anyone for any reason. Yet, what I found as a pleasant surprise from the ET via Marpurg was that same canceling effect due to the equally beating intervals. Now, if I choose to tune a temperament with no key color or someone insists upon ET because of ultra sensitivity to RBI's any wider than what ET would provide for, I have a solution that provides for a much "cleaner" sound overall than a true ET could provide.


With my research i found the opposite to be true:
Equal beating increases (worsens) beat intensities and does not cancel them.





AHA! YES! This is crazy isn't it? But the truth is, sometimes equal beating cancels and sometimes it increases sound. The scientific terms are Constructive and Destructive Interference.

Equal beating wave forms have identical periods, i.e. identical distances between peaks and valleys.

When peaks line up with peaks, and valleys line up with valleys, we have constructive interference, and that means a louder beat. Also called "being in phase".

When peaks line up with valleys, and valleys line up with peaks, we have destructive interference, and that means cancellation. (Also called "being out of phase")

See
https://www.youtube.com/watch?v=OKsmqzRFFsk (Just the beginning)
https://www.youtube.com/watch?v=YuveKkmeFWg (Describes cancelling)

That's another reason why ETD's can't tune unisons; they don't measure phase.

Also, this can explain one reason why dead on unisons are not appropriate for a piano, even though intuitively, one might think a "dead on" unison is preferable. A "dead on" unison might be in phase (louder) or out of phase (quieter), and a piano with all "dead on" unisons would have uneven tone.
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#2302203 - 07/14/14 12:39 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
BDB Online   content
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Phase differences are location-specific. You can hear this with a tuning fork. Just twirl the fork near your ear, and it will sound louder or softer, because more of the sound will be in phase or out of phase.

(Of course, everyone who is interested in tuning should have at least one high-quality tuning fork!)


Edited by BDB (07/14/14 12:39 PM)
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#2302212 - 07/14/14 12:50 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
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Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
But, tuning a pure interval in ET is a waste of time, because you will have to correct it later on.


I guess you have not read my earlier post:


Originally Posted By: Gadzar
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.

For my dayly work I tune:

A4, A3, F3, F4, C#4 (CM3s), A#3/F#3/B3, G#3/C4/G3 (setting the P4s tempering with G3B3, Sanderson/Baldassin), then expanding the mini temperament F3-C#4 to D4, D#4, E4.

I tune this as quick as I can, leaving imperfections untouched.

In the fine tuning, I retune every note with all tests I judge necessary. Kent Swafford has a very nice essay on correcting a temperament.

For me it is useless to pursue perfection in the first pass, you are going to move everything in the fine tuning, so why bother?


And if you did read this post, then you have to understand the objective of the exercise is to precisely locate the tuning of D#4, nothing more. I am not tuning the piano.

And about what you say of waste of time, let me tell you that I never tune a piano in a single pass. never!


I always do at least two passes, even if the piano is at pitch. So, all what I do in the first pass is to be moved in the fine tuning. It is in this second pass, the fine tuning pass, where I strive for stability. In this pass, more than tuning I am setting the pins and rendering the strings.

Maybe you'll say it's a waste of time, but it's the way I do it.



Clarification is the source of understanding. Thanks for the post.

PW is a wonderful medium to share different points of view but it is only useful if one can say calmly and peacefully, to one's self of course, "That guy is just plain crazy" and move on. But, yet, there may be something to be gained, and that's why we share.

So, I might suggest, or share, my way:

I only do one pass. It takes a bit longer than a regular one pass, but can be shorter than two passes.

I use a "Come Along" approach where every note is tuned with as high an accuracy as I can set.

Then, in the treble for example, I use this test starting at F5:
C#3F3 < C#3F4 < C#3F5 = C#3A#3 (The P4 window with the pure 12th test)

With this test, I can catch any drifting F4's, etc, and correct them as I go. It also allows me a window into how the pitch is reacting to soundboard settling and bridge tilting, on a pitch raise or drop.

BTW, I've found that the notes do not react the same way, which is what ETD manufacturers would want you to believe in order to espouse their overpull functions, which may be more accurate that the human ear I grant, depending on the human. ;-)

It is one way, not the only way of course.

BTW, I don't tinker, which I assume you mean practice. I have no time to practice. I have to practice on the job, so I have developed a tuning sequence/method that forces me to practice on the job. This way I feel I am getting better at each tuning. You can read some of it if you search PW for DSU.

Best Regards,
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#2302215 - 07/14/14 12:54 PM Re: Theoretical tuning sequence [Re: BDB]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
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Originally Posted By: BDB
Phase differences are location-specific. You can hear this with a tuning fork. Just twirl the fork near your ear, and it will sound louder or softer, because more of the sound will be in phase or out of phase.

(Of course, everyone who is interested in tuning should have at least one high-quality tuning fork!)


BTW, one video I watched mentioned that the loudness and softness observed is clearly audible with sine tones, which the fork is. But also said that complex waves (piano tones?) do not behave the same way. The change of phase affects their harmonic spectrum.

If true, this would explain why turning the head when trying to hear beats, can accentuate or diminish certain partials in the sound.

Neat.

But the problem of uneven tone in a dead on unison tuned piano is still possible, theoretically, because dead on unisons still have the potential to create destructive interference at the listener's ear. Whereas unisons tuned with some tone and sustain, will never create destructive interference because the strings are not the same frequency.


Edited by Mark Cerisano, RPT (07/14/14 12:56 PM)
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#2302218 - 07/14/14 01:01 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
DoelKees Offline
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Registered: 05/01/10
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Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees

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#2302235 - 07/14/14 01:41 PM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
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Registered: 11/13/08
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Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

But I don't think (anymore) that the "beat cancelling effect" is due to equal beating. First it is impractical to get two things truly equal unless they are coupled (or entangled wink ). Second, it is when things are random, like white noise, that cause them to seem consistent, or smooth. Your mind will "see" things on a blank piece of paper, but not on a piece of burlap. Since all the partials in an interval never all line up, there can be a point where they seem randomly off, like the tread pattern on a good set of tires.
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#2302248 - 07/14/14 02:17 PM Re: Theoretical tuning sequence [Re: DoelKees]
Bernhard Stopper Offline
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Registered: 09/22/08
Posts: 219
Loc: Germany
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


Your explanation rather confirms my statement that two equal beating intervals played together increase the intensity of beats compared with the beat intensity of an interval played alone. DŽaccord with human perception of equal beating as an advantage, in the case of "wishful thinking" for a canceling effect.

However, beat masking is a possible phenomenon (which i have demonstrated in my tuning class) but it certainly does not occur with equal beating intervals.


Edited by Bernhard Stopper (07/14/14 02:25 PM)
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#2302260 - 07/14/14 02:50 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Gadzar Offline
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Registered: 12/15/06
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Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
So, I might suggest, or share, my way:

I only do one pass. It takes a bit longer than a regular one pass, but can be shorter than two passes.


How are you sure that what you have just tuned won't move as you continue to tune? (Mainly soundboard and bridge).

IMHO it is a waste of time to accurately tune a note if it is going to drift later as I continue to tune.




Edited by Gadzar (07/14/14 03:09 PM)
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#2302271 - 07/14/14 03:31 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
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In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?
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#2302274 - 07/14/14 03:35 PM Re: Theoretical tuning sequence [Re: Gadzar]
Olek Offline
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Registered: 03/14/08
Posts: 7904
Loc: France
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
So, I might suggest, or share, my way:

I only do one pass. It takes a bit longer than a regular one pass, but can be shorter than two passes.


How are you sure that what you have just tuned won't move as you continue to tune? (Mainly soundboard and bridge).

IMHO it is a waste of time to accurately tune a note if it is going to drift later as I continue to tune.




When tuning with a strip, you develop a perception of the future "give" and it helps a lot when you tune unison as you go.
The second "pass" is then tweaks , not so bad.

The aural tuners always tune "high", all the zone after the plate break and a little under, all that depending of the original pitch, the kind of soundboard, height of bridge...

The amount is as a global overpull (choosing an original pitch that is a little above the final one ) then adding stretch in the vicinity of pure 12th for the melodic section.

I see no reason the instrument do not "grasp" on the resonant spots if they are strong enough. I tend to be confident in the piano for that reason.
May be psychological, but it helps.

Tuning a little slower tend to install a more table pitch, also.
That allow to optimize the firmness of the pin/NSL couple, and I notice that the gie is then minimal.

If tuning fast that tend to slip more, as you may hae experienced yet.



Edited by Olek (07/14/14 03:39 PM)
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#2302354 - 07/14/14 07:04 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Gadzar Offline
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Registered: 12/15/06
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Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?


I am not sure I follow you. You say you tune the piano in one single pass. And you also say that you are fairly sure that what you have just tuned is going to move while you continue to tune.

Doesn't that mean that it will end up out of tune?



Edited by Gadzar (07/14/14 07:07 PM)
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#2302368 - 07/14/14 08:14 PM Re: Theoretical tuning sequence [Re: DoelKees]
Chris Leslie Offline
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Iterating a method several times in order to converge towards a goal is important in piano tuning and regulating because of the interactions between various stages. However, I though this topic was meant to be concerned about a finer level of iteration. I.e. not just repeating a whole method a few times, but repeating a small and fixed element of a method, that will in theory make a small improvement, many many times over. Such concept is not meant to be practical, but rather just an armchair discussion.
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#2302390 - 07/14/14 09:40 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
DoelKees Offline
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Registered: 05/01/10
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Loc: Vancouver, Canada
Originally Posted By: Bernhard Stopper
Your explanation rather confirms my statement that two equal beating intervals played together increase the intensity of beats compared with the beat intensity of an interval played alone. DŽaccord with human perception of equal beating as an advantage, in the case of "wishful thinking" for a canceling effect.

However, beat masking is a possible phenomenon (which i have demonstrated in my tuning class) but it certainly does not occur with equal beating intervals.


What I imagine is the following: In ET play intervals C#4F4 and F4A4. You hear them beat at different rates, so you connect the beat rates to the intervals and hear they are out of just. Now suppose C#4F4 and F4A4 are equal beating (as can happen in some WT's). We now hear the same beat rates so our brain thinks the beats are not a property of the interval, but some external noise which our brain filters out, and we don't think the M3's are out of just.

I have my doubts but it seems somewhat possible.

I don't know what "beat masking" is. Can you explain?

Kees

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#2302396 - 07/14/14 09:59 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

I think it's the same thing: sound waves ride on the atmospheric pressure (the DC) and you can't hear beat cancellation on the telephone either.

If you're not convinced; I convinced myself by looking at an example. Consider tuning P4 A3D4 1bps wide and P5 A3E4 1bps narrow (equal beating). Ignore IH as it plays no role in this.

The P4 beats come from partials 4 and 3 which are at 880 and 881Hz. The P5 beats come from partials 3 and 2 which are at 660 and 659Hz. If we play A3D4E4 simultaneously we should be able to demonstrate beat cancellation by synthesizing just the aforementioned partials (880,881,659,660).

Here I put audio files of the individual beats of the P4 and P5 and the combined beats with different relative phases (0, 90 and 180 degrees). You can hear that when they are in phase you hear a stronger 1bps beat, if they are out of phase (180) the beats interleave and we effectively hear 2bps, and at 90 it's more complicated.

No cancellation can occur at any phase difference because beats are periodic variations in loudness of a carrier wave and there is no such thing as negative loudness and hence no cancellation, unlike periodic variations in pressure (deviation from atmospheric) which can be positive or negative.

Kees

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#2302433 - 07/15/14 12:29 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
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Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?


I am not sure I follow you. You say you tune the piano in one single pass. And you also say that you are fairly sure that what you have just tuned is going to move while you continue to tune.

Doesn't that mean that it will end up out of tune?



Not after I correct it as I go.

Also, for reasons I do not know why, not all the notes drift, so the high accuracy is not always wasted.


Edited by Mark Cerisano, RPT (07/15/14 12:31 AM)
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#2302436 - 07/15/14 12:34 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

I think it's the same thing: sound waves ride on the atmospheric pressure (the DC) and you can't hear beat cancellation on the telephone either.

If you're not convinced; I convinced myself by looking at an example. Consider tuning P4 A3D4 1bps wide and P5 A3E4 1bps narrow (equal beating). Ignore IH as it plays no role in this.

The P4 beats come from partials 4 and 3 which are at 880 and 881Hz. The P5 beats come from partials 3 and 2 which are at 660 and 659Hz. If we play A3D4E4 simultaneously we should be able to demonstrate beat cancellation by synthesizing just the aforementioned partials (880,881,659,660).

Here I put audio files of the individual beats of the P4 and P5 and the combined beats with different relative phases (0, 90 and 180 degrees). You can hear that when they are in phase you hear a stronger 1bps beat, if they are out of phase (180) the beats interleave and we effectively hear 2bps, and at 90 it's more complicated.

No cancellation can occur at any phase difference because beats are periodic variations in loudness of a carrier wave and there is no such thing as negative loudness and hence no cancellation, unlike periodic variations in pressure (deviation from atmospheric) which can be positive or negative.

Kees


Be careful. The "in phase" example can be out of phase if one wave form starts a micro second later. I found this out when making my beats video. But, I have to admit, I haven't listened to the recording yet. Perhaps you used a method that guaranteed "in phase".
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#2302437 - 07/15/14 12:38 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1494
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BTW, from my reading I've gathered that anything not at 0 degrees is out of phase. Did I read wrong, or read an incorrect article?

But I absolutely get what you're saying. Beats are all positive, so they can't add up to zero, ever. But the partials themselves can. And if there's no partial beating, then there's no beat. Try it. Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.

Maybe that's what's going on when I tune a "beatless" octave. I know it's not theoretically possible, yet that's what I hear.


Edited by Mark Cerisano, RPT (07/15/14 12:43 AM)
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#2302444 - 07/15/14 01:16 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
BTW, from my reading I've gathered that anything not at 0 degrees is out of phase. Did I read wrong, or read an incorrect article?

But I absolutely get what you're saying. Beats are all positive, so they can't add up to zero, ever. But the partials themselves can. And if there's no partial beating, then there's no beat. Try it. Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.

Maybe that's what's going on when I tune a "beatless" octave. I know it's not theoretically possible, yet that's what I hear.

0 degrees means in phase, 180 maximally out of phase, 90 1/4 period out of phase. Indeed if there are no partials that beat there are no beats. However if you crank up the volume in your example the beats will appear due to nonlinear distortion.

The point is, beat cancellation is not possible, because there is a fundamental difference between a beat and a sound wave.

It may however be possible to arrange the beats so that your attention is not drawn to them, giving the illusion of beat cancelling, which is of course all we need, but I have no idea how. Can you post an audio example of an "apparently beatless octave"?

Kees

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#2302465 - 07/15/14 04:29 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?


I am not sure I follow you. You say you tune the piano in one single pass. And you also say that you are fairly sure that what you have just tuned is going to move while you continue to tune.

Doesn't that mean that it will end up out of tune?



Not after I correct it as I go.

Also, for reasons I do not know why, not all the notes drift, so the high accuracy is not always wasted.


So you do correct what you just tuned! Isn't it a sort of second pass? You are tuning each note twice!

And after correcting, nothing guarantees you that it won't move again as you continue tuning the rest of the notes.
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#2302479 - 07/15/14 05:46 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark R. Offline
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Registered: 07/31/09
Posts: 2069
Loc: Pretoria, South Africa
Originally Posted By: Gadzar
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.


That may be the case.

I was only trying to say that currently, I'm using ET via Marpurg, which tunes some intervals pure (specifically, it's the whole-tone scale from F#3 to E4, i.e. six notes in total). Any short-cut that reduces the number of purely tuned intervals, is helpful to me - even though it would still be cumbersome or "tinkering" to a professional.
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#2302488 - 07/15/14 06:33 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bernhard Stopper Offline
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Originally Posted By: DoelKees

What I imagine is the following: In ET play intervals C#4F4 and F4A4. You hear them beat at different rates, so you connect the beat rates to the intervals and hear they are out of just. Now suppose C#4F4 and F4A4 are equal beating (as can happen in some WT's). We now hear the same beat rates so our brain thinks the beats are not a property of the interval, but some external noise which our brain filters out, and we don't think the M3's are out of just.

