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#1664922 - 04/22/11 03:01 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1761
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
If the difference between "can either hear the F4-A4 beat easily" and "it is so fast that you can't hear it at all." is more than 1 cent, then I doubt if all the RBIs can be made to beat progressively.

Below some error analysis of the method.

Kees

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#1664964 - 04/22/11 04:15 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Jim Moy Offline
Full Member

Registered: 05/06/07
Posts: 292
Loc: Fort Collins - Loveland, CO
You can move your CM3 ladder down to a slower beating area where the beat rates are easier to compare, to establish bearings. Then those are helpful when tuning up into the F4-A4 range.
_________________________
Jim Moy, RPT
Moy Piano Service, LLC
Fort Collins and Loveland, Colorado
http://www.moypiano.com

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#1665024 - 04/22/11 05:41 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
smile Jim, you tune(d) C#3-F3-A3-C#4, if I remember correctly?
_________________________
Patrick Wingren, RPT

Senior Lecturer (jazz piano, composition, music theory, conducting) @ Novia University of Applied Sciences, Jakobstad, Finland
- - - -
Dedicated to learning the craft of tuning. Getting better.

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#1665088 - 04/22/11 07:21 PM Re: Tuning Circle of Fifths [Re: pppat]
Jim Moy Offline
Full Member

Registered: 05/06/07
Posts: 292
Loc: Fort Collins - Loveland, CO
Originally Posted By: pppat
smile Jim, you tune(d) C#3-F3-A3-C#4, if I remember correctly?

Yup. But recently I've been doing Eric Nikiforoff's 1-2-3, which switches immediately to complementary and opposing 4/5ths after the CM3 ladder. It seems to be more fun than how I was doing it before. I'm not sure why. Perhaps it's the symmetry of the sequence.

But back to the topic of this thread -- I'm not sure 1-2-3 is as good for the beginner, as it was touted in Eric's PTG Journal article, since you need a feel for 4/5ths. When you're just starting out, you mess with octaves and unisons, and then there's this chasm you have to leap to get to a temperament, which involves learning the sound and feel of all these intervals. When you're focused on M3rds and octaves, you can get a lot closer to ET, faster. Then work on refinement. Perhaps that's another contributor to the switch in emphasis by those doing the teaching. And of course the effect of ETDs.

On the other hand, perhaps that's why ET via Marpurg works, because you don't have to be as good at gauging the 4/5th beat rates, you go for equal beating. But I didn't come at it from that way, and once you "know," it's hard to go back and be in the frame of mind of "oh yeah, that would've been easier for me to learn."
_________________________
Jim Moy, RPT
Moy Piano Service, LLC
Fort Collins and Loveland, Colorado
http://www.moypiano.com

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#1665089 - 04/22/11 07:23 PM Re: Tuning Circle of Fifths [Re: Jim Moy]
Jim Moy Offline
Full Member

Registered: 05/06/07
Posts: 292
Loc: Fort Collins - Loveland, CO
Originally Posted By: Jim Moy
...recently I've been doing Eric Nikiforoff's 1-2-3, which switches immediately to complementary and opposing 4/5ths after the CM3 ladder.

Well, that is, when I'm not tuning EBVT, and I'm not using Tunelab to set temperament. I try to do a little bit of everything just to keep myself entertained smile
_________________________
Jim Moy, RPT
Moy Piano Service, LLC
Fort Collins and Loveland, Colorado
http://www.moypiano.com

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#1665286 - 04/23/11 08:03 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3293
Loc: Madison, WI USA
Originally Posted By: UnrightTooner
If the difference between "can either hear the F4-A4 beat easily" and "it is so fast that you can't hear it at all." is more than 1 cent, then I doubt if all the RBIs can be made to beat progressively.


If the CM3s beat progressively as they should, there cannot be more than about 1/2 cent error at the most. The difference between being able to hear F4-A4 easily and for it to be too fast to be discernible is about 1 cent. Get it to where you can just barely hear it and you have it right.

