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#1674868 - 05/10/11 07:31 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: mstore
…..

This was the first time i tried this sequense by comparing the interwalls against each other. The " fourths about 1 bps wide and fifths about 0,5 cents narrow" didn´t work for me. I noticed how much more accurattely i could tune when i have to compare different intervalls against each other. especially if the note beeing tuned is a common note. for instance C4-F3 to G3-C4 If they are equal beating C4 is too low. (this didn´t happen in this sequence).

One thing i did notice was that i didn´t get very much stretch with this method. how could i add a little bit stretch?

I don't know if i was just lucky today, but it seemed pretty easy. as i wrote earlier i have made over 50 attempts to tuned by fourths and fifths but now when i found out about the beating ratios beteween the different intervalls it got a lot easier.

As a jazzpiano player i find it relatively easy to play 3 beats over 2 or 4 over 3. i use that kind of polyrythmic ideas in my playing.

Feel free to critisize...



Martin:

Congratulations on reaching your goal of setting a temperament with 4ths and 5ths! Getting SBIs to be progressive is an accomplishment beyond simply tuning the temperament with SBIs. You must be doing better with your hammer technique. thumb

You may not understand just what I mean by “about ½ bps” for the 5ths. I would say that all your fifths beat about ½ bps. And while we are on the subject, you mentioned that you did not get much stretch. If the temperament octave was 4:2 that really is satisfactory. If it was not, well, try making the 5ths beat a hair slower, like closer to ½ bps wink If the SBIs are tuned to theoretical beatrates, the octave will be narrow due to iH. The 4ths will be OK, but the fifths will be a bit too narrow.

You may think that going from 2/3 bps to ½ bps (about ½ cent) would cause a total stretch of 6 cents in an octave when going around the circle of fifths, but it does not anymore than a pure fifths tuning results in an octave that is 24 cents wide. ½ cent in a fifth is divided by 7 semitones which results in less than 1 cent for an entire octave.

Since listening to the beatrate ratios is working for you, consider trying slightly different beatrate ratios. Instead of the 3:2 and 4:3 ratios when comparing the 4ths and 5ths, try 2:1 and 3:2. This will probably only be necessary until you learn to hear the tempering of the SBIs directly instead of counting beats.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1674873 - 05/10/11 07:43 AM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: Bill Bremmer RPT
Originally Posted By: DoelKees
I tried a hybrid method today which worked out great for me. I tune F3 to A3 at 7 bps, making sure of the beatrate with a metronome.

Kees


In my opinion, this is the biggest mistake anyone can make. It is the reason why the rest f the temperament often does not work out, especially on short or irregularly scaled pianos.

I often read that with these, 4ths & 5ths sound good but the RBI's are irregular or not progressive (or digressive) across breaks, etc.

When I tutor someone, I tell them not to try to "count" or time beats with any measuring device whatsoever. The actual rate of the F3-A3 M3 depends on the inharmonicity and the size octave chosen. The contiguous thirds approach with two pairs of octaves will find that rate. If you find the F4-A4 M3 impossible to discern, the reason may well be that it is far too fast. If the F4-A4 M3 is too fast, then the F3-A3 M3 is too fast.

In theory you are right of course, but according to my calculations even on short pianos the error remains well under 1 cent and on nice grands it's more something like 0.2 cent.

Kees


Kees:

I agree that theoretical beatrates are very useable on well scaled pianos. The combined effects of iH are largely self-correcting. And the idea that the octave size makes much of a difference just doesn’t cut the mustard in my book. If you are changing the octave width enough to make a difference, then you are beyond the point of octave sounding even close to pure. An M3 would have to be changed about 1 cent before it beat the same as the next chromatic M3. Over the course of a set of CM3s, this would be about 3 cents in an octave, almost enough for a pure fifth tuning!

But when the scaling is not good, well I won’t repeat my litany again right now.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1674877 - 05/10/11 07:50 AM Re: Tuning Circle of Fifths [Re: partistic]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: partistic
Originally Posted By: UnrightTooner

Very small differences in tempering can be heard; smaller than the pin can be set.