I have my doubts but it seems somewhat possible.

I miss your legendary crackpottery alarm detector for this "equal beating/canceling" theorem grin
I stay with what i said: Equal beating generally increases (worsens) beat intensities and does not cancel (or reduce) them.

Originally Posted By: DoelKees

I don't know what "beat masking" is. Can you explain?

Kees

The effect of beat intensity reduction caused by ?summation? of beats with different rates.




Edited by Bernhard Stopper (07/15/14 06:41 AM)
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#2302489 - 07/15/14 06:40 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
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Accepting beats an not fighting them makes them more discrete in the end, and they also goes well with the piano tone, and the shape it takes.

The consonances I hear/tune are an addition of slow beats (within the 2 octaves framework for instance.


Edited by Olek (07/15/14 06:42 AM)
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#2302492 - 07/15/14 06:50 AM Re: Theoretical tuning sequence [Re: Olek]
Bernhard Stopper Offline
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Originally Posted By: Olek
Accepting beats an not fighting them makes them more discrete in the end, and they also goes well with the piano tone, and the shape it takes.

The consonances I hear/tune are an addition of slow beats (within the 2 octaves framework for instance.


A reduction of beats generally comes along with an increase of consonance, not the other way around.




Edited by Bernhard Stopper (07/15/14 06:50 AM)
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#2302494 - 07/15/14 07:12 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
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I believe that was what I (wanted to) say, there is a reduction, not a suppression.

Do they slow, also ? (if compare whith theoretical beating frequency ?

At some points they "hide" in the dwell.

If consonance = coupling it sound normal that beats reduce, if not in speed in duration.
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#2302498 - 07/15/14 07:40 AM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
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Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I am not so sure about the positive/negative thing. The sounds you hear on a telephone are an AC signal "riding" on a DC value. Maybe it's not the same thing...

I think it's the same thing: sound waves ride on the atmospheric pressure (the DC) and you can't hear beat cancellation on the telephone either.

If you're not convinced; I convinced myself by looking at an example. Consider tuning P4 A3D4 1bps wide and P5 A3E4 1bps narrow (equal beating). Ignore IH as it plays no role in this.

The P4 beats come from partials 4 and 3 which are at 880 and 881Hz. The P5 beats come from partials 3 and 2 which are at 660 and 659Hz. If we play A3D4E4 simultaneously we should be able to demonstrate beat cancellation by synthesizing just the aforementioned partials (880,881,659,660).

Here I put audio files of the individual beats of the P4 and P5 and the combined beats with different relative phases (0, 90 and 180 degrees). You can hear that when they are in phase you hear a stronger 1bps beat, if they are out of phase (180) the beats interleave and we effectively hear 2bps, and at 90 it's more complicated.

No cancellation can occur at any phase difference because beats are periodic variations in loudness of a carrier wave and there is no such thing as negative loudness and hence no cancellation, unlike periodic variations in pressure (deviation from atmospheric) which can be positive or negative.

Kees


Kees:

Thanks for your response and your patience! I am just not getting it. What about noise cancelling headsets? http://en.wikipedia.org/wiki/Noise-cancelling_headphones

Sure, it is not the same as equal beating intervals played simultaneously, because those would be in phase, but they work.

I could not get your audio link to work, but am not sure if it matters. We may be talking about two different things.
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#2302499 - 07/15/14 08:02 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
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The coupling on the bridge (3 strings one note) does not allow phase to be balanced (the best we can come near is one sting lower/higher of 2 others coupling strong).

I wonder if when another note is added, the phase effects (inversion/ in phase) do not work even if it is at some distance on the bridge.





Edited by Olek (07/15/14 08:03 AM)
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#2302501 - 07/15/14 08:23 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
pyropaul Offline
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Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.


Edited by pyropaul (07/15/14 09:01 AM)
Edit Reason: added info for graphs

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#2302504 - 07/15/14 08:36 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
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Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
With my research i found the opposite to be true: Equal beating increases (worsens) beat intensities and does not cancel them.


Indeed beats can not physically cancel, unlike pressure waves. The reason is that pressure (or rather deviation from atmospheric pressure) can be positive and negative and can add up to 0, whereas beats are fluctuations in energy, and energy is always positive and no physical cancellation is possible.

If there is any advantage of "equal beating" it will have to be a human perception thing.

Kees


I'll take the perception over the "science" and the research then. I wasn't looking for what I found but it was there. I hear it every time I tune the EBVT III and play a C Major chord in the 3rd octave. The rapid beats are just swallowed up.

This happens to the 5ths in 1/4 Meantone too. Alone, they sound very objectionably narrow but no music ever written for 1/4 Meantone has 5ths standing alone. You simply don't hear them when actual music is played.

For at least 30 years now, I have also noted how the beat also disappears when the octave-fifth and double octave are equal beating and played together. I don't think I am fooling myself about that. I also don't think I was fooling Jim Coleman, Sr. when he rushed up to tell me after a recital I had tuned for, "You've done something with the octaves. I don't know what it is, but I like it.

Call it whatever you want or try to tell me that it is not happening but I know what I am hearing or in this case, not hearing.
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#2302522 - 07/15/14 09:59 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Originally Posted By: Mark R.
Originally Posted By: Gadzar
I don't see this as a tuning sequence for my dayly work. I see it as a curiosity to tinker around.


That may be the case.

I was only trying to say that currently, I'm using ET via Marpurg, which tunes some intervals pure (specifically, it's the whole-tone scale from F#3 to E4, i.e. six notes in total). Any short-cut that reduces the number of purely tuned intervals, is helpful to me - even though it would still be cumbersome or "tinkering" to a professional.


I see what you mean. Have you something in mind to resume the temperament from the whole tone scale F3 G3 A3 B3 C#3 D#4 F4 ?

Maybe tuning A#3 between F3 and D#4 to have the same tempering in both P4s F3A#3 and A#3D#4. Then tune the CM3s F#3 A#3 D4. Then C4 between G3 and F4 and the CM3s G#3 C4 E4.

Must try it. I don't know. I guess ET Via Marpurg is easier. But this one is shorter and gives true ET.

PS: This sequence is a good way to correctly temper ET P4s.


Edited by Gadzar (07/15/14 10:08 AM)
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#2302553 - 07/15/14 11:34 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark R. Offline
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Originally Posted By: Gadzar
Have you something in mind to resume the temperament from the whole tone scale F3 G3 A3 B3 C#3 D#4 F4 ?


You mean, after having obtained that whole tone scale with Marpurg? Not really, because at that stage, I am almost done. The only thing remaining is to correct the F# whole tone scale using P4s/P5s. Each note is part of a pure interval (e.g. F#3-C#4) and a doubly tempered interval (F#3-B3). So, the note (F#3 in this case) must be moved to the equally tempered mid-point between the two.

But if you meant:

If I could get to the F3-F4 whole tone scale in a quicker way, have I thought about tuning the other whole-tone scale? Yes, I have. Your suggestion comes to mind. Or:
1) tuning D4 using F3, G3 and B3 ("inside third, outside sixth" test), and similarly
2) tuning E4, using G3, A3 and C#4, thereafter
3) completing both ladders of CM3s.

[Edit: I hope it makes sense; at the moment, I'm playing around with sequences, and I easily get confused.]


Edited by Mark R. (07/15/14 11:37 AM)
Edit Reason: given in post.
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#2302563 - 07/15/14 12:25 PM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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I meant after setting the whole tone scale with A4 A3 F3 F4 C#4
pure P4 A3D4 pure P4 D4G4
pure P4 E4A4 pure B3E4
D#4 B3 G3. (or D#3 G3 B3).


Edited by Gadzar (07/15/14 12:27 PM)
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#2302581 - 07/15/14 01:23 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
DoelKees Offline
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Originally Posted By: UnrightTooner

Kees:

Thanks for your response and your patience! I am just not getting it. What about noise cancelling headsets? http://en.wikipedia.org/wiki/Noise-cancelling_headphones

They work by cancelling a pressure wave with another pressure wave of opposite phase. But beats are not pressure waves.

Kees

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#2302603 - 07/15/14 02:31 PM Re: Theoretical tuning sequence [Re: DoelKees]
prout Online   content
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A beat is simply a frequency too low to be perceived by a human as pitch.

If you create clicks (remember the original sounds produced by a computer back in the 80s?) at the rate of 5 clicks per second, you will hear 5 clicks per second.

But, if you create clicks at the rate of 440 clicks per second, you will hear A4.

In fact, if you create a 3 against 2 click pattern, you will hear a nice 3:2 rhythm if it is slow enough, and you will hear a perfect fifth if the rate is high enough.

In both cases, the energy is positive.

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#2302604 - 07/15/14 02:33 PM Re: Theoretical tuning sequence [Re: pyropaul]
DoelKees Offline
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Originally Posted By: pyropaul
Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees

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#2302613 - 07/15/14 02:54 PM Re: Theoretical tuning sequence [Re: DoelKees]
prout Online   content
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Originally Posted By: DoelKees
Originally Posted By: pyropaul
Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees


My guess is that our brain creates the resultant of 661 and 440, for example, as 221, which will produce a harmonic at 442, which will beat at 2bps.

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#2302624 - 07/15/14 03:14 PM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
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I seem to recall some years ago that someone told me that the "canceling" effect that I was hearing was not the same as what happens with noise cancellation systems. That is why I always use the word, "effect" when I talk about it. If it isn't truly a cancelation, then it is something else which mimics that effect.

When I tune the EBVT or ET via Marpurg, I always check my equally beating intervals by playing them simultaneously. If the two intervals are not quite equal, the slow beat between them emerges. When the two intervals, whether slowly or rapidly beating are truly equal, the beating sound becomes fainter, certainly not louder. The entire cluster of tones, whether a consonant, mildly dissonant or sharply disonant sound becomes quieter, not louder than if either interval is played alone. If the two intervals have very slow beats, the beat seems to vanish entirely.

If someone comes up with a better word than "canceling effect" to describe that phenomenon, I will certainly consider using that term, whatever it may be. I have long known that this is a way to take the "noise" out of a piano. Now, I am being told it will make it twice as noisy but I know that simply is not true.
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#2302661 - 07/15/14 04:40 PM Re: Theoretical tuning sequence [Re: prout]
DoelKees Offline
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Originally Posted By: prout

My guess is that our brain creates the resultant of 661 and 440, for example, as 221, which will produce a harmonic at 442, which will beat at 2bps.

You could check that by playing the notes separately to each ear with headphones. If you still hear beats they must be made in the brain.

Kees

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#2302676 - 07/15/14 05:00 PM Re: Theoretical tuning sequence [Re: DoelKees]
pyropaul Offline
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Originally Posted By: DoelKees

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees


I can hear them clearly at low volume. Two sines at 440Hz and 441Hz also have constant energy over time in the simple summation case surely - yet we still hear the beats as an AM effect. I wish my old analog synthesiser was in a place where I could use it - easy to play around with two sine wave oscillators to see how all of this is perceived. Of course, as you state, our ears are not linear anyway - so there will always be more than just summation occurring. Even without any partials, though, it's easy to tune pure intervals with only sinewaves.

Paul.

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#2302678 - 07/15/14 05:07 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Herr Weiss Online   content
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Originally Posted By: Bill Bremmer RPT

If someone comes up with a better word than "canceling effect" to describe that phenomenon, I will certainly consider using that term, whatever it may be.


Don't know if they are better but here are some alternatives.

Invalidate, Negate, Neutralize, Void, Annul, (render null and void), Obliterate, (reduce a good effect), Nullify. smile


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#2302704 - 07/15/14 05:46 PM Re: Theoretical tuning sequence [Re: pyropaul]
DoelKees Offline
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Originally Posted By: pyropaul
Originally Posted By: DoelKees

I don't hear beats at low volume, only when I crank it up nonlinear distortion, either in my ear or in my speakers, kicks in.

The amplitude modulation you see is a visual effect only. If you plot the energy over say 50ms windows you'll see it is constant.
Unlike when you have a true beat when it oscillates at the beat rate.

Kees


I can hear them clearly at low volume. Two sines at 440Hz and 441Hz also have constant energy over time in the simple summation case surely

Not over a (say) 50ms window: the energy oscillates at 1Hz, which is what you hear, unlike for the 440 661 case.

Kees

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#2302727 - 07/15/14 06:24 PM Re: Theoretical tuning sequence [Re: DoelKees]
prout Online   content
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Registered: 11/14/13
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Originally Posted By: DoelKees
Originally Posted By: prout

My guess is that our brain creates the resultant of 661 and 440, for example, as 221, which will produce a harmonic at 442, which will beat at 2bps.

You could check that by playing the notes separately to each ear with headphones. If you still hear beats they must be made in the brain.

Kees


I have checked it, and it is the case that the brain creates the beats.

Here is a binaural wav file that has the a 440Hz sine wave on the left track and a 661Hz sine wave on the right track. The crosstalk of the tracks is below -160db and the spectral analysis shows no energy at any frequency other than at 440Hz on the one track and 661Hz on the other.

Nevertheless, there is a phantom partial heard at (I assume) 221Hz and a clear 2 beats per second pulsing.

Edit: Corrected track separation value to -160db.


Edited by prout (07/15/14 06:27 PM)

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#2302821 - 07/15/14 10:55 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
DoelKees Offline
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Originally Posted By: Bill Bremmer RPT
I seem to recall some years ago that someone told me that the "canceling" effect that I was hearing was not the same as what happens with noise cancellation systems. That is why I always use the word, "effect" when I talk about it. If it isn't truly a cancelation, then it is something else which mimics that effect.

When I tune the EBVT or ET via Marpurg, I always check my equally beating intervals by playing them simultaneously. If the two intervals are not quite equal, the slow beat between them emerges. When the two intervals, whether slowly or rapidly beating are truly equal, the beating sound becomes fainter, certainly not louder. The entire cluster of tones, whether a consonant, mildly dissonant or sharply disonant sound becomes quieter, not louder than if either interval is played alone. If the two intervals have very slow beats, the beat seems to vanish entirely.

If someone comes up with a better word than "canceling effect" to describe that phenomenon, I will certainly consider using that term, whatever it may be. I have long known that this is a way to take the "noise" out of a piano. Now, I am being told it will make it twice as noisy but I know that simply is not true.

I certainly didn't mean to say that. If equal beats are coincident they will sound like 1 beat but more pronounced, but if they are interleaved you will hear a beat twice as fast but softer. In practice the beats will never be exactly equal so you will get some mix between these two extreme theoretical cases.

My main point is that true "beat cancellation" analogous to noise cancellation in headphones is not possible so can't explain the phenomena you observe. This does not mean the phenomena does not exist.

I like Bernhard's term "beat masking". If this is best achieved by equal or unequal beatrates or if it exists at all I don't know, but I keep an open mind on it.

"Auditory masking" is a well developed field of study. They measure basically how effective a sine wave at frequency f1 can be made inaudible by playing simultaneously a sine wave at frequency f2 depending on their relative loudness. In that case the masking is always most effective when the frequencies are the same.

Kees

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#2302828 - 07/15/14 11:08 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
DoelKees Offline
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Originally Posted By: Bernhard Stopper
Originally Posted By: DoelKees

What I imagine is the following: In ET play intervals C#4F4 and F4A4. You hear them beat at different rates, so you connect the beat rates to the intervals and hear they are out of just. Now suppose C#4F4 and F4A4 are equal beating (as can happen in some WT's). We now hear the same beat rates so our brain thinks the beats are not a property of the interval, but some external noise which our brain filters out, and we don't think the M3's are out of just.

I have my doubts but it seems somewhat possible.

I miss your legendary crackpottery alarm detector for this "equal beating/canceling" theorem grin
Well I don't consider it crackpottery as it is comprehensible. I admit it is somewhat speculative, to make an understatement.
Originally Posted By: Bernhard Stopper
Originally Posted By: DoelKees

I don't know what "beat masking" is. Can you explain?

Kees

The effect of beat intensity reduction caused by ?summation? of beats with different rates.