I suggest for anyone who has trouble hearing the F4-A4 M3 to do what I said for novices who are trying to hear the F3-A3 M3. Tune A4 to the fork, then move F4 sharp and flat until you can hear the beats. Surely, you will be able to hear the beats when that interval beats slowly.

Now, flatten F4 until the beats increase to the point where they are too fast to hear. Sharpen F4 again until you can just barely perceive the very rapid beat. F4 should then be about right. Tune F3 from F4 as the same type of octave you have tuned for A3-A4, then fill in C#4. The entire sequence should come out either correctly or within a range that you can make small adjustments for it to be exactly right.

Yes, you can tune the CM3s lower down first, such as from C3-E4, C#3-F4, D3-F#4, etc., but the only way to be sure that A4 ends up exactly at 440 is to start with A4 at A-440 and work from there. The F4-A4 interval needs to end up correctly at some point. If you start somewhere else and don't even check it, chances are that it will be incorrect.

Thanks to Kees and Jim M. for your posts.

Unfortunately, Jeff, we have been through all of this before. Gadzar provided some excellent analysis in the past as well. It seems that no matter what anyone says about this, you still come up with the "I doubt..." and "I still don't think..." remarks. Have you ever really followed the directions even one time yet? Or did you read the directions and then make up your own and find they did not work and then proclaim that the CM3s are inaccurate?

Braide-White wrote nothing of this but the CM3s have been taught by PTG now for thirty years.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1665384 - 04/23/11 12:26 PM Re: Tuning Circle of Fifths [Re: DoelKees]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner
If the difference between "can either hear the F4-A4 beat easily" and "it is so fast that you can't hear it at all." is more than 1 cent, then I doubt if all the RBIs can be made to beat progressively.

Below some error analysis of the method.

Kees


Excellent table! It shows clearly that one can easily detect a 1 cent error in any note of the CM3s by hearing at the progression of the beat rates in the CM3s set.

In every row of this table a significant jump is found in the beat rates of the CM3s that tells us exactly how to correct the tuning of which notes.

thumb
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1665463 - 04/23/11 04:16 PM Re: Tuning Circle of Fifths [Re: Gadzar]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
Hi!
I studied the chart of the ladder of M3's and one question came up. Since the thirds are sensitive to adjustment, and if you adjust the common tone of two contigous thirds you can find the exact spot for the notes very accurattely. My question is: If I tune F3-A3-C#4-F4-A4 correctly, what happens if i tune D4 pure to A4, and F#3 pure to C#4, what if i tune A#3 so that F#3-A#3 and A#3-D4 are equalbeating, would this be the right spot for A#3 ?

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#1665753 - 04/24/11 12:04 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
Lets see.

D4 pure to A4 = 440/1,5
F#3 pure to C#4 = 2^(-8/12)*440/1,5

Beatrate of F#3-A#3 is 4*A#3-5*F#3
Beatrate of A#3-D4 is 4*D4-5*A#3

The thirds beat equally, their beatrates are the same, so 4*A#3-5*F#3=4*D4-5*A#3

Which gets down to 9*A#3=4*D4+5*F#3
A#3=(4*D4+5*F#3)/9

Popping in D4 and F#3 from above gives us A#3=233,0306041
Real A##=233,0818808

Difference in cents=log(A#3/A#3real;2)*1200 which is -0,3809 cents.

A#3 would be 0.3909 cents flat, theoretically. I hope I didn't make a math error somewhere.


On tuning the contiguous thirds, assuming that A3 is spot on at 220hz, when F3-A3 beats at 6 bps I got that F3 is 1,8419 cents sharp. But then it's hard to get the others beat progressively. For example, when F3-A3 is 6bps, and you make A3-C#3 9 bps, C#4-F4 is 12,15 bps and F4A4 is 12 bps, but if you make A3C#3 10 bps, C#4-F4 is 10,9 bps and F4-A4 is 12 bps. In the first one, an upper third would be beating faster than a lower one, in the second the beatrates doesn't get progressively faster. I haven't tried it too much so I cant say how noticeable the flaw in the second beat rate progression would be, but I guess it would be.

