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#1668566 - 04/29/11 01:29 PM Re: Tuning Circle of Fifths [Re: partistic]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: partistic
Here's how I calculated it:

A4=440hz
D4=(2*440+0,5)/3=293,5
D4-A4 beatrate=3*293,5-2*440=0,5
G3=(2*293,5+0,5)/3=195,833..
G3-D4 beatrate=3*195,833..-2*293,5=0,5
C4=(4*195,833..+1)/3=261,44..
G3-C4 beatrate=3*261,44..-4*195,833..=1
F3=(2*261,44..+0,5)/3=174,462963
F3-C4 beatrate=3*174,462963-2*261,44..=0,5

F3 should be 440*2^(-16/12)

Difference in cents = log(174,462963/(440*2^(-16/12)))to base 2 * 1200=-1,499 cents


We are talking about the F3-A3 M3. You started on A4.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1668572 - 04/29/11 01:36 PM Re: Tuning Circle of Fifths [Re: Thomas Dowell]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: Thomas Dowell
Originally Posted By: UnrightTooner
But how would YOU set three notes with an absolute error of 1 cent across a jump in iH, and know that the 4ths and 5ths will be properly tempered?


Remember, there are different perspectives on which intervals to compromise, the RBI's or SBI's. It seems that you feel that the SBI's are what make a piano sound "in-tune", while others will say that it is the RBI's. I remember an article that Owen Jorgensen published shortly before he died, in which he recommended tuning progressive minor thirds below the break, and leaving the atrocious sounding octave, as he felt musicians were more sensitive to changes in the RBI of the m3 than the quality of the octaves, fourths and fifths.

The idea behind CM3's is the have evenly tempered RBI's, not SBI's.


Yes, I do believe it is better to have good sounding SBIs. It matters most when there is a jump in scaling. But I think it matters on well scaled pianos, too. You can have pretty darn progressive RBIs and still have so-so SBIs. But when SBIs are tuned, with the parameter also being progressive RBIs (on well scaled pianos) then you have the best of both worlds.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1668859 - 04/30/11 02:45 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
Jeff: Remember the old discussion we had on how ET can actually be defined precisely/mathematically given a realistic but smooth IH curve? I thought I had that figured out: it's the tuning where all intervals change as smoothly as possible in size (in cents).

The assumption however was a smooth IH curve. Now how can we define ET when there is a discontinuity in the IH curve? I haven't come up with an answer yet but am thinking of how to tune a hypothetical piano which has 12000 keys per octave equally, across the break, for a superior being that can hear intervals of 0.1 cents. Once we figure that out we can keep 1/1000 of the keys an have a good ET across the break.

Looking forward to hearing your approach which will undoubtedly be quite different.

Kees

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#1669006 - 04/30/11 01:20 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
You are right, if I start at A3 the F3 will be 0,5 cents flat. But if I add in human error in the right direction, 0,1 bps per interval, I can make the F3 an additional cent flat. If you made the F3-A3 interval sound correct and divided the difference evenly to the fifhts and fourths, maybe that is the right way they should sound? After all, they aren't all supposed to be half or 1 bps, the error is small but it adds up.

If you were to divide the error in the F3-A3 to the fifths and fourths, would you notice an error in them? And if there is no noticeable error, ie all the intervals sound correct, isn't it the better way to set the temperament?

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#1669868 - 05/02/11 07:12 AM Re: Tuning Circle of Fifths [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: DoelKees
Jeff: Remember the old discussion we had on how ET can actually be defined precisely/mathematically given a realistic but smooth IH curve? I thought I had that figured out: it's the tuning where all intervals change as smoothly as possible in size (in cents).

The assumption however was a smooth IH curve. Now how can we define ET when there is a discontinuity in the IH curve? I haven't come up with an answer yet but am thinking of how to tune a hypothetical piano which has 12000 keys per octave equally, across the break, for a superior being that can hear intervals of 0.1 cents. Once we figure that out we can keep 1/1000 of the keys an have a good ET across the break.