So whenever you have unequal beats they mask each other? Or are there specific conditions for this masking to occur? Would you care to elaborate? (I have read everything you've written on the subject here in the past.)

Kees

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#2302829 - 07/15/14 11:13 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
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Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
In fact, I'm fairly sure that it will move. That's why I use the P4 test.

With this test, the P4 window is so small, that you would be surprised how tiny a movement can be caught by it.

You are right though, it is a waste of time to tune a note with high accuracy if it is going to drift later on, unless of course your method is incredibly fast at getting that high accuracy. If so, why not?


I am not sure I follow you. You say you tune the piano in one single pass. And you also say that you are fairly sure that what you have just tuned is going to move while you continue to tune.

Doesn't that mean that it will end up out of tune?



Not after I correct it as I go.

Also, for reasons I do not know why, not all the notes drift, so the high accuracy is not always wasted.


So you do correct what you just tuned! Isn't it a sort of second pass? You are tuning each note twice!

And after correcting, nothing guarantees you that it won't move again as you continue tuning the rest of the notes.




Yes, it is a kind of second pass. If it drifts again, it doesn't drift as much since things are all settling down as we go along.

The real benefit is that, as I said, all notes don't drift as much, some don't need correcting, and not all drift for the same reason. So, using a high accuracy technique right from the beginning, if it's not to far out, and you can get a high accuracy fairly quickly, just keeps the focus, for me anyway.

BTW, I'm not trying to tell you to change how you're tuning, just sharing how I do it.

Keep the questions coming.
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#2302835 - 07/15/14 11:33 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Gadzar Offline
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Posts: 1910
Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
Yes, it is a kind of second pass. If it drifts again, it doesn't drift as much since things are all settling down as we go along.

The real benefit is that, as I said, all notes don't drift as much, some don't need correcting, and not all drift for the same reason. So, using a high accuracy technique right from the beginning, if it's not to far out, and you can get a high accuracy fairly quickly, just keeps the focus, for me anyway.

BTW, I'm not trying to tell you to change how you're tuning, just sharing how I do it.

Keep the questions coming.


I guess I must see you in action to really understand how you do it.

Are you talking about the double string unison technique?
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#2302837 - 07/15/14 11:34 PM Re: Theoretical tuning sequence [Re: pyropaul]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: pyropaul
Originally Posted By: Mark Cerisano, RPT
Create two sine waves. One at 440 and one at 665. A horribly wide fifth. No beats. It's weird.



I tried this with audacity - both 665 and 661 plus 440. It sure sounds like beating to me as I can hear periodic variations in loudness. You definitely can have beats that are not due to partials near the same frequency - just do the summation of the two sines and you'll see periodic loudness variations in the 440+661 case.

[edit] just throw graph sin(4.4*pi*x)+sin(6.61*pi*x) and graph sin(4.4*pi*x)+sin(6.60*pi*x) into google, zoom out horizontally and you'll see the amplitude modulation in the 440+661Hz case.
Paul.


Make sure the volume is not too high. That will distort the sine wave and, in effect, produce partials.

I did the graph thing. Didn't see what you were talking about.
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#2302842 - 07/15/14 11:42 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Hey Kees,

I get what your saying, but what about this:

Two beats are created that are identical in frequency and 180 degrees out of phase. They are positive pressure waves so they can never add up to zero anywhere.

BUT, they can add up to a constant! Isn't a constant pressure wave the same as no sound?
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#2302844 - 07/15/14 11:51 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
Yes, it is a kind of second pass. If it drifts again, it doesn't drift as much since things are all settling down as we go along.

The real benefit is that, as I said, all notes don't drift as much, some don't need correcting, and not all drift for the same reason. So, using a high accuracy technique right from the beginning, if it's not to far out, and you can get a high accuracy fairly quickly, just keeps the focus, for me anyway.

BTW, I'm not trying to tell you to change how you're tuning, just sharing how I do it.

Keep the questions coming.


I guess I must see you in action to really understand how you do it.

Are you talking about the double string unison technique?



Nope, but the whole thing comes together with it.

I've decided that the benefits of a particular technician's temperament sequence can not be understood completely, without knowing their stability method and their tuning method in general.

That is why I am refraining from being more specific with regards to my sequence or method. I am writing a book on it now and it will describe everything, including my highly accurate temperament sequence with windows for ET, the DSU method, and stability analysis for slow pull and impact, as well as philosophy of tuning.

I know it sounds arrogant, but I don't know any other way to explain it.

I'm still looking for proof readers. Let me know. You get a free copy and get to rake me over the coals.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2302847 - 07/16/14 12:18 AM Re: Theoretical tuning sequence [Re: DoelKees]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
In this video https://www.youtube.com/watch?v=5BrcWplvGJY it is claimed (around 38s) that the final chord (F2F4A4C5F5) shows beat masking of the M3.

Here's the final chord: final chord.

To me the 7bps of the F2F4A4 is very clear and not masked at all (what could it be masked by?), but of course I'm comparing it perhaps unfairly to how nice it sounds on my piano where it beats at 4bps.

I guess we'd have to hear the final chord on the same piano tuned not in Stopper tuning to really judge.

For comparison here http://persianney.com/misc/richter.mp3 is the same chord from a Richter performance which I grabbed from youtube.

To me the M3 is less offensive there, perhaps because the slow beat from the F3F4C5 masks it?

I think I like the Stopper tuning better, but just because the FC is better, not because of any beat masking.

Kees

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#2302854 - 07/16/14 01:46 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
Hey Kees,
Two beats are created that are identical in frequency and 180 degrees out of phase. They are positive pressure waves so they can never add up to zero anywhere.

Beats are not pressure waves.

Kees

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#2302919 - 07/16/14 07:32 AM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner

Kees:

Thanks for your response and your patience! I am just not getting it. What about noise cancelling headsets? http://en.wikipedia.org/wiki/Noise-cancelling_headphones

They work by cancelling a pressure wave with another pressure wave of opposite phase. But beats are not pressure waves.

Kees


OK, a periodic change in amplitude (beats) is not a periodic change in pressure (acoustic wave). So... if one acoustic wave can be cancelled by another why can't one beat be cancelled by another?
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#2302924 - 07/16/14 07:49 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
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Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
I will see if I have some nice grands today to make a brief video.
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Madison WI USA
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#2302926 - 07/16/14 07:51 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Mark R. Offline
2000 Post Club Member

Registered: 07/31/09
Posts: 2069
Loc: Pretoria, South Africa
Originally Posted By: Mark Cerisano, RPT
I did the graph thing. Didn't see what you were talking about.


Once the graph has been drawn for you, go to the zoom tool at the top left corner. Hover over the pop-out arrow on the right-hand side of the zoom tool. This pops out selectors for horizontal-only or vertical-only zooming. Select the horizontal-only mode. Then press on the "minus" a few times, to zoom out. Soon you will see a beat pattern emerging, after 7 or 8 zoom-outs. It repeats every 100 x-units.
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#2302943 - 07/16/14 08:31 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: Mark Cerisano, RPT

I've decided that the benefits of a particular technician's temperament sequence can not be understood completely, without knowing their stability method and their tuning method in general.

That is why I am refraining from being more specific with regards to my sequence or method. I am writing a book on it now and it will describe everything, including my highly accurate temperament sequence with windows for ET, the DSU method, and stability analysis for slow pull and impact, as well as philosophy of tuning.

I know it sounds arrogant, but I don't know any other way to explain it.

I'm still looking for proof readers. Let me know. You get a free copy and get to rake me over the coals.


Mark,

If you promote your way of doing things but don't have the same amount of experience with other ways and try to show and say that another way is inferior, all you are doing is showing that you don't have experience with the other way and therefore it doesn't work for you as well as your way.

Take for example the typical 4ths & 5ths sequence. I passed my exam using it. I know how to do it. But I have also seen so many people fail using that method that I came up with something else. Every time I promote the idea of using Contiguous Major Thirds as a foundation for ET, somebody tells me that they don't do that and still get perfect results.

So, instead of trying to say that you have the only and best solution, try looking for a way to say that if other methods have not worked, then try this.

When I see you say how you "only tune one time" but go back and correct strings which have drifted, I think immediately that you only "fight with it one time". You say that you still think it would take less time than trying to do it twice and maybe for you, it would but not for me. For me, the pitch correction phase of any tuning is very low stress and takes about 15 minutes to go through the entire piano. The fine tuning phase is then also very low stress because most of the strings are already in tune. It is then a matter of finding and stabilizing only the recalcitrant ones.

I would never try to fool myself into thinking I could go through any piano just one time and have it be in tune when I finish but that is because I wouldn't fight with it the way you and anyone else who can't imagine doing two passes do.

I hope in your book that you also don't repeat the same false information about how temperament suddenly swung from Meantone to ET one day when Bach wrote the Well Tempered Clavier music. If you don't know what you are talking about in that regard, I suggest you leave the history of temperament subject alone entirely.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#2302953 - 07/16/14 09:11 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
David Jenson Online   content
2000 Post Club Member

Registered: 10/22/06
Posts: 2199
Loc: Maine
Originally Posted By: Bill Bremmer RPT

If you promote your way of doing things but don't have the same amount of experience with other ways and try to show and say that another way is inferior, all you are doing is showing that you don't have experience with the other way and therefore it doesn't work for you as well as your way.

I agree. All through my aural tuning career I have tried (as time and intellect would allow) to explore other temperament setting schemes to see if they would allow me to get a better understanding of the process. I'm being deliberately brief, but it works!
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#2302962 - 07/16/14 09:34 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Mark Cerisano, RPT

I've decided that the benefits of a particular technician's temperament sequence can not be understood completely, without knowing their stability method and their tuning method in general.

That is why I am refraining from being more specific with regards to my sequence or method. I am writing a book on it now and it will describe everything, including my highly accurate temperament sequence with windows for ET, the DSU method, and stability analysis for slow pull and impact, as well as philosophy of tuning.

I know it sounds arrogant, but I don't know any other way to explain it.

I'm still looking for proof readers. Let me know. You get a free copy and get to rake me over the coals.


Mark,

If you promote your way of doing things but don't have the same amount of experience with other ways and try to show and say that another way is inferior, all you are doing is showing that you don't have experience with the other way and therefore it doesn't work for you as well as your way.

Take for example the typical 4ths & 5ths sequence. I passed my exam using it. I know how to do it. But I have also seen so many people fail using that method that I came up with something else. Every time I promote the idea of using Contiguous Major Thirds as a foundation for ET, somebody tells me that they don't do that and still get perfect results.

So, instead of trying to say that you have the only and best solution, try looking for a way to say that if other methods have not worked, then try this.

When I see you say how you "only tune one time" but go back and correct strings which have drifted, I think immediately that you only "fight with it one time". You say that you still think it would take less time than trying to do it twice and maybe for you, it would but not for me. For me, the pitch correction phase of any tuning is very low stress and takes about 15 minutes to go through the entire piano. The fine tuning phase is then also very low stress because most of the strings are already in tune. It is then a matter of finding and stabilizing only the recalcitrant ones.

I would never try to fool myself into thinking I could go through any piano just one time and have it be in tune when I finish but that is because I wouldn't fight with it the way you and anyone else who can't imagine doing two passes do.

I hope in your book that you also don't repeat the same false information about how temperament suddenly swung from Meantone to ET one day when Bach wrote the Well Tempered Clavier music. If you don't know what you are talking about in that regard, I suggest you leave the history of temperament subject alone entirely.


Does anyone else find Bill's post a bit in left field? I think I was clear that this is my way and works for me and I'm not trying to change anyone's method. Wasn't I? Please chime in here. I write and rewrite my posts many times to be clear that all I want to do is share, and not lecture.

Has anyone else had their words twisted and then thrown back at them as literal quotes that are wrong and make you look like an amateur? Isn't that fun?
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2302963 - 07/16/14 09:56 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Mark:

I find both your's and Bill's posts to be "a bit in left field." I barely skim over them and then wonder why I bother. There is something similar in your personalities that you are each blind to. I am sure some lack of insight exists in all of us. Otherwise we would be either utterly depraved or utterly depressed. In otherwords, don't show me mine, and I won't show you yours! laugh
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Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2302978 - 07/16/14 10:49 AM Re: Theoretical tuning sequence [Re: DoelKees]
bkw58 Offline

Silver Supporter until December 19, 2014


Registered: 03/14/09
Posts: 1847
Loc: Conway, AR USA
Effective communication is 10% words; and that's provided both have a decent command of the same language. The other 90% is body language, voice inflection, and so on. Text forum is a formula for misunderstanding. We've all been on both the giving and the receiving end. I don't have answers. Even an extra effort to choose words more wisely will only help about half of the time. Which half? I haven't a clue. wink

That's my fractured axiom for the day. crazy
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Bob W.
Retired piano technician
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#2302980 - 07/16/14 10:50 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
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Registered: 03/14/08
Posts: 7904
Loc: France
I think beats can be perceived from sounds with pure harmonics, or even without harmonics.

Then what we hear with earphones may relate more to the phase motions between speakers than the effect graphed above, or in any case it may modify the output if I am not wrong
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#2303023 - 07/16/14 12:52 PM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
I appreciate all Bill Bremmer posts here in Piano World, because he always teaches me something I do not knew.

Contrary to what Mark Cerisano posts. Last one was a "what you do is a waste of time".
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Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2303044 - 07/16/14 01:44 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
I don't understand Gadzar. I did not say doing two passes is a waste of time. I said sometimes using a correct as you go approach is faster. For me. Sometimes. For me.

Was I not clear?


Edited by Mark Cerisano, RPT (07/16/14 01:51 PM)
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#2303051 - 07/16/14 01:56 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
I will apologize for some of my posts here. I agree that some of them appear self righteous but I did not intend for them to be. Forum writing is a skill I still need to learn.

I liked your post Jeff. Thanks, and I agree with you.


Edited by Mark Cerisano, RPT (07/16/14 01:59 PM)
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#2303088 - 07/16/14 03:32 PM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM
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Bill Bremmer RPT
Madison WI USA
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#2303090 - 07/16/14 03:40 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
I don't understand Gadzar. I did not say doing two passes is a waste of time. I said sometimes using a correct as you go approach is faster. For me. Sometimes. For me.

Was I not clear?




It is funny how you forget what you have just posted.


Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Gadzar
Mark,

If you are good at tempering proportional M3s, all you need is one note of a CM3s chain.

Here we tune

A4 to fork
A3 to A4, the octave size you like.
D4 to A3, as a pure fourth
G4 to D4, as a pure fourth
E4 to A4, as a pure fourth
B3 to E4, as a pure fourth
D#4 to B3/G4, as a...


But, tuning a pure interval in ET is a waste of time, because you will have to correct it later on.
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Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2303092 - 07/16/14 03:46 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner

Kees:

Thanks for your response and your patience! I am just not getting it. What about noise cancelling headsets? http://en.wikipedia.org/wiki/Noise-cancelling_headphones

They work by cancelling a pressure wave with another pressure wave of opposite phase. But beats are not pressure waves.

Kees


OK, a periodic change in amplitude (beats) is not a periodic change in pressure (acoustic wave). So... if one acoustic wave can be cancelled by another why can't one beat be cancelled by another?

Because amplitude (or rather, energy) is positive, and two positive numbers can't add up to zero.

Or try to visualize two sine wave at say 440 Hz and another at 660 Hz. Now visualize oscillating the amplitude of both waves at 1 oscillation per second (not necessarity synchronous) and put the result together. How can you possibly end up with two original sine waves again?

Kees
PS On the other hand, if you had two acoustic waves of 1Hz you can shift one by 1/2 a period, add them up and end up with a flat line.


Edited by DoelKees (07/16/14 03:50 PM)

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#2303095 - 07/16/14 04:01 PM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Wow Bill, in the second video when you play CE then GE I clearly hear the beats, then when you play the triad GCE it sounds smooth, harmonious, the beats just disappear! thumb


Edited by Gadzar (07/16/14 04:04 PM)
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Rafael Melo
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2303107 - 07/16/14 04:44 PM Re: Theoretical tuning sequence [Re: Gadzar]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: Gadzar
Wow Bill, in the second video when you play CE then GE I clearly hear the beats, then when you play the triad GCE it sounds smooth, harmonious, the beats just disappear! thumb


Yes, that is what I hear too. The first second or so, I hear the rapid beat but then it gets "swallowed". In the Slowly Beating Interval samples, in this and every time I do it, I hear what sounds to me like a beat "trying" to happen but it can't.