Let's say you make F3-A3 6,5 bps, then A3-C#4 8,9 bps, which gives C#-4F4 of 11,475 bps and F4A-4 13 bps. Errors for F3 and F4 is 0,85 cents and for C#4 0,26 cents. Is it possible to notice the error in such a beat rate progression?

I put together a small excel file where you put in F3-A3 and A3-C#3 beatrates and it gives you the other beatrates and how many cents each note is off. It uses perfect octaves

http://www.speedyshare.com/files/28124849/Contiguous_thirds_beatrates_calc.xls

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#1665823 - 04/24/11 02:38 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
interesting, how would things change if i tuned D4 pure from A3 instead of A4? the A3-A4 octave is 4:2.
How would things change if F#3 is temporarly tuned pure from B3 if B3 is at its correct position.I'm looking for a way to find B3s correct position by tuning it between other interwalls that are equalbeating. I don't know how to calculate it myself... got any tips on links for theoretical calculations?

// martin

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#1666132 - 04/25/11 07:10 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Bill:

If you remember, you recently posted a question about how many cents a note can be off before a ladder of CM3s is no longer progressive. It is about 3 cents:

http://www.pianoworld.com/forum/ubbthreads.php/topics/1553498/ET%20via%20Marpurg%20Revisited.html

I am going to spend some time and find the place in Dr. White’s book where he considers how an octave can be divided by M3s (and maybe m3s?) and his reason for not using it to set a temperament.

But certainly it is fine to use ladders of CM3s if the major goal is to have progressive M3s. But if the goal is to have ALL RBIs progressive, a ladder of CM3s may not be sufficient. Perhaps it is for those that can really hear a 4:5 beat ratio. Not everyone can, especially when it is over 10bps. I certainly cannot.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666134 - 04/25/11 07:14 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
I didn't take into account inharmonicity, but in that case the A3 would come a little down, D4 also with A#3, I guess making it a little more flat than it is theoretically, but inharmonicity would complicate everything further, because it changes from note to note and we use different partials of the same notes, which are sharp by different amounts.

Anyway, I got that A#3 would be 1,34 cents sharp if you tune F#3 pure to a correct B3 and make the thirds equal beating.

You can get the A#3 pretty close using the method you suggested, if you then tune F#3-A#3 as a chromatic third after F3-A3, same with A#3-D4, and then start it over again for B3, you would probably get it pretty close.

Basically you are doing the up a third up a third down a fifth sequence, but instead of estimating a tempered fifth to get the first note of the first third, you do it pure, then do another fifth pure for the second note of the second third and move the note common to the two thirds so that they are equal beating. Not a bad idea I think and I guess you could use all the other tests used in the up M3, up M3, down P5 sequence as well and I don't think you will be any worse off.

For calculating the difference of two notes in cents:

http://en.wikipedia.org/wiki/Cent_%28music%29#Use

For calculating the theoretical frequency:

2^((+-semitones from A4)/12)*440

G4 is 2^(-2/12)*440

To calculate the beatrate, you have to know at which partials the frequencies are close and then calculate the difference of those partials. For a M3 it is the 5th partial of the lower note and the 4th of the higher, for P5 it's 3rd partial and 2nd, for p4 its 4th and 3rd, for m3 it's 6th and 5th.

For example:

Beatrate of A3-C4 m3 is 6*A3-5*C4, of A3-C#4 is 4*C#4-5*A3

For a pure interval, multiply or divide by the just intonation ratios, 3/2 for P5, 4/3 for P4, 5/4 for M3, 6/5 for m3.

A pure m3 down from A5 is A5/(6/5)


Edited by partistic (04/25/11 07:15 AM)

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#1666135 - 04/25/11 07:18 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Doel:

Thanks for posting the error analysis table. You did not say what you think it shows.