Looking forward to hearing your approach which will undoubtedly be quite different.

Kees


I will give you a direction I have thought about, and maybe you can make it work. smile

Rather than a smooth curve at the first partial, as we were playing with before, what about a smooth curve at the 3rd or the 4th or the 3-1/3rd or the root mean square or weighted average or something. But perhaps there would be a more direct approach by concentrating on the beatrates of the SBIs. Some algorithm should certainly be possible. And while I am typing this I remembered the simplest way of all: pure 12ths. But Mr. Stopper has already done that. - sigh - Still, a 12th beatrate curve is another option.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1669886 - 05/02/11 08:16 AM Re: Tuning Circle of Fifths [Re: partistic]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: partistic
You are right, if I start at A3 the F3 will be 0,5 cents flat. But if I add in human error in the right direction, 0,1 bps per interval, I can make the F3 an additional cent flat. If you made the F3-A3 interval sound correct and divided the difference evenly to the fifhts and fourths, maybe that is the right way they should sound? After all, they aren't all supposed to be half or 1 bps, the error is small but it adds up.

If you were to divide the error in the F3-A3 to the fifths and fourths, would you notice an error in them? And if there is no noticeable error, ie all the intervals sound correct, isn't it the better way to set the temperament?


The best way to set a temperament is the way that works best for the particular tuner on a particular piano smile

Because of iH, the error will be less than 0.5 with the ½ and 1 bps SBIs. 5ths do beat a little slower than theoretical. But you are mistaken to look at tuning with 4ths and 5ths as a textbook thing. It is an experience thing. Very small differences in tempering can be heard; smaller than the pin can be set. (I think tuning 4ths and 5ths directly as much as possible, such as when expanding the temperament, will assist in learning to set the pin.) What often ends up happening is leaving the pin in a stable condition as close to where the SBI is correctly tempered as possible. Then if down the road an RBI relationship can be improved, the SBIs are listened to and the ones that are a little out of line with the others are adjusted.

I had thought as it seems you do. I had thought, as others have posted, “Who knows how the SBIs should sound for any given piano? And how could they be tuned that accurately? All that can be done is to take your best guess and fix the problems as the crop up.” What this leads to is poor tuning of the individual SBIs, just roughing it in, not even setting the pins very well because it will probably have to be changed later, and then trying to tune to notes that aren’t even staying where they were put! And then when a break in scaling is encountered, trying to get the RBIs to beat theoretically or at least progressive. To do this the SBIs are mushed around and somehow the circle is sloppily closed in frustration.

I remember something the old timers said when I was first tuning. They said the theoretical beatrates are only approximate. They can be different, sometimes very different, especially in spinets. I wanted to ask which ones would be faster and which ones would be slower and how would you know how much? I never did ask, partly because I did not want to seem ignorant, and partly because I didn’t think they really knew, otherwise they would have said how.

Now I know how. Tune properly tempered SBIs. Make minor adjustments for RBIs relationships except where scaling problem show themselves, then let the chips fall where they will. As long as each 5th beats about ½ bps and each 4th beats about 1 bps the resulting beatspeed of the RBIs will be acceptable.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1670297 - 05/02/11 09:29 PM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
Jeff: Remember the old discussion we had on how ET can actually be defined precisely/mathematically given a realistic but smooth IH curve? I thought I had that figured out: it's the tuning where all intervals change as smoothly as possible in size (in cents).

The assumption however was a smooth IH curve. Now how can we define ET when there is a discontinuity in the IH curve? I haven't come up with an answer yet but am thinking of how to tune a hypothetical piano which has 12000 keys per octave equally, across the break, for a superior being that can hear intervals of 0.1 cents. Once we figure that out we can keep 1/1000 of the keys an have a good ET across the break.

Looking forward to hearing your approach which will undoubtedly be quite different.