Now to me, that always meant that one beat was "canceling" the other. If the scientists say that because beats are always "positive" (whatever that means) and therefore two or more positives cannot amount to a zero or anything close to that, OK, fine by me. It is not beat cancellation. Is it therefore, beat interference that mimics cancellation?

Whatever the reason is for the effect, I have known about it for some 30 years and I keep discovering more ways to put it to use. I will call it whatever somebody finally determines the right word is. What I certainly do not hear is a "doubling" of beats or a louder sound.

What I learned how to do, I learned by actually listening to the piano and not listening to what other technicians say and certainly not what scientists who theorize about everything say but who never actually tuned a piano.
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#2303119 - 07/16/14 05:31 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM

It sound nice, but I hear nothing unusual that I can attribute to equal beatings.

To demonstrate the effect of equal beating we'd have to hear that with equal beating it sounds better than without equal beating.

If I am not mistaken in EBVT3 F4A4 and G4B4 have comparable beat rates, C3A4 and F4A4 are not equal beating, but D3G4 and G4B4 are equal beating.

So C3F4A4 should sound less quiet than D3G4B4.

Can you demonstrate that?

Kees

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#2303145 - 07/16/14 07:25 PM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: DoelKees
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM

It sound nice, but I hear nothing unusual that I can attribute to equal beatings.

To demonstrate the effect of equal beating we'd have to hear that with equal beating it sounds better than without equal beating.

If I am not mistaken in EBVT3 F4A4 and G4B4 have comparable beat rates, C3A4 and F4A4 are not equal beating, but D3G4 and G4B4 are equal beating.

So C3F4A4 should sound less quiet than D3G4B4.

Can you demonstrate that?

Kees


Doel, nothing sounds better than a pure 4th or 5th. In the 3rd octave, the F3-A3 and G3-B3 M3's beat at the same rate by design but the key of F and the key of G still have distinctly different characters. That is because the key of F has a pure fifth but the key of G has a fifth that is tempered about 1.5 as much as in ET.

So, I don't know if a triad with a pure fifth sounds "quieter" than the same triad as it would be tuned in ET but expect it would. You, of all people should know about this kind of thing. The ET only crowd is focused only on equality as the goal of perfection but people like you and me have long known of other characteristics that are far more desirable than having every key signature sound alike.

When you get to the point on the scale of F4-A4, you are at or near the limit of discernibility of beating in an M3. You want me to prove that a C4-F4-A4 triad sounds "louder" than a C4-G4-B4 triad? Sorry, I don't have the time. I know they won't sound the same in the EBVT but I will leave it at that.

I have to admit that what I wrote that I thought would support your topic, equally beating intervals and the value that there is in them, has now drifted off topic. The value that I know is there and have known is there for more than 30 years is now being undermined with "research" that says there is no such value at all.

As usual, it is only theoretical: it wouldn't work, couldn't work and shouldn't be tried. Why bother when it is only in your imagination and nobody can hear the difference anyway? Why not just tune ET like everybody else? Why not do it MY way?

I guess we all have our theories and our own experiences. We all have our own product to sell. We all do what we do because it works for us. We all get testimonials from our clients.

I'll say it again just to make it very clear. I am not a scientist, nor a mathematician nor a physicist or anything else that may apply. My education has been in music and foreign languages. I started tuning pianos at the age of 17 and I did it by listening to the piano. I still do that. I know what it is that I hear. It has often been very difficult to put into words what I do but there, I do have some skill.

I respond, not to what other technicians may say who know nothing really about what I do, only what they perceive through their own bias; I respond to what my clients say. I also respond to what other technicians say who have tried my techniques and found the results to be to their liking. Any other methods and theories by other technicians find similar gratification.

I found your idea to be fascinating. I certainly remember how you also found an equally beating way to arrive at 6 beats per second for the F3-A3 M3 that is called for in the EBVT. It was great thinking, even if it isn't a very practical way to do it. It was, however an example of the power and potential of equally beating intervals.

Now, I am confronted with someone who says that equally beating intervals are worse, not better. They are louder, not softer when played together. Beats cannot "cancel" each other so the result of equally beating intervals can only be worse, not better than non-equally beating intervals. Chords with equally beating intervals would be twice as loud!

It is simply not true and musicians and tuners from past centuries knew that for a much longer time than any people who think that complete eradication of tonality is the ultimate goal. I will continue doing what I do, knowing that it produces the most musical satisfaction for the most people. I know what I hear when I tune and no theorist or researcher can tell me that it is only in my imagination.
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Bill Bremmer RPT
Madison WI USA
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#2303149 - 07/16/14 07:45 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
I don't understand Gadzar. I did not say doing two passes is a waste of time. I said sometimes using a correct as you go approach is faster. For me. Sometimes. For me.

Was I not clear?




It is funny how you forget what you have just posted.


Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Gadzar
Mark,

If you are good at tempering proportional M3s, all you need is one note of a CM3s chain.

Here we tune

A4 to fork
A3 to A4, the octave size you like.
D4 to A3, as a pure fourth
G4 to D4, as a pure fourth
E4 to A4, as a pure fourth
B3 to E4, as a pure fourth
D#4 to B3/G4, as a...


But, tuning a pure interval in ET is a waste of time, because you will have to correct it later on.




Sorry, I thought you were referring to the double vs single correct-as-you-go pass.

Re: using pure intervals to tune ET, that was arrogant of me to say it is a waste of time. I apologize. What I meant to say was, I have a sequence that tunes proper ET size intervals right away. It is like CM3, except for all the notes of the temperament. I'll post it when I have figured out an efficient and concise way to present it.
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www.howtotunepianos.com

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#2303152 - 07/16/14 07:47 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Bill Bremmer RPT
When you get to the point on the scale of F4-A4, you are at or near the limit of discernibility of beating in an M3. You want me to prove that a C4-F4-A4 triad sounds "louder" than a C4-G4-B4 triad? Sorry, I don't have the time. I know they won't sound the same in the EBVT but I will leave it at that.

I really don't want you do anything in particular.

I just have never seen anything that support the advantage of equal beating except to make it easier to tune something by ear.
I don't believe there is any (dis)advantage to equal beating until I see evidence otherwise. Claiming you can demonstrate otherwise but "don't have the time" to show it does not make a very good case for it IMHO.

Kees

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#2303162 - 07/16/14 08:36 PM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Am I alone in hearing those beats in CE and GE and no beats at all in GCE?
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Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2303184 - 07/16/14 10:19 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
I hear an octave G ringing all over the place. Maybe it's my speaker or the quality of the recording. I don't hear any beat cancellation, or whatever we want to call it, although I have experienced it.
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www.howtotunepianos.com

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#2303243 - 07/17/14 03:06 AM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
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Registered: 03/14/08
Posts: 7904
Loc: France
if it add something to the tone it is interesting, if it retracts something, way less in my opinion.

I hear 2 intervals riding approx the same beat . I feel it can be done in additive or substractive modes, and that the result will differ in regard of global consonance.
I ten to prefer a sound that flows without being retained, to one that seem to have some slowing.

It makes me think of the Viennese style unison, where the original conflict around center string provides a thickened tone but the process have absorbed/ruled part of the attack energy so the tone is shortened.

In a goal of providing different tonal outputs between intervals I understand that effect can be included - it sound too present to me, not sounding "naturally" but I am not used to that "extreme"



Edited by Olek (07/17/14 03:10 AM)
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#2303279 - 07/17/14 07:42 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Chris Leslie Offline
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Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


Edited by Chris Leslie (07/17/14 07:42 AM)
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#2303284 - 07/17/14 07:56 AM Re: Theoretical tuning sequence [Re: Chris Leslie]
Bill Bremmer RPT Offline
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Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: Chris Leslie
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


I hear the beating completely disappear after a few seconds.
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#2303285 - 07/17/14 08:00 AM Re: Theoretical tuning sequence [Re: Olek]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: Olek
if it add something to the tone it is interesting, if it retracts something, way less in my opinion.

I hear 2 intervals riding approx the same beat . I feel it can be done in additive or substractive modes, and that the result will differ in regard of global consonance.
I ten to prefer a sound that flows without being retained, to one that seem to have some slowing.

It makes me think of the Viennese style unison, where the original conflict around center string provides a thickened tone but the process have absorbed/ruled part of the attack energy so the tone is shortened.

In a goal of providing different tonal outputs between intervals I understand that effect can be included - it sound too present to me, not sounding "naturally" but I am not used to that "extreme"



I use this method to tune 99% of the pianos that I tune, including for concert artists. They get on the stage to announce to the public how wonderful the piano sounds, so I will go with their opinion, not yours.
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Bill Bremmer RPT
Madison WI USA
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#2303286 - 07/17/14 08:02 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Bill Bremmer RPT Offline
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Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Originally Posted By: Mark Cerisano, RPT
I hear an octave G ringing all over the place. Maybe it's my speaker or the quality of the recording. I don't hear any beat cancellation, or whatever we want to call it, although I have experienced it.


You tune your pianos your way and I will tune mine my way. I didn't hear what you hear and you didn't hear what I hear.
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Bill Bremmer RPT
Madison WI USA
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#2303344 - 07/17/14 11:31 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Mark Cerisano, RPT
I hear an octave G ringing all over the place. Maybe it's my speaker or the quality of the recording. I don't hear any beat cancellation, or whatever we want to call it, although I have experienced it.


You tune your pianos your way and I will tune mine my way. I didn't hear what you hear and you didn't hear what I hear.


Why do I have this image in my mind of a parakeet fighting it's reflection in a mirror?
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#2303479 - 07/17/14 06:14 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Chris Leslie Offline
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Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Chris Leslie
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


I hear the beating completely disappear after a few seconds.


Just to confirm I listened again:

Firstly, there is a definite G2 ringing out from somewhere when the G3 is played in some combination.
Secondly, with the G3C4E4 inversion, there is a significant reduction in apparent beating, but the beats are still very audible.
Thirdly, the C3E3G3(C4) inversion, the is hardly any apparent reduction in beating of the CE interval, just a slight reduction in volume but replaced by a muddy quality.

I am just trying to give an honest evaluation.
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Chris Leslie
Piano technician
http://www.chrisleslie.com.au

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#2303504 - 07/17/14 08:11 PM Re: Theoretical tuning sequence [Re: DoelKees]
Bill Bremmer RPT Offline
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Registered: 08/21/02
Posts: 3322
Loc: Madison, WI USA
Am I supposed to just give up and tune ET from now on because everything I have done for the last 30 years has all been an illusion? Did Bach really write the Well Tempered Clavier Music for ET as Jeff "proved"? Was ET "firmly in place" by the time of Brahms as the PTG Journal guy claimed? So Brahms just had a girl like Vanna White spin the Wheel of Fortune to determine which key signature he would use for each piece he wrote because one key signature was the same as another?

Equal Beating only makes things sound worse, not better?

Sorry folks, I don't buy any of it. I know what I hear and so do my clients. I haven't tuned a piano in true ET now for 25 years, almost exactly to the date when I heard a set of Brahms performed in the Rameau-Rousseau-Hall composite 18th Century Modified Meantone Temperament from Owen Jorgensen's Handbook of Equal Beating Temperaments.

I can't prove anything with a few examples recorded on a cellphone. I only know what I have heard and experienced in the last 25 years and I am not about to turn back from it. There is a reason why I have so many loyal clients and why performing artists choose to acknowledge what I have done publicly and why they also do the same for my local colleagues who also choose the non-equal temperaments: Musical satisfaction and often great epiphanies that they have never experienced from ET.
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#2303522 - 07/17/14 09:24 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
prout Online   content
500 Post Club Member

Registered: 11/14/13
Posts: 902
Originally Posted By: Bill Bremmer RPT
Am I supposed to just give up and tune ET from now on because everything I have done for the last 30 years has all been an illusion? Did Bach really write the Well Tempered Clavier Music for ET as Jeff "proved"? Was ET "firmly in place" by the time of Brahms as the PTG Journal guy claimed? So Brahms just had a girl like Vanna White spin the Wheel of Fortune to determine which key signature he would use for each piece he wrote because one key signature was the same as another?

Equal Beating only makes things sound worse, not better?

Sorry folks, I don't buy any of it. I know what I hear and so do my clients. I haven't tuned a piano in true ET now for 25 years, almost exactly to the date when I heard a set of Brahms performed in the Rameau-Rousseau-Hall composite 18th Century Modified Meantone Temperament from Owen Jorgensen's Handbook of Equal Beating Temperaments.

I can't prove anything with a few examples recorded on a cellphone. I only know what I have heard and experienced in the last 25 years and I am not about to turn back from it. There is a reason why I have so many loyal clients and why performing artists choose to acknowledge what I have done publicly and why they also do the same for my local colleagues who also choose the non-equal temperaments: Musical satisfaction and often great epiphanies that they have never experienced from ET.


The more I attempt to wring out the physics of piano tuning using sophisticated electronic equipment, the more I realize that the equipment does not hear what we hear. A centimetre shift in the microphone will entirely change the partial amplitudes and phases, which means that your recordings do not capture the quality of the tuning that you hear.

I find that what the tuner hears from the piano bench and what the pianist hears from that same bench is all that matters. Your tunings clearly work and your clientele are happy. Keep up the good work.

Cheers.

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#2303532 - 07/17/14 10:03 PM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Bill Bremmer RPT
There is a reason why I have so many loyal clients and why performing artists choose to acknowledge what I have done publicly and why they also do the same for my local colleagues who also choose the non-equal temperaments: Musical satisfaction and often great epiphanies that they have never experienced from ET.

You are confusing the issue. It is possible that people like EBVT3 tuning (or some other unequal temperament) but this may have nothing to do with supposed beat (equal or unequal) cancellation/masking.

Please note the word "may" in the previous sentence. I keep an open mind, but I haven't seen any evidence for equal beat cancellation or unequal beat masking in my own experiments on my piano or in any recordings by others.

If this really worked it should be easy to demonstrate by showing a chord with and without equal beats for comparison.

Of course in a chord individual beats are always less prominent. For example play F4A4 and hear it beating. Now put your forearm on that octave: you can't hear F4A4 beating any more.

Kees

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#2303539 - 07/17/14 10:53 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Kees:

Just some general comments, because you know what you are doing and what you are talking about. That is, what I am going to mention, I am sure you have already thought about.

You have described an algorithm. It favors the 2nd, 3rd and 4th partials when iH exists. I expect that in the case of a jump in iH, the RBIs would not be progressive.

I will often use the relationship of the SBI beatrates to smooth out a tuning, or when touching up a tuning. It is the same idea.

I had been toying with the idea of a sequence that is based on the M3/M6 test. Of course this requires a temperament span of greater than an octave. It may also work well as an algorithm, I think... Something like:

A3 = 220hz
A3-C#3 = 9bps
A3-E4 = -0.5bps
G3-E4 = 9bps
G3-D4/A3-D4 = -1/2 ratio

Of course, so far these are just rule-of thumb numbers. As the algorithm progresses, any errors would be corrected only part way. I would think three times thru the sequence would be sufficient. I'll have to play with it on my simulator.

This would continue with something like:

B3-E4/E4-A4 = 2/3 ratio AND
G3-B3/A3-C#3 = 7/8 ratio (both won't happen, so the error is averaged between the two)
F3-D4 = G3-B3

Then next M3/M6 test can produce a A3-D#4-A4 contiguous tritone, but the m3/M3 inversion of the M3/M6 test would probably be used.

Then three more M3/M6 tests should complete the temperament. Of course then the errors are checked and corrected by averaging. I suppose the averaging could be weighted according to a preference...

I'll see if I can find the time to play with this. Not as an aural tuning sequence, but as an algorithm.

I fooled around a bit with this idea, modified to suit my own interest.