This is another point I was making in another thread some time ago, the tuning pin system we have today doesn't have enough accuracy, because as you say, the speaking portion's tension changes, we can hear the difference in frequency and tempering, but the pin cannot be set that accurately.

You say that when a break in scaling occurs, the thirds will cause the fifths to be mushed around to fit. But the fifths and fourths are supposed to be mushed a little from ½ and 1 bps, they aren't supposed to beat exactly at that rates, plus the mushing effect of human error, you said humans can't tune consistently within 0,1 bps. Instead of doing the fourths and fifths in a row using one tuned note for another and then finding that F3-A3 beats faster than F#3-A#3, if you would make the thirds correct and let the fifths fall where they will, would you say the fifths and fourths are tempered wrong when let's say 1 cent is divided between four fourths and fifths, keeping in mind that they aren't all supposed to beat ½ or 1 bps? And if the end result is all intervals apparently sounding correct, isn't that the purpose?


” You say that when a break in scaling occurs, the thirds will cause the fifths to be mushed around to fit.”

Yes, if you use RBIs to set the temperament. That is why I use SBIs.

You really should use the Forum’s quote feature so what is said is kept in context.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1675111 - 05/10/11 02:11 PM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: DoelKees
.....

Do bother, it sounds very interesting.

I have played ney on top of Haleakalā mountain and got the almost extinct native ney-ney bird to reply to me.

Kees


I herded Alaskan Brown Bear with a NOAA Hydrographic Survey Launch:

_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1675324 - 05/10/11 10:07 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1736
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner

Kees:

I agree that theoretical beatrates are very useable on well scaled pianos. The combined effects of iH are largely self-correcting. And the idea that the octave size makes much of a difference just doesn’t cut the mustard in my book. If you are changing the octave width enough to make a difference, then you are beyond the point of octave sounding even close to pure. An M3 would have to be changed about 1 cent before it beat the same as the next chromatic M3. Over the course of a set of CM3s, this would be about 3 cents in an octave, almost enough for a pure fifth tuning!

According to my calculation on a poorly scaled piano the difference in F3A3 beatrate between 4:2 and 6:3 octaves is something like 0.1 bps. On a well scaled piano much less.

Quote:
But when the scaling is not good, well I won’t repeat my litany again right now.

Again according to my calculations on a small piano the beatrate of F3A3, when based on a 4:2/6:3 compromise octave gets as low as 6.7 bps. That is only 0.2 bps less than the ideal number (6.9) and corresponds to an error of 0.4 cent. Surely on crummy pianos you can live with that. On well scaled concert grands the error is less than 0.1 cents if you go for 6.9 bps with a metronome.

Of course I could have made an error in my calculations. It would be nice to know what is the bps of F3A3 on spinets in your practical experience, if you know?

Kees

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#1675339 - 05/10/11 10:46 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
SM Boone Offline
Full Member

Registered: 09/04/10
Posts: 303
Loc: VA USA
too bad there's no "like" button on here, I like the boat c/o Jeff.

Personally I just balance it out, hear it, go with it, ... every piano is different and to get the most pleasing and aesthetically perfect sound from it requires personal presence and attention.
SM

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#1675353 - 05/10/11 11:15 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1736
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
.....

Do bother, it sounds very interesting.

I have played ney on top of Haleakalā mountain and got the almost extinct native ney-ney bird to reply to me.

Kees


I herded Alaskan Brown Bear with a NOAA Hydrographic Survey Launch:


Maybe slightly off topic, but I though brown bears were land animals.

Kees

Top
#1675477 - 05/11/11 07:39 AM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: DoelKees
.....

Maybe slightly off topic, but I though brown bears were land animals.