Kees


I will give you a direction I have thought about, and maybe you can make it work. smile

Rather than a smooth curve at the first partial, as we were playing with before, what about a smooth curve at the 3rd or the 4th or the 3-1/3rd or the root mean square or weighted average or something. But perhaps there would be a more direct approach by concentrating on the beatrates of the SBIs. Some algorithm should certainly be possible. And while I am typing this I remembered the simplest way of all: pure 12ths. But Mr. Stopper has already done that. - sigh - Still, a 12th beatrate curve is another option.


Jeff, you are too predictable: I predicted you'd come up with something unpredictable. smile Indeed there will be a jump in at least all but one of the partials (including 1) at the break, so this will have to be weighted in some way. Interesting to think about.

How do you tune the notes around the break? Do you tune "normally" above the break, then tune the notes below the break, or do you also adjust notes above the break to help the transition to be smooth?

I think pure 12ths is not the answer as we want something that reduces to standard ET when inharmonicity goes to zero.

Kees

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#1670458 - 05/03/11 07:30 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Doel:

I tune properly tempered SBIs<Period> These produce progressive RBIs above, below and while straddling the break, but not when going from one to another. To do this, very minor corrections are sometimes made to the SBIs, but no major ones like would be needed to make RBIs progressive when transiting (good word for it I think) a break. What happens is an RBI won't be in progression, so then I listen to the SBIs. Sure enough I find one or two that really aren't quite tempered right. I slap my hand and say Bad Tuner! You are sloughing off by tuning improperly tempered SBIs. You can do better than that! And when I do really good, there are no corrections.

I was more interested in tuning calculations in order to understand how it can be done rather than to actually do it. And when I wrote my program I also wanted to have any automatic tuning calculations result in theoretical ET with no iH. What I came up with was pretty poor, automatic-tuning-wise, but answered most of the questions I had.

But consider what it means to have a tuning scheme that produces zero stretch with zero iH, but max stretch with high iH. That really is not what is desired. It is best to get as much stretch as appropriate in low iH pianos so that the high treble does not sound flat. 12ths are a great tool for this. Not that they need be pure, but working with just the 1st and 3rd partials should simplify things and create wider octave types on lower iH pianos.

Would it be difficult for you to use your tuning calculation tools to see just what happens to the RBI and SBI beatrates when 12ths, pure or otherwise, are tuned across a jump in scaling? I could never quite trust my program's results on this. I used the original Young's equation for partial frequencies and I also have reason to suspect that the partial frequencies that I was kindly given were "cooked" by Verituner.

Do I sense a new Topic coming up? smile smile smile
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1671921 - 05/05/11 10:07 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
Ron Voy Offline
Full Member

Registered: 02/16/11
Posts: 37
Thanks to all contributors of this thread. There's so much interesting theory and guidance to read, sometimes I have to remind myself it's more important to practice tuning than to spend time reading about it!

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#1671926 - 05/05/11 10:12 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
Les Koltvedt Offline
3000 Post Club Member

Registered: 04/13/05
Posts: 3195
Loc: Canton, MI
Originally Posted By: Ron Voy
Thanks to all contributors of this thread. There's so much interesting theory and guidance to read, sometimes I have to remind myself it's more important to practice tuning than to spend time reading about it!


I hear ya
_________________________
Les Koltvedt
LK Piano
Servicing the S. Eastern Michigan Area
PTG Associate

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#1672039 - 05/05/11 01:52 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: Ron Voy
Thanks to all contributors of this thread. There's so much interesting theory and guidance to read, sometimes I have to remind myself it's more important to practice tuning than to spend time reading about it!


Yep, but remember to always practice stability. Nothing else works well without that.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1672395 - 05/06/11 07:12 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
Ron Voy Offline
Full Member

Registered: 02/16/11
Posts: 37
Originally Posted By: UnrightTooner
Originally Posted By: Ron Voy
Thanks to all contributors of this thread. There's so much interesting theory and guidance to read, sometimes I have to remind myself it's more important to practice tuning than to spend time reading about it!