Temperament range F3-C#5 so you have all possible M3/M6 tests. Then pick a random M3/M6 test and adjust the upper note to make them equal beating. Unless it's an A. This does not work: it gets worse at every iteration. Picking the lower note is no better.

Not sure why.

Kees

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#2303552 - 07/18/14 12:04 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Bill Bremmer RPT
Am I supposed to just give up and tune ET from now on because everything I have done for the last 30 years has all been an illusion? Did Bach really write the Well Tempered Clavier Music for ET as Jeff "proved"? Was ET "firmly in place" by the time of Brahms as the PTG Journal guy claimed? So Brahms just had a girl like Vanna White spin the Wheel of Fortune to determine which key signature he would use for each piece he wrote because one key signature was the same as another?

Equal Beating only makes things sound worse, not better?

Sorry folks, I don't buy any of it. I know what I hear and so do my clients. I haven't tuned a piano in true ET now for 25 years, almost exactly to the date when I heard a set of Brahms performed in the Rameau-Rousseau-Hall composite 18th Century Modified Meantone Temperament from Owen Jorgensen's Handbook of Equal Beating Temperaments.

I can't prove anything with a few examples recorded on a cellphone. I only know what I have heard and experienced in the last 25 years and I am not about to turn back from it. There is a reason why I have so many loyal clients and why performing artists choose to acknowledge what I have done publicly and why they also do the same for my local colleagues who also choose the non-equal temperaments: Musical satisfaction and often great epiphanies that they have never experienced from ET.


Re-listen to your recording. Try to confirm what other people are saying. Re-record with better equipment so that you can confirm that what you hear in person, is there on the recording. Don't give them any opportunity to say what you know is there, is not there.
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www.howtotunepianos.com

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#2303554 - 07/18/14 12:11 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
Kees:

Just some general comments, because you know what you are doing and what you are talking about. That is, what I am going to mention, I am sure you have already thought about.

You have described an algorithm. It favors the 2nd, 3rd and 4th partials when iH exists. I expect that in the case of a jump in iH, the RBIs would not be progressive.

I will often use the relationship of the SBI beatrates to smooth out a tuning, or when touching up a tuning. It is the same idea.

I had been toying with the idea of a sequence that is based on the M3/M6 test. Of course this requires a temperament span of greater than an octave. It may also work well as an algorithm, I think... Something like:

A3 = 220hz
A3-C#3 = 9bps
A3-E4 = -0.5bps
G3-E4 = 9bps
G3-D4/A3-D4 = -1/2 ratio

Of course, so far these are just rule-of thumb numbers. As the algorithm progresses, any errors would be corrected only part way. I would think three times thru the sequence would be sufficient. I'll have to play with it on my simulator.

This would continue with something like:

B3-E4/E4-A4 = 2/3 ratio AND
G3-B3/A3-C#3 = 7/8 ratio (both won't happen, so the error is averaged between the two)
F3-D4 = G3-B3

Then next M3/M6 test can produce a A3-D#4-A4 contiguous tritone, but the m3/M3 inversion of the M3/M6 test would probably be used.

Then three more M3/M6 tests should complete the temperament. Of course then the errors are checked and corrected by averaging. I suppose the averaging could be weighted according to a preference...

I'll see if I can find the time to play with this. Not as an aural tuning sequence, but as an algorithm.

I fooled around a bit with this idea, modified to suit my own interest.

Temperament range F3-C#5 so you have all possible M3/M6 tests. Then pick a random M3/M6 test and adjust the upper note to make them equal beating. Unless it's an A. This does not work: it gets worse at every iteration. Picking the lower note is no better.

Not sure why.

Kees


Kees,

I have discovered another equality test. (No one has every told me about it nor have I read of it anywhere, but that doesn't mean anything) But I thought you might be able to prove it mathematically. I call it the m7b5 equality. Example: FA# = BD#.

I know it works in my sequence, but is there any theoretical proof that it is valid?
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www.howtotunepianos.com

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#2303562 - 07/18/14 12:41 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT

Kees,

I have discovered another equality test. (No one has every told me about it nor have I read of it anywhere, but that doesn't mean anything) But I thought you might be able to prove it mathematically. I call it the m7b5 equality. Example: FA# = BD#.

I know it works in my sequence, but is there any theoretical proof that it is valid?

FA# = BD#? Typo?

Kees

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#2303580 - 07/18/14 01:41 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Whoops. Yes.

FG# = BD#

Thanks.
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2303592 - 07/18/14 02:38 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
Whoops. Yes.

FG# = BD#

Thanks.


The M3/M6 test is (for example)
F3A3 = D3#C4.
However the M6 is really a tiny bit faster theoretically.
Your test, when you invert the m3 is
F3A3 = D3B3
and here the M6 is a little bit slower, but not a tiny bit.

So it may be a good bracketing test: the M3 has to beat at a rate in-between those two, but closer to D#3C4.

Kees

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#2303594 - 07/18/14 03:09 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
There is no "mathematical proof". It all depends on how much you stretch (contract) the 6:3 octaves.

If you have a pure 6:3 octave F#3F#4 then F#3A3=A3F#4 and with the inside M3 outside M6, we have B3D#4=A3F#4=F#3A3

But if you tune slightly narrow 6:3 octaves then you can have B3D#4=F3G#3
Or even B3D#4=E3G3.


Edited by Gadzar (07/18/14 03:11 AM)
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Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#2303603 - 07/18/14 04:14 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 219
Loc: Germany
Originally Posted By: DoelKees
For example play F4A4 and hear it beating. Now put your forearm on that octave: you can't hear F4A4 beating any more.
Kees


(With "putting the forearm on that octave" Kees means striking all the notes together within that octave)
At least one example, where you confirm that beat masking is possible. We have a good starting point here, more later...
_________________________
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www.piano-stopper.de

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#2303604 - 07/18/14 04:19 AM Re: Theoretical tuning sequence [Re: Bill Bremmer RPT]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 219
Loc: Germany
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Chris Leslie
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


I hear the beating completely disappear after a few seconds.


There is a certain degree of beat masking blending in after some time, caused by the fact that the intervals are NOT equally beating. Maybe Kees can provide us the beat rate differences of your examples?




Edited by Bernhard Stopper (07/18/14 06:05 AM)
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#2303642 - 07/18/14 08:53 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT
Whoops. Yes.

FG# = BD#

Thanks.


The M3/M6 test is (for example)
F3A3 = D3#C4.
However the M6 is really a tiny bit faster theoretically.
Your test, when you invert the m3 is
F3A3 = D3B3
and here the M6 is a little bit slower, but not a tiny bit.

So it may be a good bracketing test: the M3 has to beat at a rate in-between those two, but closer to D#3C4.

Kees


Thank you Kees.

You say the M6 is faster in the dom7 theoretically. Is there a mathematical proof? Thanks.

I use that relational logic to prove the m7b5 relationship but thought there might be a numerical one.

I think your relationship logic assumed a pure 6:3, but I couldn't completely follow it because, while you say my test's m3 inverted is a D3B3, that would refer to B3D4 and that equality is B3D3=F4A4 so I'm completely confused. I'm hoping a few more instructions will clear it up for me. Thanks for your time.

Like I said, I'm looking for a mathematical proof. Here's my relational proof, with assumptions.

Gadzar, I'm always tuning wide 4:2 and narrow 6:3 in the temperament octave.

The m7b5 Proof.

Assumptions:
Dom7 equality. GB=FD and all transpositions within and near the temperament octave, but not over the break.
Narrow 6:3 octaves given by F3G#3>G#3F4 and all transpositions within the temperament octave and nearby, where > means "every so slightly faster; barely noticeable."
The difference in beat speed between the m3 and M6 in a narrow 6:3, is equal to the difference between chromatic M6's in ET.

(These assumptions are valid for the level of accuracy I am going for, which is high compared to some other popular tests, especially since I am using "bracketing" exclusively in my temperament sequence, which seems to produce good precision. My sequence requires that you bisect all the windows equally when setting beat speeds.)

Relational Proof

F3G#3>G#3F4 (narrow 6:3)
A3F#4>G#3F4 (ET relationship)

Therefore,
F3G#3=A3F#4 (assuming beat speed differences are equal)

A3F#4=B3D4 (Dom7 equality)

Therefore,
F3G#3=B3D#4

I'm tuning high accuracy ET temperaments (increasing RBI's and P4's) using these relationships to produce windows into which other beat speeds must bisect (that's the beauty, the bisecting may not be 100% accurate, but it seems to be way more accurate than any other one sided tests like F3A3<F3D4 for the P4, for example. Just how much faster is F3D4 supposed to be? I know some people know the answer intuitively, but how to explain that to a beginner? The windows sequence I've developed gives a solid relationship that students have to reproduce, and even if the formulas and bisecting are not 100% accurate, the process of constantly fitting beat speeds into such small windows develops aural beat speed difference sensitivity, which is the most important skill for tuning aurally using RBI, IMHO. The tolerances on the windows I've developed are 3x more precise than CM3's)

Sorry for the long winded thesis, but that's what this is; my thesis. Your help and criticism is invaluable to helping me produce a method that other technicians and students will find credible.

As always, your objective and scientific criticism is appreciated by me and many others on this forum.

(Addendum. Gadzar, your post was much more concise than mine and proved the relationship nicely, given that the 6:3 was narrow as you say. Nice job.)


Edited by Mark Cerisano, RPT (07/18/14 09:01 AM)
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#2303647 - 07/18/14 09:10 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: Mark Cerisano, RPT
The difference in beat speed between the m3 and M6 in a narrow 6:3, is equal to the difference between chromatic M6's in ET.


Why? It may be greater or lesser, depending on how much the 6:3 octaves are stretched, in this case contracted.

There is no mathematical proof here.
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#2303657 - 07/18/14 09:55 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
P.S. In the treble we tune narrow 6:3 octaves. In the tenor we tune still narrow 6:3 octaves but less narrow than in the treble. In the bass we tune pure 6:3 octaves. And in the low bass, in some pianos, we even tune wide 6:3 octaves. So your equality will only work on a particular region of the scale where the 6:3 octaves have the required size.
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#2303733 - 07/18/14 02:24 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Originally Posted By: Mark Cerisano, RPT
The difference in beat speed between the m3 and M6 in a narrow 6:3, is equal to the difference between chromatic M6's in ET.


Why? It may be greater or lesser, depending on how much the 6:3 octaves are stretched, in this case contracted.

There is no mathematical proof here.


The accuracy of the assumption allows me to tune extremely high accuracy, compared to the way I used to tune. (Don't say it!) You need to see the sequence to get it.

Anyway, we don't tune 6:3 octaves in the temperament, unless you're going for some excessive stretch like pure 19ths.

The purpose if this analysis is to explore a sequence that gets good accuracy and precision by placing beat speeds evenly within a window, so that beginners can get decent results and improve their beat speed difference sensitivity.

In the end, it is that sensitivity, and stability, that allow a tuner to accurately make decisions on which way to adjust a note.

The only thing a good sequence can do is get you there faster with less refining.

A bad sequence allows you to get through without showing you the errors, thereby allowing you to move on with a false sense of accomplishment, if you choose not to refine.

Before anybody gets their knickers in a twist, I am NOT saying my sequence is the only one that can do that, or even the best one. I'm just making generalizations on what I think a good sequence should allow you to do.


Anyway, I see what you are saying. Because of the variable size of the 6:3 octave, we can't have a mathematical proof. I'm just wondering how accurate a sequence can be if we assume the m7b5 relationship, when the octave stretch really only confirms FG#=CE? Kees?
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#2303738 - 07/18/14 02:28 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
P.S. In the treble we tune narrow 6:3 octaves. In the tenor we tune still narrow 6:3 octaves but less narrow than in the treble. In the bass we tune pure 6:3 octaves. And in the low bass, in some pianos, we even tune wide 6:3 octaves. So your equality will only work on a particular region of the scale where the 6:3 octaves have the required size.



Agreed. I only use it in the temperament.
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#2303824 - 07/18/14 07:04 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT
Whoops. Yes.

FG# = BD#

Thanks.


The M3/M6 test is (for example)
F3A3 = D3#C4.
However the M6 is really a tiny bit faster theoretically.
Your test, when you invert the m3 is
F3A3 = D3B3
and here the M6 is a little bit slower, but not a tiny bit.

So it may be a good bracketing test: the M3 has to beat at a rate in-between those two, but closer to D#3C4.

Kees


Thank you Kees.

You say the M6 is faster in the dom7 theoretically. Is there a mathematical proof? Thanks.

I use that relational logic to prove the m7b5 relationship but thought there might be a numerical one.

I think your relationship logic assumed a pure 6:3, but I couldn't completely follow it because, while you say my test's m3 inverted is a D3B3, that would refer to B3D4 and that equality is B3D3=F4A4 so I'm completely confused. I'm hoping a few more instructions will clear it up for me. Thanks for your time.

Like I said, I'm looking for a mathematical proof. Here's my relational proof, with assumptions.

Gadzar, I'm always tuning wide 4:2 and narrow 6:3 in the temperament octave.

The m7b5 Proof.

Assumptions:
Dom7 equality. GB=FD and all transpositions within and near the temperament octave, but not over the break.
Narrow 6:3 octaves given by F3G#3>G#3F4 and all transpositions within the temperament octave and nearby, where > means "every so slightly faster; barely noticeable."
The difference in beat speed between the m3 and M6 in a narrow 6:3, is equal to the difference between chromatic M6's in ET.

(These assumptions are valid for the level of accuracy I am going for, which is high compared to some other popular tests, especially since I am using "bracketing" exclusively in my temperament sequence, which seems to produce good precision. My sequence requires that you bisect all the windows equally when setting beat speeds.)

Relational Proof

F3G#3>G#3F4 (narrow 6:3)
A3F#4>G#3F4 (ET relationship)

Therefore,
F3G#3=A3F#4 (assuming beat speed differences are equal)

A3F#4=B3D4 (Dom7 equality)

Therefore,
F3G#3=B3D#4

I'm tuning high accuracy ET temperaments (increasing RBI's and P4's) using these relationships to produce windows into which other beat speeds must bisect (that's the beauty, the bisecting may not be 100% accurate, but it seems to be way more accurate than any other one sided tests like F3A3<F3D4 for the P4, for example. Just how much faster is F3D4 supposed to be? I know some people know the answer intuitively, but how to explain that to a beginner? The windows sequence I've developed gives a solid relationship that students have to reproduce, and even if the formulas and bisecting are not 100% accurate, the process of constantly fitting beat speeds into such small windows develops aural beat speed difference sensitivity, which is the most important skill for tuning aurally using RBI, IMHO. The tolerances on the windows I've developed are 3x more precise than CM3's)

Sorry for the long winded thesis, but that's what this is; my thesis. Your help and criticism is invaluable to helping me produce a method that other technicians and students will find credible.

As always, your objective and scientific criticism is appreciated by me and many others on this forum.

(Addendum. Gadzar, your post was much more concise than mine and proved the relationship nicely, given that the 6:3 was narrow as you say. Nice job.)


I was just being simple minded and looked at the beat rates for zero IH and 2^(1/12) tuning. Then it is just a numerical coincidence that M3 and M6 beat about the same in the 3d inversion of dom 7th chord. They are not exactly the same though, M6 is a touch faster.

When there is IH and octave stretch I don't know what happens.

Regarding your proof attempt:

If x>y and z>y it does not follow that x=z unless you assume (as you did in your post) that x-y = z-y, but that is the same as assuming x=z so all you prove is that x=z if x=z.

Generally I like very much the idea of bracketing beatrates between two other beatrates.

Kees

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#2303846 - 07/18/14 09:18 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
What makes the relationship unique is that x>y for a different reason that z>y. That's why it is not as trivial as you say. Does that make sense?
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#2303882 - 07/18/14 11:11 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
What makes the relationship unique is that x>y for a different reason that z>y. That's why it is not as trivial as you say. Does that make sense?

Not really. No matter what the reason, it still doesn't follow that x=z unless you assume x=z (i.e., the beat rate differences (x-y and x-z are the same).

Why would they be the same in your example?