What I see is, generally, a one cent error will produce a 1 bps change in beat rate. Since chromatically progressive RBIs have a difference of about 1/2bps in the temperament, I see this as a problem. There can be difficulties later in the sequence in trying to get ALL the RBIs to beat progressively.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666145 - 04/25/11 08:11 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
All:

Here it is from page 72 of Dr. White’s book:

http://www.archive.org/stream/modernpianotunin00whit#page/72/mode/2up

”We have reached the central position in the science of tuning. What has gone before has been enough to show that one cannot obtain a series of pure diatonic scales, in the quantity required for the performance of music, with a key-board comprising only twelve keys to the octave. The particular method adopted in Chapter I for the purpose of showing the truth of this assertion might of course be matched by a dozen others; without altering the facts in the least. For example, I might have pointed out that an ascending series of perfectly tuned perfect Fifths, although nominally equal to seven Octaves, yet actually exceeds them. I might have shown that three major Thirds should be equal to an Octave, if tuned pure one above the other; but that in fact they fall considerable short thereof. There are many other possible illustrations; but I have already shown, in the simplest manner, that some form of compromise is needed if pianos are to be tuned so as to make the performance of music in all tonalities tolerable despite the defective and inadequate 12-to-the-octave key-board.” (Bold added for emphasis.)

And from page 85:

http://www.archive.org/stream/modernpianotunin00whit#page/84/mode/2up

Experience shows that it is easiest to tune by Octaves, Fifths and Fourths; by Fifths and Fourths for the octave of tones, usually F2-F3 chosen for the “bearings” or foundation work and by Octaves up and down thereafter. The other intervals involved are best used for testing the correctness of the work as it proceeds. (Bold added for emphasis.)

Since Dr. White knew an octave can be divided by M3s and “Experience shows that it is easiest to tune by Octaves, Fifths and Fourths” I think he knew about the possibility of starting with a ladder of CM3s and chose another method based on experience. Just because he did not write about a sequence does not mean he did not know of it. Even today there are those that know of tuning with CM3s and choose not to, for the same reasons.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666156 - 04/25/11 09:06 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3293
Loc: Madison, WI USA
Originally Posted By: UnrightTooner
Bill:

If you remember, you recently posted a question about how many cents a note can be off before a ladder of CM3s is no longer progressive. It is about 3 cents:



You must mean 0.3 cents.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1666160 - 04/25/11 09:15 AM Re: Tuning Circle of Fifths [Re: Bill Bremmer RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Originally Posted By: Bill Bremmer RPT
Originally Posted By: UnrightTooner
Bill:

If you remember, you recently posted a question about how many cents a note can be off before a ladder of CM3s is no longer progressive. It is about 3 cents:



You must mean 0.3 cents.


Here is the link, again. Look for yourself:

http://www.pianoworld.com/forum/ubbthreads.php/topics/1553498/ET%20via%20Marpurg%20Revisited.html
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666161 - 04/25/11 09:23 AM Re: Tuning Circle of Fifths [Re: Bill Bremmer RPT]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1085
Loc: Sicily - Italy

Hello.

Perhaps this article about 4ths and 5ths makes more sense in this thread:

By A.L.Silver (1955): "An unequal temperament is described in which the fifths and fourths of the tuning chain have the same beat rate."

http://gfax.ch/literature/Equal_Beating_Chromatic_Scale--Silver.pdf

Regards, a.c.
_________________________
alfredo

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#1666164 - 04/25/11 09:28 AM Re: Tuning Circle of Fifths [Re: partistic]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Originally Posted By: partistic
.....

A#3 would be 0.3909 cents flat, theoretically. I hope I didn't make a math error somewhere.

.....


Your math looks right to me, but you had a typo. It is 0.3809 cents flat like you also posted.

When it comes to looking at the relationship of beatrates, you can pretty much ignore iH. The beatrates, and especially the beatrate relationships in the temperament, are largely self-correcting. What iH giveth in one place, iH taketh away in another. Until you cross a jump in scaling... smile
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666203 - 04/25/11 10:51 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
UnrightTooner, but the nearly 3 cent error is when F3-A3 and A3-C#4 beat almost the same and then there is a jump of almost twice in beatrate with C#4-F4 and F4-A4 beating almost the same. I guess you could call it progressive, but I think such a mistake could be noticed easily. When I try various combinations in the excel file, I can't get an error of more than 1 cent of any note without making the beatrates rather uneven.