Kees


I have seen them swimming across Shelikof Straight, like 30 miles.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1675486 - 05/11/11 07:55 AM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: DoelKees
Originally Posted By: UnrightTooner

Kees:

I agree that theoretical beatrates are very useable on well scaled pianos. The combined effects of iH are largely self-correcting. And the idea that the octave size makes much of a difference just doesn’t cut the mustard in my book. If you are changing the octave width enough to make a difference, then you are beyond the point of octave sounding even close to pure. An M3 would have to be changed about 1 cent before it beat the same as the next chromatic M3. Over the course of a set of CM3s, this would be about 3 cents in an octave, almost enough for a pure fifth tuning!

According to my calculation on a poorly scaled piano the difference in F3A3 beatrate between 4:2 and 6:3 octaves is something like 0.1 bps. On a well scaled piano much less.

Quote:
But when the scaling is not good, well I won’t repeat my litany again right now.

Again according to my calculations on a small piano the beatrate of F3A3, when based on a 4:2/6:3 compromise octave gets as low as 6.7 bps. That is only 0.2 bps less than the ideal number (6.9) and corresponds to an error of 0.4 cent. Surely on crummy pianos you can live with that. On well scaled concert grands the error is less than 0.1 cents if you go for 6.9 bps with a metronome.

Of course I could have made an error in my calculations. It would be nice to know what is the bps of F3A3 on spinets in your practical experience, if you know?

Kees


One of the biggest jumps in scaling I have come across was the Wurlitzer Petite Grand. I have to make F3-A3 and A3-C#4 beat at the same speed for the SBIs to sound best. On a Kimball Spinet (not a Whitney, different scaling...) F3-A3 beats the same as G3-B3. But I often wonder just what I am hearing in the 5ths. There is often much trash. And there would be a big difference between the 3:2 and 6:4 partial matches. It could very well be that I am tuning for the least obnoxious sound. I may not actually be tuning "about 1/2 bps" for the fifths.

Here is a scaling graph of a Wurlitzer Petite Grand. It isn't the same scaling as the one I encountered. That one had bichords up to G3 or so. But notice what happens around the break:

_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

Top
#1675599 - 05/11/11 11:42 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1736
Loc: Vancouver, Canada
Jeff:

Yes if the break occurs in the temperament octave all bets are off. If not, I claim F3A3 stays pretty darn close to 6.9 on any instrument.

Why would you not move the temperament octave up to be above the break on that Wurlitzer Petite Grand?

Naively I would assume that the highest M3 that crosses the break will beat slower than you would expect compared to its upper neighbor, as the lowest note of this M3 will have a higher IH constant than expected, so the 5th partial will be closer to the 4th partial of the upper note. Does this conform to reality?

Kees

Top
#1675606 - 05/11/11 12:21 PM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4943
Loc: Bradford County, PA
Originally Posted By: DoelKees
Jeff:

Yes if the break occurs in the temperament octave all bets are off. If not, I claim F3A3 stays pretty darn close to 6.9 on any instrument.

.....


I agree, but there are always exceptions.

Originally Posted By: DoelKees
…..

Why would you not move the temperament octave up to be above the break on that Wurlitzer Petite Grand?

.....


Then the RBIs beat too fast for me to be sure that they are progressive. As a compromise, I have modified Dr. White’s sequence so that the first RBI is A#3-G4, about 10.5bps. Then when E4 is tuned, I have an inside/outside check (A#3-G4, C4-E4) to make sure things are on track before there is an RBI progression that transits a break, such as F3-A3, G3-B3.

Originally Posted By: DoelKees
…..

Naively I would assume that the highest M3 that crosses the break will beat slower than you would expect compared to its upper neighbor, as the lowest note of this M3 will have a higher IH constant than expected, so the 5th partial will be closer to the 4th partial of the upper note. Does this conform to reality?

Kees



Ugh! In my haste this morning (more bears to brand…) I chose a poor example for a challenging scale. It is definitely different than the Wurly I tuned. This one shows a more typical example where the M3s straddling a break causes them to beat faster than those above the break. Tuning the SBIs and then listening to the resulting RBIs will tell the story.

Steinway S:


_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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