Somehow you have to mention that not only x>y and z>y, but also that both x and z are very close to y, in math speak |x-y|<=epsilon and |z-y|<=epsilon with epsilon the typical beat rate difference of your example.

In that case you can conclude |x-z|<epsilon, i.e., x is closer to z than the maximum of |x-y| and |z-y| but x could be larger or smaller than z.

To tighten the bound you need another assumption, namely that the difference between the beat rate differences d=||x-y|-|z-y|| is small, smaller than epsilon. (In your writeup you assumed this to be zero.) Suppose you know that d<q*epsilon with 0<=q<1.

The equations are now:
x>y
z>y
x-y<=epsilon
z-y<=epsilon
|(x-y)-(z-y)|<q*epsilon

Then from the last equation it follows that
|x-z|<q*epsilon

Kees

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#2303894 - 07/19/14 12:03 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT

I have discovered another equality test. (No one has every told me about it nor have I read of it anywhere, but that doesn't mean anything) But I thought you might be able to prove it mathematically. I call it the m7b5 equality. Example: FA# = BD#.

I know it works in my sequence, but is there any theoretical proof that it is valid?


I have written a program for this. It computes a temperament range with IH data from any piano, using tunelab's model. I tune octaves as 4:2 or 6:3 or in-between equal beating. Then I compute F3A3C#4F4A4 to be progressive, and interpolate the notes in between assuming the stretch does not change over a M3.

Below the beat rates computed for 4 IH models.

If we take the usual M3/M6 test on A3 as an example, we should
see that the M3 on A3 beats the same as the M6 on G3. For ih=0 we see the M6 is 0.2 bps is faster, whereas the M6 on F#3 is 0.3 slower. So it would be more accurate to say M3 on A3 is in-between M6's on F#3 and G3.

On the Steinway D the Cerisano M3/M6 test (A3C#4=F#3D#4) is already more accurate than the usual test (A3C#4=G3E4): M3 on A3 is closer to M6 on F#3 than on G3. On the uprights the Cerisano M3/M6 test is the more accurate one.

So it seems the usual M3/M6 test should be replaced by the Cerisano M3/M6 test (or bracketing). I ran the simulation also with 4:2 and 6:3 octaves with the same results.

Did I earn a complementary copy of your book?

Kees
--
octave: equal beating 4:2 and 6:3
ih=0

M3 M6 m3 m6 P4 P5
C#3 5.5 6.3 -7.5 -8.7 0.6 -0.5
D3 5.8 6.7 -7.9 -9.3 0.7 -0.5
D#3 6.2 7.1 -8.4 -9.8 0.7 -0.5
E3 6.5 7.5 -8.9 -10.4 0.8 -0.6
F3 6.9 7.9 -9.4 -11.0 0.8 -0.6
F#3 7.3 8.4 -10.0 -11.7 0.8 -0.6
G3 7.8 8.9 -10.6 -12.4 0.9 -0.7
G#3 8.2 9.4 -11.2 -13.1 0.9 -0.7
A3 8.7 10.0 -11.9 -13.9 1.0 -0.7
A#3 9.3 10.6 -12.6 -14.7 1.1 -0.8
B3 9.8 11.2 -13.3 -15.6 1.1 -0.8
C4 10.4 11.9 -14.1 -16.5 1.2 -0.9
C#4 11.0 -- -15.0 -17.5 1.3 -0.9
D4 11.7 -- -15.9 -- 1.3 -1.0
D#4 12.4 -- -16.8 -- 1.4 --
E4 13.1 -- -17.8 -- 1.5 --
F4 13.9 -- -18.9 -- -- --
F#4 -- -- -20.0 -- -- --

ih = Steinway D

M3 M6 m3 m6 P4 P5
C#3 5.5 6.3 -7.8 -9.1 0.7 -0.5
D3 5.8 6.7 -8.3 -9.7 0.7 -0.5
D#3 6.2 7.1 -8.9 -10.3 0.7 -0.5
E3 6.5 7.5 -9.4 -10.9 0.8 -0.6
F3 6.9 8.0 -10.1 -11.6 0.8 -0.6
F#3 7.3 8.5 -10.7 -12.4 0.9 -0.6
G3 7.8 9.0 -11.4 -13.2 0.9 -0.7
G#3 8.2 9.5 -12.2 -14.1 1.0 -0.7
A3 8.7 10.1 -13.1 -15.0 1.1 -0.7
A#3 9.2 10.7 -13.9 -16.0 1.1 -0.8
B3 9.8 11.3 -14.9 -17.1 1.2 -0.8
C4 10.3 12.0 -16.0 -18.2 1.3 -0.9
C#4 10.9 -- -17.1 -19.5 1.4 -0.9
D4 11.6 -- -18.3 -- 1.5 -1.0
D#4 12.3 -- -19.7 -- 1.6 --
E4 13.0 -- -21.1 -- 1.7 --
F4 13.8 -- -22.7 -- -- --
F#4 -- -- -24.5 -- -- --

ih = HellasHelsinki
M3 M6 m3 m6 P4 P5
C#3 5.4 6.3 -7.9 -10.8 0.7 -0.3
D3 5.7 6.7 -8.4 -11.4 0.8 -0.3
D#3 6.1 7.1 -8.9 -12.0 0.8 -0.3
E3 6.4 7.5 -9.5 -12.7 0.9 -0.3
F3 6.8 8.0 -10.1 -13.4 0.9 -0.4
F#3 7.2 8.4 -10.8 -14.2 1.0 -0.4
G3 7.7 9.0 -11.5 -15.1 1.0 -0.4
G#3 8.1 9.5 -12.2 -16.0 1.1 -0.5
A3 8.6 10.1 -13.1 -17.0 1.2 -0.5
A#3 9.1 10.7 -13.9 -18.0 1.2 -0.6
B3 9.6 11.3 -14.8 -19.1 1.3 -0.6
C4 10.2 12.0 -15.8 -20.4 1.4 -0.6
C#4 10.8 -- -16.9 -21.7 1.5 -0.7
D4 11.4 -- -18.1 -- 1.6 -0.7
D#4 12.1 -- -19.3 -- 1.7 --
E4 12.8 -- -20.6 -- 1.8 --
F4 13.6 -- -22.1 -- -- --
F#4 -- -- -23.7 -- -- --

ih = large Heintzmann upright

M3 M6 m3 m6 P4 P5
C#3 5.4 6.3 -8.2 -10.6 0.7 -0.3
D3 5.7 6.7 -8.7 -11.2 0.8 -0.3
D#3 6.1 7.1 -9.3 -11.9 0.8 -0.4
E3 6.4 7.6 -9.9 -12.6 0.9 -0.4
F3 6.8 8.0 -10.6 -13.5 0.9 -0.4
F#3 7.2 8.5 -11.4 -14.3 1.0 -0.5
G3 7.7 9.0 -12.2 -15.3 1.1 -0.5
G#3 8.1 9.5 -13.0 -16.3 1.1 -0.5
A3 8.6 10.1 -13.9 -17.5 1.2 -0.6
A#3 9.1 10.8 -15.0 -18.7 1.3 -0.6
B3 9.6 11.4 -16.1 -20.0 1.4 -0.6
C4 10.2 12.1 -17.3 -21.5 1.4 -0.7
C#4 10.7 -- -18.6 -23.1 1.6 -0.7
D4 11.4 -- -20.0 -- 1.7 -0.7
D#4 12.1 -- -21.5 -- 1.8 --
E4 12.8 -- -23.2 -- 1.9 --
F4 13.5 -- -25.0 -- -- --
F#4 -- -- -27.1 -- -- --

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#2303916 - 07/19/14 02:20 AM Re: Theoretical tuning sequence [Re: DoelKees]
Hakki Offline
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Registered: 05/26/01
Posts: 2778
Nice work Kees.

But whether you get a free copy depends on the accuracy of your inharmonicity model.

Did you measure all the ih values? Or what equation are you using for the ih values? Did you verify the accuracy of your ih model?
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#2303917 - 07/19/14 02:24 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Kees,

You deserve a free copy of your own book. As the M3/M6 test you propose is not Mark Cerisano's test.

You see, what Cerisano proposes is a m3/M3 test, i.e. FG#/BD#.

I've seen his video. He checks his temperament with the normal M3/M6 test.

He plays:

F3D4/G3B3
F#3D#4/G#3C4
G3E4/A3C#4
G#3F4/A#3D4

and here, as his temperament is set from F3 to F4, he can not check A3F#4/B3D4, because F#4 is not yet tuned. So instead of playing A3F#4 he plays the inversion F#3A3 and continues as follows:

F#3A3/B3D#4
G3A#3/C4E4
G#3B3/C#4F4

Of course this is wrong, because the 6:3 octave is narrow and the m3 beats faster than its inversion, the M6.

I don't know when nor how but since he made this video, he has discovered his error and now he lowers a half step the m3 hopping it would beat the same as the M3, so instead of testing F#3A3/B3D#4 he tests F3G#3/B3D#4.

In sum what he tests is:

F3G#3/B3D#4
F#3A3/C4E4
G3A#3/C#4F4

For the Steinway D this gives:

F3G#3/B3D#4 10.1/9.8 0.3 bps.
F#3A3/C4E4 10.8/10.3 0.5 bps.
G3A#3/C#4F4 11.4/10.9 0.5 bps.

The normal M3/M6 test gives

A3F#4/B3D#4 10.1/9.8 0.3 bps.
A#3G4/C4E4 10.7/10.3 0.4 bps.
B3G#4/C#4F4 11.3/10.9 0.4 bps.

So the Cerisano's proposal is no better than the usual M3/M6 test.

But if we lower the m3 a half step again, as I suggested in my post

Originally Posted By: Gadzar
There is no "mathematical proof". It all depends on how much you stretch (contract) the 6:3 octaves.

If you have a pure 6:3 octave F#3F#4 then F#3A3=A3F#4 and with the inside M3 outside M6, we have B3D#4=A3F#4=F#3A3

But if you tune slightly narrow 6:3 octaves then you can have B3D#4=F3G#3
Or even B3D#4=E3G3.



Then we have:

E3G3/B3D#4 9.5/9.8 0.3
F3G#3/C4E4 10.1/10.3 0.2
F#3A3/C#4F4 10.7/10.9 0.2

This is better than the normal M3/M6 test.


What you propose is to modify the normal M3/M6 test by lowering the M6 a half step, without inverting it to a m3, which of course takes out of play the contracted 6:3 octave, and you compare the beat rates of:

B3D#4/G#3F4 9.8/9.5 0.3 bps.
C4E4/A3F#4 10.3/10.1 0.2 bps.
C#4F4/A#3G4 10.9/10.7 0.2 bps.

which is better than the normal M3/M6 test.


Anyway, as we can see here, this tests are not accurate, there is not a true equal beating, so I do not use them to set my temperament. I can use them to check and detect erros, but not for tuning.



Edited by Gadzar (07/19/14 02:43 AM)
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#2303923 - 07/19/14 02:37 AM Re: Theoretical tuning sequence [Re: Hakki]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Hakki
Nice work Kees.

But whether you get a free copy depends on the accuracy of your inharmonicity model.

Did you measure all the ih values? Or what equation are you using for the ih values? Did you verify the accuracy of your ih model?

Right, I left that job for you.

Kees

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#2303924 - 07/19/14 02:39 AM Re: Theoretical tuning sequence [Re: Hakki]
Hakki Offline
2000 Post Club Member

Registered: 05/26/01
Posts: 2778
Originally Posted By: Hakki
Nice work Kees.

But whether you get a free copy depends on the accuracy of your inharmonicity model.

Did you measure all the ih values? Or what equation are you using for the ih values? Did you verify the accuracy of your ih model?


Oh btw, how accurate the Tunelab model can also make your results invalid.
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#2304114 - 07/19/14 04:59 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Bernhard Stopper
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Chris Leslie
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


I hear the beating completely disappear after a few seconds.


There is a certain degree of beat masking blending in after some time, caused by the fact that the intervals are NOT equally beating. Maybe Kees can provide us the beat rate differences of your examples?

CE 6.4bps
GE 6.6bps
GC 1.2bps

That's equal beating within the accuracy of my reading of the beat rates from the spectrogram.

In ET GE would beat about 1bps slower than CE.

So if in the example we'd raise G a tiny beat to make GE beat at 5.4bps it should sound better according to you, and worse according to Bill. (The P4 will of course improve a bit from 1.2bps (which is correct for EBVT) to about 1bps which hopefully does not affect our perception of the rapid beats.)

That should be easy to demonstrate.

Kees

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#2304235 - 07/19/14 11:55 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT
What makes the relationship unique is that x>y for a different reason that z>y. That's why it is not as trivial as you say. Does that make sense?

Not really. No matter what the reason, it still doesn't follow that x=z unless you assume x=z (i.e., the beat rate differences (x-y and x-z are the same).

Why would they be the same in your example?

Somehow you have to mention that not only x>y and z>y, but also that both x and z are very close to y, in math speak |x-y|<=epsilon and |z-y|<=epsilon with epsilon the typical beat rate difference of your example.

In that case you can conclude |x-z|<epsilon, i.e., x is closer to z than the maximum of |x-y| and |z-y| but x could be larger or smaller than z.

To tighten the bound you need another assumption, namely that the difference between the beat rate differences d=||x-y|-|z-y|| is small, smaller than epsilon. (In your writeup you assumed this to be zero.) Suppose you know that d<q*epsilon with 0<=q<1.

The equations are now:
x>y
z>y
x-y<=epsilon
z-y<=epsilon
|(x-y)-(z-y)|<q*epsilon

Then from the last equation it follows that
|x-z|<q*epsilon

Kees


Touché
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#2304247 - 07/20/14 12:35 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
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Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Wait, the Cerisano M3/M6 test? What is that? I did what?

My test is the m7b5 test, which is based on the usual 3/6 test being accurate, and the 6:3 octave being narrow by the smallest amount.

But you are doing exactly what I was hoping to find out. In fact, my next question to you was going to be how to calculate partial frequencies based on iH models, for the purpose of calculating beat rates, and there you go and do the whole thing already!

Ok, so if I use your numbers for my m7b5 equality:

Does F3G#3 = B3D#4?

(Each number refers to the four charts you made.)
F3 m3=-9.4/-10.1/-10.1/-10.6
B3 M3=9.8/9.8/9.6/9.6
Differences 0.4/-0.3/-0.5/-1.0 (Where "-" means slower on top)

That does NOT prove my m7b5 test, but shows that the relationship is affected by iH.

How narrow are the 6:3's on each piano?
For A3A4.
A3 m3=-11.9/-13.1/-13.1/-13.9
C4 M6=11.9/12.0/12.0/12.1
Diff = 0/1.1/1.1/1.8

It's funny, because when I tune A3A4, I fit it between 4:2 and 6:3 by making 4:2 wide and 6:3 narrow. I assess the wideness and narrowness by the difference in the beat speed tests.

But, on some pianos, while I hear definite differences between the tests, on others, the differences are almost zero, (as for as I can tell with my current beat speed difference sensitivity), which I conclude means, on those pianos, I can tune 4:2 OR 6:3 and be pretty close to a good octave each time. BUT, whether or not this window is large or zero (and once inverted!?) doesn't seem to depend on the length of the strings, and by inference, the iH of the piano, as your numbers infer.

Comments?

Also, notice how all the P4 increase. That's my final test. (Where SBI is actually more precise than RBI, IMHO. Whodathought?)

BTW, you earned the book a long time ago!
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#2304255 - 07/20/14 01:04 AM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar
Kees,

You deserve a free copy of your own book. As the M3/M6 test you propose is not Mark Cerisano's test.

You see, what Cerisano proposes is a m3/M3 test, i.e. FG#/BD#.

I've seen his video. He checks his temperament with the normal M3/M6 test.

He plays:

F3D4/G3B3
F#3D#4/G#3C4
G3E4/A3C#4
G#3F4/A#3D4

and here, as his temperament is set from F3 to F4, he can not check A3F#4/B3D4, because F#4 is not yet tuned. So instead of playing A3F#4 he plays the inversion F#3A3 and continues as follows:

F#3A3/B3D#4
G3A#3/C4E4
G#3B3/C#4F4

Of course this is wrong, because the 6:3 octave is narrow and the m3 beats faster than its inversion, the M6.