I cannot say how big of a mistake in the beatrates could be noticed. In the example I posted before, with beatrates of the contiguous M3s of 6,5 8,9 11,475 and 13, the biggest error is in the F's: 0,85 cents. I'm guessing it isn't that easy to notice a flaw in that progression and it might get accepted by the tuner.

Increasing F3 by 0,8 cents for example increases the F3-C4 P5 beat rate by about 0,24 bps. Double that an octave higher. Is it possible to lose 0,24-0,48 bps somewhere a little at a time and make up for it somewhere else when tuning a series of 12 fifths? That would mean an error of 0,8 cents. But on the other hand when tuning contiguous thirds and the F is already 0,85 cents off, you'd probably make other small errors tuning the other notes as well.

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#1666205 - 04/25/11 11:01 AM Re: Tuning Circle of Fifths [Re: Bill Bremmer RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Originally Posted By: Bill Bremmer RPT
.....

Unfortunately, Jeff, we have been through all of this before. Gadzar provided some excellent analysis in the past as well. It seems that no matter what anyone says about this, you still come up with the "I doubt..." and "I still don't think..." remarks. Have you ever really followed the directions even one time yet? Or did you read the directions and then make up your own and find they did not work and then proclaim that the CM3s are inaccurate?

.....


Yes we have been through all of this before. I have already told you what I have done. You act as if it is impossible for CM3s to be progressive and still have errors - even across a break. Of course what is an error to one tuner may not be to another…

But here is something I haven’t mentioned before. When I was first tuning, back in the 70’s, I noticed a check that became available when tuning C#4 using the classic sequence by Dr. White. I noticed that if F4 was also tuned, C#4 could be checked by listening to the M3 higher and lower. I thought I was really onto something. My excitement was short lived. I soon found out that yes, of course, any note must be placed so that the M3 below and above are progressive. This is the idea behind CM3s. But it does not help much when chromatic M3s AND M6s are the goal. Then I understood the power of 4th and 5th tuning. EVERTHING has to be right or errors will show up. And besides, anyone that is tuning aurally should be able to hear the difference between 7, 9 and 11 bps anyway. That’s about all CM3s do for you.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666248 - 04/25/11 11:58 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Originally Posted By: partistic
UnrightTooner, but the nearly 3 cent error is when F3-A3 and A3-C#4 beat almost the same and then there is a jump of almost twice in beatrate with C#4-F4 and F4-A4 beating almost the same. I guess you could call it progressive, but I think such a mistake could be noticed easily. When I try various combinations in the excel file, I can't get an error of more than 1 cent of any note without making the beatrates rather uneven.

I cannot say how big of a mistake in the beatrates could be noticed. In the example I posted before, with beatrates of the contiguous M3s of 6,5 8,9 11,475 and 13, the biggest error is in the F's: 0,85 cents. I'm guessing it isn't that easy to notice a flaw in that progression and it might get accepted by the tuner.

Increasing F3 by 0,8 cents for example increases the F3-C4 P5 beat rate by about 0,24 bps. Double that an octave higher. Is it possible to lose 0,24-0,48 bps somewhere a little at a time and make up for it somewhere else when tuning a series of 12 fifths? That would mean an error of 0,8 cents. But on the other hand when tuning contiguous thirds and the F is already 0,85 cents off, you'd probably make other small errors tuning the other notes as well.


Yes, I agree that a beatrate sequence that has two beatrates nearly the same would not sound progressive. 3 cents is a maximum number. But look at Doel’s table (Thanks again, Doel!) Every scenario shows progressive beatrates. But what would sound evenly progressive is another story. And looking at a table is different than actually listening to beatrates. Some claim to be able to hear the difference between a 4:5 and a 5:6 beatrate ratio. I cannot.