I don't know when nor how but since he made this video, he has discovered his error and now he lowers a half step the m3 hopping it would beat the same as the M3, so instead of testing F#3A3/B3D#4 he tests F3G#3/B3D#4.

In sum what he tests is:

F3G#3/B3D#4
F#3A3/C4E4
G3A#3/C#4F4

For the Steinway D this gives:

F3G#3/B3D#4 10.1/9.8 0.3 bps.
F#3A3/C4E4 10.8/10.3 0.5 bps.
G3A#3/C#4F4 11.4/10.9 0.5 bps.

The normal M3/M6 test gives

A3F#4/B3D#4 10.1/9.8 0.3 bps.
A#3G4/C4E4 10.7/10.3 0.4 bps.
B3G#4/C#4F4 11.3/10.9 0.4 bps.

So the Cerisano's proposal is no better than the usual M3/M6 test.

But if we lower the m3 a half step again, as I suggested in my post

Originally Posted By: Gadzar
There is no "mathematical proof". It all depends on how much you stretch (contract) the 6:3 octaves.

If you have a pure 6:3 octave F#3F#4 then F#3A3=A3F#4 and with the inside M3 outside M6, we have B3D#4=A3F#4=F#3A3

But if you tune slightly narrow 6:3 octaves then you can have B3D#4=F3G#3
Or even B3D#4=E3G3.



Then we have:

E3G3/B3D#4 9.5/9.8 0.3
F3G#3/C4E4 10.1/10.3 0.2
F#3A3/C#4F4 10.7/10.9 0.2

This is better than the normal M3/M6 test.


What you propose is to modify the normal M3/M6 test by lowering the M6 a half step, without inverting it to a m3, which of course takes out of play the contracted 6:3 octave, and you compare the beat rates of:

B3D#4/G#3F4 9.8/9.5 0.3 bps.
C4E4/A3F#4 10.3/10.1 0.2 bps.
C#4F4/A#3G4 10.9/10.7 0.2 bps.

which is better than the normal M3/M6 test.


Anyway, as we can see here, this tests are not accurate, there is not a true equal beating, so I do not use them to set my temperament. I can use them to check and detect erros, but not for tuning.



Hi Gadzar,

I am flattered that you analyzed my video. Thank you. That is what the academic community calls necessary and why I posted it and refer to it on PW because I KNOW nobody is going to let me get away with anything. You guys are great.

However, with my quick reading, I think I see some typos/errors.

After the highest 3/6 test, I used
F3G#3/B3D#4
F#3A3/C4E4
G3A#3/C#4F4

The tests you quoted are wrong, and not mine. I never discovered those tests and have never used those tests. Go back and check the video again. Unless I had a seizure and blacked out (I won't discount that possibility) you won't find them.

"So the Cerisano's proposal [m7b5] is no better than the usual M3/M6 test."

I'll accept that. The 3/6 test is very popular.

But, I am intrigued by your even narrower 6:3 conclusion. In fact, I may devise multiple bisecting window sequences that depend on the conclusion of the 6:3 when tuning A3A4 and F3F4. As you see above, I have found some pianos to have almost 6:3=4:2 and others; a very wide difference, although the degree of narrowness is not easy to assess.

"Anyway, as we can see here, this tests are not accurate, there is not a true equal beating,"

But the question is, how close are they? Within how many cents of perfect ET, defined by Kees' criteria?

"I do not use them to set my temperament. I can use them to check and detect erros, but not for tuning."

If they can detect errors after the tuning, aren't they more accurate than the methods you are now using to tune the temperament?

I don't mean to be facetious. Actually, for me, I did not use these to tune either before I developed the bisecting window sequence. Because, as Bill put it correctly one time, with the 3/6 test, if it doesn't work, you've got four possible notes to correct. I.e. it is only useful when all the notes are tuned to a very high accuracy.

With the bisecting window method, each note is tuned to a very high accuracy right from the beginning. After the tuning there is little or no refining because the technique used to check the tuning, is the same as the one used to make the tuning.

The P4 tests have a smaller tolerance in my experience, so I use them at the end.

The bisecting window method gives a CM3 accuracy for each note as you tune it. In fact, it is more accurate than the CM3 method because the windows get smaller as you tune.

I promise to post it once I have finalized the best presentation format.


Edited by Mark Cerisano, RPT (07/20/14 01:05 AM)
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#2304262 - 07/20/14 02:18 AM Re: Theoretical tuning sequence [Re: DoelKees]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
I guess everybody better draw there own conclusions from those beatrate tables.

What I get is that usual M3/M6 test should be replaced by (for example):

Not
"G3B3 = F3D4"
but
"E3C#4 < G3B3 < F3D4 and G3B3 should be closer to the leftmost M6."

This of course assumes the M6's are tuned progressive but nobody can apparently get all the M3 and M6 progressive by ear, so I'm not sure if this is of any practical use.

Tests involving m3's have the problem that the m3 is more sensitive to inharmonicity than the M3/M6 as the 6th partial is less stable.

Kees

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#2304267 - 07/20/14 02:52 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City

Originally Posted By: Mark Cerisano, RPT
If they can detect errors after the tuning, aren't they more accurate than the methods you are now using to tune the temperament?


No! The methods I use to tune the temperament are the same used in the M3/M6 test. The methods consist in adjusting the beat rates of M3s, M6s, P4s, P5s and m3s in even smooth progressions.

I do not use the M3/M6 test to tune my temperament because:

1.- The notes involved are not available until the last steps of my sequence. I tune: A4 A3 F3 F4 C#4 A#3 F#3 B3 G#3 C4 G3 D4 D#4 E4 the first available M3/M6 tests are F3D4/G3B3 and G#3F4/A#3D4 and D4 is tuned at step 12 of 14.

2.- If a M3/M6 test proves wrong, there may be from 1 to as much as 4 notes mistuned and it does not informs us which note or notes is/are in fault, nor if they are flat or sharp, nor by how much. We only know that the M3 doesn't beat at the same speed than the M6, but we have no clue on how to correct the error. In order to correct it we must do other tests to identify which notes in which direction and by how much are to be retuned.

For all the above this test is better suited to check but not for setting the temperament.
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#2304278 - 07/20/14 04:43 AM Re: Theoretical tuning sequence [Re: DoelKees]
Chris Leslie Offline
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Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Originally Posted By: DoelKees
I guess everybody better draw there own conclusions from those beatrate tables.

What I get is that usual M3/M6 test should be replaced by (for example):

Not
"G3B3 = F3D4"
but
"E3C#4 < G3B3 < F3D4 and G3B3 should be closer to the leftmost M6."

This of course assumes the M6's are tuned progressive but nobody can apparently get all the M3 and M6 progressive by ear, so I'm not sure if this is of any practical use.

Tests involving m3's have the problem that the m3 is more sensitive to inharmonicity than the M3/M6 as the 6th partial is less stable.

Kees

For high iH instruments, and with a generous stretch in the mid-range, E3C#4 is very close to, or even faster than, G3B3. Given that, the M3/M6 inside/outside test is not consistent enough to use as a temperament setter, or as in a beat rate window.


Edited by Chris Leslie (07/20/14 08:07 AM)
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#2304293 - 07/20/14 07:08 AM Re: Theoretical tuning sequence [Re: DoelKees]
Bernhard Stopper Offline
Full Member

Registered: 09/22/08
Posts: 219
Loc: Germany
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Chris Leslie
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


I hear the beating completely disappear after a few seconds.


There is a certain degree of beat masking blending in after some time, caused by the fact that the intervals are NOT equally beating. Maybe Kees can provide us the beat rate differences of your examples?

CE 6.4bps
GE 6.6bps
GC 1.2bps

That's equal beating within the accuracy of my reading of the beat rates from the spectrogram.

In ET GE would beat about 1bps slower than CE.

So if in the example we'd raise G a tiny beat to make GE beat at 5.4bps it should sound better according to you, and worse according to Bill. (The P4 will of course improve a bit from 1.2bps (which is correct for EBVT) to about 1bps which hopefully does not affect our perception of the rapid beats.)

That should be easy to demonstrate.

Kees


No, i did not say that if you raise G to beat at 5.4 bps it must sound necessarily better. What i did say is that the masking that was blending in after some time in this example, comes from the tiny difference of bps of the two intervals. And that the masking effect would not blend in, if the beating is exactly the same.



Edited by Bernhard Stopper (07/20/14 07:13 AM)
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#2304384 - 07/20/14 12:18 PM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
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Registered: 03/14/08
Posts: 7904
Loc: France
So what is more prone to happen with similar beating ?
My gut feeling is still there is an "additive" way and a "substractive one"

WHat is it related to ? phasing, or frequency coupling ?
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#2304415 - 07/20/14 01:38 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Re: the 3/6 test. I always heard it wasn't exact. Now I have more motivation to analyze the 6:3 A3A4 and F3F4 at the beginning, to determine the best sequence if I will be using the 3/6 and m7b5 or neighbouring tests to tune the temperament.

However, using the sequence as it is now, allows me to produce an ET temperament that is within my beat speed sensitivity tolerance, meaning I don't have to refine as much.

Again, the real elephant in the room is beat speed sensitivity. If you can't tell if F#3A#3 is between FA and GB, you won't be able to get good accuracy on ET, IMHO.

Does anyone else feel this way? What have you done, what is your approach to developing this sensitivity to the highest level possible. IMHO, this is the information beginning techs really need.

Please don't reply "Tune 1000 pianos". I think we should be beyond that with all the technology we have that can speed up learning.
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#2304472 - 07/20/14 04:11 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Bernhard Stopper
Originally Posted By: DoelKees
Originally Posted By: Bernhard Stopper
Originally Posted By: Bill Bremmer RPT
Originally Posted By: Chris Leslie
Originally Posted By: Bill Bremmer RPT
Here are two short videos that show how equally beating intervals, when played together, tend to suppress the beating sound and reduce slightly the overall volume of sound.

https://www.youtube.com/watch?v=qiCDrkPzCnI

https://www.youtube.com/watch?v=qnwnA1dXkJM


In the lower CEG sample, the clarity of the beating in the triad is lessened and muddied but I still hear the same beating.


I hear the beating completely disappear after a few seconds.


There is a certain degree of beat masking blending in after some time, caused by the fact that the intervals are NOT equally beating. Maybe Kees can provide us the beat rate differences of your examples?

CE 6.4bps
GE 6.6bps
GC 1.2bps

That's equal beating within the accuracy of my reading of the beat rates from the spectrogram.

In ET GE would beat about 1bps slower than CE.

So if in the example we'd raise G a tiny beat to make GE beat at 5.4bps it should sound better according to you, and worse according to Bill. (The P4 will of course improve a bit from 1.2bps (which is correct for EBVT) to about 1bps which hopefully does not affect our perception of the rapid beats.)

That should be easy to demonstrate.

Kees


No, i did not say that if you raise G to beat at 5.4 bps it must sound necessarily better. What i did say is that the masking that was blending in after some time in this example, comes from the tiny difference of bps of the two intervals. And that the masking effect would not blend in, if the beating is exactly the same.

No beats will ever be exactly the same, making that a tautology.
Or did you have some tolerance (smaller than 0.2) in mind for the equality?

Kees


Edited by DoelKees (07/20/14 04:11 PM)

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#2304495 - 07/20/14 05:33 PM Re: Theoretical tuning sequence [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7904
Loc: France
Why wanting to compare beats only at one particular partial match.?

How efficient is it?
Comparing beats of similar intervals can be precise but from 2 different ones I always find that nebulous.
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#2304513 - 07/20/14 06:46 PM Re: Theoretical tuning sequence [Re: Bernhard Stopper]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1085
Loc: Sicily - Italy
Originally Posted By: Bernhard Stopper
Originally Posted By: Olek
Accepting beats an not fighting them makes them more discrete in the end, and they also goes well with the piano tone, and the shape it takes.

The consonances I hear/tune are an addition of slow beats (within the 2 octaves framework for instance.


A reduction of beats generally comes along with an increase of consonance, not the other way around.




Hi Bernhard,

I cannot agree with the above statement of yours, perhaps because I relate '..increase of consonance..' to (frequencies and) beats_order and proportion. Infinite (ordered) ways in which beats can blend and add color.

Perhaps I am misinterpreting your statement, would you like to expand?

Regards, a.c.
.
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#2304516 - 07/20/14 06:57 PM Re: Theoretical tuning sequence [Re: DoelKees]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: DoelKees

No beats will ever be exactly the same, making that a tautology.
Or did you have some tolerance (smaller than 0.2) in mind for the equality?

I tried an experiment with A3D4F#4 by moving the A3 by 0.5 a cent.
Here are the beat rates:
D4F#4 9.0 bps
A3: -0.5 0 +.5 +1
A3F#4 9.0 8.7 8.4 8.1

Here's the chord for those 4 cases (left to right), the first beating "exactly" equal beating. http://persianney.com/misc/all4.mp3

Can more sensitive ears than mine hear any of the beat masking/cancellation effects discussed?

Kees

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#2304612 - 07/21/14 12:16 AM Re: Theoretical tuning sequence [Re: DoelKees]
Chris Leslie Offline
500 Post Club Member

Registered: 01/01/11
Posts: 759
Loc: Canberra, ACT, Australia
Originally Posted By: DoelKees
Originally Posted By: DoelKees

No beats will ever be exactly the same, making that a tautology.
Or did you have some tolerance (smaller than 0.2) in mind for the equality?

I tried an experiment with A3D4F#4 by moving the A3 by 0.5 a cent.
Here are the beat rates:
D4F#4 9.0 bps
A3: -0.5 0 +.5 +1
A3F#4 9.0 8.7 8.4 8.1

Here's the chord for those 4 cases (left to right), the first beating "exactly" equal beating. http://persianney.com/misc/all4.mp3

Can more sensitive ears than mine hear any of the beat masking/cancellation effects discussed?

Kees



Well, not claims about having more sensitive ears, but can hardly tell any difference at all with the RBIs. They all beat obviously. If anything, the first chord could be very slightly more clear but that may be just an illusion because it came first. The SBI seems to perturb slightly differently for each chord, but hardly by much.
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#2304757 - 07/21/14 09:43 AM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
Kees:

Just some general comments, because you know what you are doing and what you are talking about. That is, what I am going to mention, I am sure you have already thought about.

You have described an algorithm. It favors the 2nd, 3rd and 4th partials when iH exists. I expect that in the case of a jump in iH, the RBIs would not be progressive.

I will often use the relationship of the SBI beatrates to smooth out a tuning, or when touching up a tuning. It is the same idea.

I had been toying with the idea of a sequence that is based on the M3/M6 test. Of course this requires a temperament span of greater than an octave. It may also work well as an algorithm, I think... Something like:

A3 = 220hz
A3-C#3 = 9bps
A3-E4 = -0.5bps
G3-E4 = 9bps
G3-D4/A3-D4 = -1/2 ratio

Of course, so far these are just rule-of thumb numbers. As the algorithm progresses, any errors would be corrected only part way. I would think three times thru the sequence would be sufficient. I'll have to play with it on my simulator.

This would continue with something like:

B3-E4/E4-A4 = 2/3 ratio AND
G3-B3/A3-C#3 = 7/8 ratio (both won't happen, so the error is averaged between the two)
F3-D4 = G3-B3

Then next M3/M6 test can produce a A3-D#4-A4 contiguous tritone, but the m3/M3 inversion of the M3/M6 test would probably be used.

Then three more M3/M6 tests should complete the temperament. Of course then the errors are checked and corrected by averaging. I suppose the averaging could be weighted according to a preference...

I'll see if I can find the time to play with this. Not as an aural tuning sequence, but as an algorithm.

I fooled around a bit with this idea, modified to suit my own interest.

Temperament range F3-C#5 so you have all possible M3/M6 tests. Then pick a random M3/M6 test and adjust the upper note to make them equal beating. Unless it's an A. This does not work: it gets worse at every iteration. Picking the lower note is no better.

Not sure why.