I am not sure where you meant to go with your last paragraph. You certainly can fudge any tuning sequence to get things to work fairly well if there is a bit of an error here and there. And if the piano has an unfriendly pinblock you pretty much have to. So, how much is too much of an error to “sweep under the rug?” I’ll just quote what I said before that was not taken favorably:

Originally Posted By: UnrightTooner
If the difference between "can either hear the F4-A4 beat easily" and "it is so fast that you can't hear it at all." is more than 1 cent, then I doubt if all the RBIs can be made to beat progressively.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1666262 - 04/25/11 12:19 PM Re: Tuning Circle of Fifths [Re: alfredo capurso]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: alfredo capurso

Hello.

Perhaps this article about 4ths and 5ths makes more sense in this thread:

By A.L.Silver (1955): "An unequal temperament is described in which the fifths and fourths of the tuning chain have the same beat rate."

http://gfax.ch/literature/Equal_Beating_Chromatic_Scale--Silver.pdf

Regards, a.c.




Very interesting!

Have you tried this tuning? How does it sound?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1666317 - 04/25/11 01:34 PM Re: Tuning Circle of Fifths [Re: partistic]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: partistic
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I cannot say how big of a mistake in the beatrates could be noticed.
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.
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It is easy to measure if you have an ETD.

Just tune by ear the set of CM3s, and then check with the ETD the error made.

With some practice you will notice that you can tune F3 with an accuraty of +/- 0.3 cents.

And this is almost the greatest accuraty a good aural tuner can achieve.

If you try the same experiment for tuning a fifth using usual tests, i.e.: m3-M3, M6-M10, you will find a lesser accurate result.

That is why top tuners like Jim Coleman, George Defebaugh, Rick Baldassin, and many others, who learned to tune with the "Classical 5th/4th method" switched to the RBIs based sequences.

Take also for example Virgil Smith, who used a sequence based on M3s and m3s, to establish the correct tempering of the 4ths in his temperament.

The question here is why do all these top tuners tune RBIs to find out the correct tempering of SBIs? (Opposed to what Braid White's method does: tuning SBIs using RBIs as checks).

I believe this is because an octave is hardly divided into 12 equally tempered 5ths, compared to the easier job of dividing it into 3 equally tempered M3s.

I can not understand how a tuner would be able to tune a 5th with the m3-M3 test, which involves comparing a m3 to its contiguous M3, which have beat rates in the ratio of nearly 8:7, while this same tuner is not able to tune two contiguous M3s in a ratio of approximately 5:4.(see the edit note)


It is not a matter of accuraty in the ratio. It is a matter of eveness in the progression of the CM3s. That's why the set of CM3s tuning is more accurate than the tuning of a single 5th using contiguous m3-M3, in the later you are estimating a single ratio. In the CM3s you are striving for an even progression, which gives you more accuraty.


Edit: I guess the difference in tuning a m3-M3 compared to the M3-M3 is the fact that you can hear at the 5th and you can not hear at the augmented 5th. But that means that you are not really tuning a 8:7 ratio between the m3 and the M3, but rather tuning a 5th directly by its colour or tempering and using the check only to ensure that the 5th is narrow and not wide, that is the m3 beats indeed faster than the M3.



Edited by Gadzar (04/25/11 01:48 PM)
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Rafael Melo
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#1666338 - 04/25/11 02:17 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1085
Loc: Sicily - Italy

Yes Gadzar, I find Silver's model interesting too, especially when I think it was elaborated in 1955. I've not heard it on a piano but the author says it is easyer to tune than ET. And I believe him, since he could only refer to our first ET model, and he must have gone through what many of us have experienced.

But perhaps, even today, for many tuners it would be more confortable a regular approximation than a messy ET attempt (as the author suggests) and perhaps that simple beat-rule is also time-saving. It would be nice to know what the first EBS 12th (D3-A4) sounds like.

Regards, a.c.
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alfredo

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#1666342 - 04/25/11 02:29 PM Re: Tuning Circle of Fifths [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4954
Loc: Bradford County, PA
Originally Posted By: Gadzar
.....

The question here is why do all these top tuners tune RBIs to find out the correct tempering of SBIs? (Opposed to what Braid White's method does: tuning SBIs using RBIs as checks).

.....


It could be because they tune well scaled pianos. If I tuned well scaled pianos I would probably use ET via Marpurg.

Originally Posted By: Gadzar
.....

I can not understand how a tuner would be able to tune a 5th with the m3-M3 test, which involves comparing a m3 to its contiguous M3, which have beat rates in the ratio of nearly 8:7, while this same tuner is not able to tune two contiguous M3s in a ratio of approximately 5:4.(see the edit note)

.....


The primary reason that I do not use CM3s is because they give me poorer result than 4ths and 5ths. Do you have a problem with people preferring what you do not?


Originally Posted By: Gadzar
.....


It is not a matter of accuraty in the ratio. It is a matter of eveness in the progression of the CM3s. That's why the set of CM3s tuning is more accurate than the tuning of a single 5th using contiguous m3-M3, in the later you are estimating a single ratio. In the CM3s you are striving for an even progression, which gives you more accuraty.

Edit: I guess the difference in tuning a m3-M3 compared to the M3-M3 is the fact that you can hear at the 5th and you can not hear at the augmented 5th. But that means that you are not really tuning a 8:7 ratio between the m3 and the M3, but rather tuning a 5th directly by its colour or tempering and using the check only to ensure that the 5th is narrow and not wide, that is the m3 beats indeed faster than the M3.

.....


Why use a single or even three or four intervals to obtain high accuracy? Until the 9th note is tuned, you cannot be sure any intervals are really correct.
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Part-Time Tuner
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#1666347 - 04/25/11 02:37 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Gadzar Offline
1000 Post Club Member

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

What would be the effect of the beat rate of 5ths doubling every octave?

This will have a "stairs" shaped beat rate curve.

Is it really easy to tune equal beating 5ths? We have so long heared equal tempered 5ths, that EB can sound "bizarre" and "wrong" to our modern ears.



Edited by Gadzar (04/25/11 03:12 PM)
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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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#1666366 - 04/25/11 03:20 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Gadzar Offline
1000 Post Club Member

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

Thank you, but I am not interested in talking with you as you strive to "control" people by making them getting upset.

For all who may be interested in what I am talking about, here is the thread:

How to "control" people on the internet

Or this other one:

How to "get fun" at the expense of others

Bye.



Edited by Gadzar (04/25/11 04:13 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1666393 - 04/25/11 04:14 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1761
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Yes, I agree that a beatrate sequence that has two beatrates nearly the same would not sound progressive. 3 cents is a maximum number. But look at Doel’s table (Thanks again, Doel!) Every scenario shows progressive beatrates. But what would sound evenly progressive is another story. And looking at a table is different than actually listening to beatrates. Some claim to be able to hear the difference between a 4:5 and a 5:6 beatrate ratio. I cannot.

Here's the original table as powerpoint, which includes a column with idealized audio. http://www.cs.ubc.ca/~kvdoel/tmp/cm3ppt.zip

Kees

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#1666580 - 04/25/11 10:44 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
Gadzar Offline
1000 Post Club Member

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

Excellent demonstration!

Of course there are not piano sounds but the uneveness in the progressions can clearly be heard!

(I can not get the presentation to work, but I heard directly the .wav files)



Edited by Gadzar (04/25/11 11:44 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1666624 - 04/26/11 12:34 AM Re: Tuning Circle of Fifths [Re: Gadzar]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1761
Loc: Vancouver, Canada
Originally Posted By: Gadzar

It is easy to measure if you have an ETD.

Just tune by ear the set of CM3s, and then check with the ETD the error made.

With some practice you will notice that you can tune F3 with an accuraty of +/- 0.3 cents.


I practiced for about 3 weeks a while ago when I thought I might take the RPT exam soon. My errors went down from 2 cents to at most 1 cent on one note. It's encouraging to hear that when I would have kept going I could get it that accurate. (Assuming you don't have a special secret diet that allows you to achieve this.) smile

Do you even run into bad piano's where you just can't hear the higher M3's?

Kees

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