Kees


I played around with it some, too. I decided on a different goal - the same as yours with 4ths and 5ths: Given random errors, produce a refining algorithm. I ran into the same sort of problems, things getting worse, at least for some notes.

I tried correcting two notes at once, one from each interval, in hopes that it would be self-correcting. Maybe I'll try a different pair...
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#2304773 - 07/21/14 10:25 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: Mark Cerisano, RPT
.....

I know it works in my sequence, but is there any theoretical proof that it is valid?


The M6/M3 equal beating test and its m3/M3 inversion work just because of happenstance. But there are "theoretical proofs" that show where this comes from.

Take the M6/M3 test with the intervals of F3-D4 and G3-B3. And also consider two other intervals: F3-A3, A3-D4. This gives us the following approximate beatrates (disregarding iH and stretch):

F3-A3 7bps
F3-D4 8bps
G3-B3 8bps
A3-D4 1bps

Hmmm, 8-7 = 1 and that is the M3-M6 test for a P4. In otherwords, the reason there is a 1bps difference between F3-A3 and F3-D4 is because A3-D4 is 1 bps.

And hmmm, the ratio of the two M3s, G3-B3 and F3-A3 is 8/7. This is because they are two semitones apart. Since beatrates double each octave, they follow the same pattern as theoretical frequencies. The ratio of frequencies (and beats) two semitones apart is the square of the twelfth-root-of-two, or about 8/7.

See, it is just a happenstance with theoretical 12-TET with 2:1 octaves. It would not happen with 11-TET nor with 2.5:1 octaves.
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#2305092 - 07/21/14 09:38 PM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT

Again, the real elephant in the room is beat speed sensitivity. If you can't tell if F#3A#3 is between FA and GB, you won't be able to get good accuracy on ET, IMHO.

Does anyone else feel this way? What have you done, what is your approach to developing this sensitivity to the highest level possible. IMHO, this is the information beginning techs really need.

Please don't reply "Tune 1000 pianos". I think we should be beyond that with all the technology we have that can speed up learning.

It think it has two components:

1) developing beat speed sensitivity when the beats are clearly audible. Some training app with synthetic tones of even with metronome clicks would be a great learning tool for this I think.

2) actually being able to focus on listening to the correct beat on a real piano where there is interference from higher partials and other distractions. Developing training software for this would probably have to work with recorded samples of a real piano.

I think such training tools would be a vast improvement over the traditional "tune 1000 pianos" method.

Kees

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#2305151 - 07/22/14 12:28 AM Re: Theoretical tuning sequence [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
I have been focusing my ears into estimating the amount of tempering in the M3s, instead of counting beats.

For example play two distant M3s and tell which one is more tempered. Obviously the upper third will beat faster but that doesn't mean it is more tempered.

Another exercise I like to practice is to tune CM3s over any note and hear if the resulting octave is good. If it isn't repeat the exercise.

After some time and practice, I have a good idea of how the M3s must sound on that piano, without counting beats. Once I know it I am able to set the temperament in this piano quickly and accurately at once.

So I never really strive to hear which M3 is faster but which is "more tempered" or "harsher".



Edited by Gadzar (07/22/14 12:30 AM)
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

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#2305253 - 07/22/14 08:26 AM Re: Theoretical tuning sequence [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Originally Posted By: Mark Cerisano, RPT

Again, the real elephant in the room is beat speed sensitivity. If you can't tell if F#3A#3 is between FA and GB, you won't be able to get good accuracy on ET, IMHO.

Does anyone else feel this way? What have you done, what is your approach to developing this sensitivity to the highest level possible. IMHO, this is the information beginning techs really need.

Please don't reply "Tune 1000 pianos". I think we should be beyond that with all the technology we have that can speed up learning.


Let's say the goal is to have M3s and M6s progressive. That requires an accuracy of +/- 0.2 cents. When tuning aurally, it requires the discernment of the difference of a beat ratio of +/- 1/16 (difference between 16 bps and 17 bps or 8 bps and 8.5 bps). The scaling also has to make it possible to have both M3s and M6s progressive.

Considering that none of these tolerances will be zero, the stability needed is actually greater than 0.2 cents.

Given a particular piano and tuner any of these factors may be the weak link. Like does it really matter if the tuner can discern the difference between 8 bps and 8.5 bps if the pins are horribly jumpy?
_________________________
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Part-Time Tuner
Who taught the first chicken how to peck?

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#2305460 - 07/22/14 03:20 PM Re: Theoretical tuning sequence [Re: Olek]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Olek
Why wanting to compare beats only at one particular partial match.?

How efficient is it?
Comparing beats of similar intervals can be precise but from 2 different ones I always find that nebulous.


Nebulous? Perhaps. Impossible? No. Accurate? Heck ya.

But, I know what you are saying.

Basically, the big difference between tuning with partials using check notes, and just tuning intervals so they sound good, is that the tuner is using an indirect judgement, instead of a direct judgement.

An indirect judgement is when the tuner makes a conclusion about the quality of an interval, by playing test intervals, or check intervals created using the check note, instead of just listening to the interval directly.

Tuning an interval like an octave, so it sounds good directly, means playing the octave, and adjusting one note, while listening to the octave, and making a judgement about when it sounds best.

Tuning an interval indirectly means playing an interval, testing it with check notes, making a decision about which way one of the notes needs to go, making that change (and possibly listening to the direct interval to confirm), then checking the interval with check notes again. Ending with a direct assessment by playing the interval itself.

I can't tell you how many times I've tuned an interval directly, thinking it sounded good, then checked it indirectly with check notes, adjusted it, then re-listened directly to the interval, and it sounds better to me.

It has never happened the other way around. I.e. tuned an interval directly, adjusted it with check notes, and the interval sounds worse.

The only exception I can think of are the low bass strings that have poor iH, and unisons on mismatched strings. Those need to be tuned directly so that all the beating partials can be reduced as much as possible. Perhaps some beat masking is helping here too.

The direct relationship between check notes and the quality of the interval is - if the check intervals are equal, there is no beating at the coincidental partial. If there is only one coincidental partial in hearing range, this is the only one that needs to be considered.

Sometimes the fifth's 2nd coincidental partial can reek havoc when trying to tune fifths using the M6/M10 test.

Octaves have many coincidental partials that we need to be concerned with.

By identifying a certain sound with a certain check interval relationship, you can accurately reproduce the same interval sound. That's precision. Example, tuning midrange octaves between a 4:2 and a 6:3.

Tuning intervals can be done by ear, using a direct approach, but that is the same as tuning A4 to the fork directly, instead of using F2. Here, the check note gives us more accuracy and precision.

It's the same with other intervals, if the check interval relationships have tight tolerances. I.e., trying to just make an octave a wide 4:2 without checking the 6:3 can lead to a wide 6:3 and an octave that could sound better. Also, the precision of octaves produced with only 4:2 checks is low.
_________________________
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www.howtotunepianos.com

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#2305464 - 07/22/14 03:33 PM Re: Theoretical tuning sequence [Re: Gadzar]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: Gadzar

Originally Posted By: Mark Cerisano, RPT
If they can detect errors after the tuning, aren't they more accurate than the methods you are now using to tune the temperament?


No! The methods I use to tune the temperament are the same used in the M3/M6 test. The methods consist in adjusting the beat rates of M3s, M6s, P4s, P5s and m3s in even smooth progressions.

I do not use the M3/M6 test to tune my temperament because:

1.- The notes involved are not available until the last steps of my sequence. I tune: A4 A3 F3 F4 C#4 A#3 F#3 B3 G#3 C4 G3 D4 D#4 E4 the first available M3/M6 tests are F3D4/G3B3 and G#3F4/A#3D4 and D4 is tuned at step 12 of 14.

2.- If a M3/M6 test proves wrong, there may be from 1 to as much as 4 notes mistuned and it does not informs us which note or notes is/are in fault, nor if they are flat or sharp, nor by how much. We only know that the M3 doesn't beat at the same speed than the M6, but we have no clue on how to correct the error. In order to correct it we must do other tests to identify which notes in which direction and by how much are to be retuned.

For all the above this test is better suited to check but not for setting the temperament.



Hi Rafael,

I assume you tune the CM3's by creating an accurate C# first, then following with an accurate F4? That's what I do.

But then for A#, what do you have?
A# from F? C#3F3<C#3A#3 and C#3F4<C#3A#3? That leaves A#3 on the same side of both tests. I.e. A#3 can be too sharp and still confirm the tests.

The level of accuracy of tuning A#3, IMHO, is much lower than that of the CM3's. But then again it depends on a tuner's aural beat difference sensitivity. If it's poor, his CM3's won't be of much help.

But by using the 3/6 equality indirectly, where GB = FD, we can tune D so that FA<FD<AC# and D must be tuned so that FD is exactly between FA and AC#.

High accuracy, early on in the temperament, using the 3/6 equality, not the test.


Edited by Mark Cerisano, RPT (07/22/14 03:34 PM)
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www.howtotunepianos.com

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#2305474 - 07/22/14 03:41 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: UnrightTooner
Originally Posted By: Mark Cerisano, RPT
.....

I know it works in my sequence, but is there any theoretical proof that it is valid?


The M6/M3 equal beating test and its m3/M3 inversion work just because of happenstance. But there are "theoretical proofs" that show where this comes from.

Take the M6/M3 test with the intervals of F3-D4 and G3-B3. And also consider two other intervals: F3-A3, A3-D4. This gives us the following approximate beatrates (disregarding iH and stretch):

F3-A3 7bps
F3-D4 8bps
G3-B3 8bps
A3-D4 1bps

Hmmm, 8-7 = 1 and that is the M3-M6 test for a P4. In otherwords, the reason there is a 1bps difference between F3-A3 and F3-D4 is because A3-D4 is 1 bps.

And hmmm, the ratio of the two M3s, G3-B3 and F3-A3 is 8/7. This is because they are two semitones apart. Since beatrates double each octave, they follow the same pattern as theoretical frequencies. The ratio of frequencies (and beats) two semitones apart is the square of the twelfth-root-of-two, or about 8/7.

See, it is just a happenstance with theoretical 12-TET with 2:1 octaves. It would not happen with 11-TET nor with 2.5:1 octaves.


Maybe not, but these are wide intervals. Stretch would increase all their beat rates. Perhaps not identically, but my work is to create a method and sequence that beginners can use to get repeatable results, once they improve their beat speed difference sensitivity.

Continuation of these relationships with close to high accuracy across multiple iH, makes it very useful in determining the best sequence with windows.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2305497 - 07/22/14 04:09 PM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT

Again, the real elephant in the room is beat speed sensitivity. If you can't tell if F#3A#3 is between FA and GB, you won't be able to get good accuracy on ET, IMHO.

Does anyone else feel this way? What have you done, what is your approach to developing this sensitivity to the highest level possible. IMHO, this is the information beginning techs really need.

Please don't reply "Tune 1000 pianos". I think we should be beyond that with all the technology we have that can speed up learning.

It think it has two components:

1) developing beat speed sensitivity when the beats are clearly audible. Some training app with synthetic tones of even with metronome clicks would be a great learning tool for this I think.

2) actually being able to focus on listening to the correct beat on a real piano where there is interference from higher partials and other distractions. Developing training software for this would probably have to work with recorded samples of a real piano.

I think such training tools would be a vast improvement over the traditional "tune 1000 pianos" method.

Kees


Thanks Kees,

1. I hope to soon create an app that references actual interval recordings from a piano. Each interval is recorded multiple times, at different sizes.

You start with one set of check intervals and have to decide which way to change the note to be tuned. Based on that choice, the recorded interval set changes.

When satisfied, you move onto another note to tune, with a new set of recorded check intervals, which are based on the choice you made to tune the previous note.

In this way, there is really only one "path" to the correct end. It's like passing through multiple rooms, each room with multiple doors. Only one set of doors (tunings) leads to the correct room at the other end.

But, depending on which room you do end up in, you would get a score that would rate your beat speed difference sensitivity.

2. I have an idea for a unit that would focus in on the coincidental partial by filtering out the extra noise in a real piano using a band pass filter. This could help beginners train their ears faster.

The deluxe model listens to the interval and determines the coincidental partial based on the Fourier Transform calculation. If it returns the two lowest frequencies as less than an octave, that means we are listening to an interval, and not one string. Based on those frequencies, the unit creates a band pass filter around that coincidental partial.

Example. We play 400 and 505 Hz. A complex waveform is produced. The unit returns the lowest two frequencies that are contained in the waveform as 400 and 505. Some common ratios are stored in the algorithm and 5/4 is the closest, hence it is a M3. A bandpass filter is created around 2000Hz, perhaps something like -100bD and 100Hz wide.

Anybody know how doable that Is?

The regular model, which is more analog, could just have two knobs; a pass frequency, and a width. The tuner has to "tune" tyne unit.

The basic model could just have a high pass filter set at 880Hz. (Most coincidental partials are above that, and all the temperament fundamentals are below that.)

Anybody know enough about electronics and DSP to confirm or criticize if this could even be done? I've had the idea for about 8 years now.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2305512 - 07/22/14 04:28 PM Re: Theoretical tuning sequence [Re: UnrightTooner]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Originally Posted By: UnrightTooner
Originally Posted By: Mark Cerisano, RPT

Again, the real elephant in the room is beat speed sensitivity. If you can't tell if F#3A#3 is between FA and GB, you won't be able to get good accuracy on ET, IMHO.

Does anyone else feel this way? What have you done, what is your approach to developing this sensitivity to the highest level possible. IMHO, this is the information beginning techs really need.

Please don't reply "Tune 1000 pianos". I think we should be beyond that with all the technology we have that can speed up learning.


Let's say the goal is to have M3s and M6s progressive. That requires an accuracy of +/- 0.2 cents. When tuning aurally, it requires the discernment of the difference of a beat ratio of +/- 1/16 (difference between 16 bps and 17 bps or 8 bps and 8.5 bps). The scaling also has to make it possible to have both M3s and M6s progressive.

Considering that none of these tolerances will be zero, the stability needed is actually greater than 0.2 cents.

Given a particular piano and tuner any of these factors may be the weak link. Like does it really matter if the tuner can discern the difference between 8 bps and 8.5 bps if the pins are horribly jumpy?


Stability is the first and last skill a tuner will learn. As their beat speed difference sensitivity improves, they will demand better of their stability technique.

So, if a tuner can tell the difference between 8 and 8.5 bps, then it certainly will matter if the pins are jumpy.

Let's not forget that an attempt to achieve an accuracy of 0.2 cents will result in a better accuracy than if we didn't try to reach this goal.
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2305731 - 07/23/14 02:04 AM Re: Theoretical tuning sequence [Re: Mark Cerisano, RPT]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7904
Loc: France
thanks Mark, of course I know that and compare intervals, but I use more consonance than intervals comparation anyway as a primary but supplementary test.
On another (?) subject,
I wonder if beat masking can be used when tuning FBI, then you can obtain intervals with a certain amount of activity but no particularly striking beats.
More precisely, the activity make beat discriminating too difficult.

Best regards.


Edited by Olek (07/23/14 02:05 AM)
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#2306238 - 07/24/14 12:03 AM Re: Theoretical tuning sequence [Re: DoelKees]
Mark Cerisano, RPT Online   content
1000 Post Club Member

Registered: 01/24/10
Posts: 1494
Loc: Montreal, Quebec, Canada
Well, FGBD has a certain sound that GBDF doesn't (when GB = FD). Try it.

Also, I sometimes use "phasing" to determine if I have a pure 12th.

Play Ab2F3C5 all together.
Ab2F3 = Ab2C5 for a pure 12th.

Ab2F3 beats.
Ab2C5 beats.

If they are not equal, their beating will beat. Like this:
waa-Waa-WAA-Waa-waa-Waa-WAA-Waa-waa-Waa-WAA-Waa-waa
(Does that make sense?)

When you can only hear one clean beat from Ab2F3C5, that means Ab2F3 = Ab2C5.
(I got 98% on the RPT exam treble portion with that little trick, and my stretch curve followed the string diameters. Can an ETD do that? Does anybody care? Don't answer that last question.)

BTW, I know Verituner can do that.
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www.howtotunepianos.com

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