Yep, but remember to always practice stability. Nothing else works well without that.


You mean stability, as in setting the pins? Absolutely the hardest skill to master.

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#1672419 - 05/06/11 08:07 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Yep!
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1672559 - 05/06/11 01:50 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
So, you guys that did learn to tune with fourths and fifhts, how did you practise and how long did it take until you could set a working temperament?

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#1672567 - 05/06/11 02:13 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
I took lessons from a blind floor tuner. He had me read parts of Dr. White's book. At the second or third lesson he demonstrated how the temperament was set. Then I set a working temperament on the first try. Getting a good temperament took a couple more tries during practice. At the fifth lesson he said that there was nothing more he could teach me.

BUT, that did not prepare me for when I tried to tune a temperament across a break, like is common with spinets. I thought at the time that I wasn’t tempering the 4ths and 5ths correctly. It was a real blow to my self-confidence. I thought the warning about beatrates on spinets meant that the RBIs would beat slower or faster, but still be progressive. It was some things that I read on this great Forum that clued me into what really happens. smile
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1672639 - 05/06/11 04:26 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
I can´t believe that you did that so fast, I think i tried tuning by fourths and fifths maybe 50 times and didn´t get it even once... I have been trying bills sequences now for a while and i think i´m starting to get deacent results now...

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#1672651 - 05/06/11 04:49 PM Re: Tuning Circle of Fifths [Re: mstore]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3191
Loc: Madison, WI USA
Originally Posted By: mstore
I can´t believe that you did that so fast, I think i tried tuning by fourths and fifths maybe 50 times and didn´t get it even once... I have been trying bills sequences now for a while and i think i´m starting to get deacent results now...


Touché!
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1672683 - 05/06/11 05:38 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
Bill: what sequence to you use yourself? and how did you learn to tune in first place?

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#1672924 - 05/07/11 07:29 AM Re: Tuning Circle of Fifths [Re: mstore]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: mstore
I can´t believe that you did that so fast, I think i tried tuning by fourths and fifths maybe 50 times and didn´t get it even once... I have been trying bills sequences now for a while and i think i´m starting to get deacent results now...

You asked, so I told you. Rather than tell you to go pound sand, I will consider how frustrated you must be and reply to your Topic about tight pinblocks. It really is OK. I understand. If the strings don’t stay at pitch, no temperament sequence will work very well. It is like trying to chain rolling logs on a moving truck. smile
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1672932 - 05/07/11 08:18 AM Re: Tuning Circle of Fifths [Re: Bill Bremmer RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4916
Loc: Bradford County, PA
Originally Posted By: Bill Bremmer RPT
Originally Posted By: mstore
I can´t believe that you did that so fast, I think i tried tuning by fourths and fifths maybe 50 times and didn´t get it even once... I have been trying bills sequences now for a while and i think i´m starting to get deacent results now...


Touché!


Then I guess I won't bother telling about some really amazing things I have done, like herding bear.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1672951 - 05/07/11 09:17 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
partistic Offline
Full Member

Registered: 11/27/10
Posts: 90
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?

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#1672973 - 05/07/11 10:15 AM Re: Tuning Circle of Fifths [Re: Ron Voy]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
today i actually set my first temperament within the range of 1 cent (partial2) by tuning fourths and fifhts. The key was to use the following formula:

contiguous 5ths ratio 2:3
5th and 4th top common note 2:3

5th and 4th bottom common note 3:4
contiguous 4ths ratio 3:4

D4 from A3 about 1 bps

G3 from D4 so that G3-D4 beats 2 times in the same time as A3-D4 beats 3 times.

C4 from G3 so that C4-G3 is a little faster than A3-D4 and G3-D4 beats 3 times in the same time as G3-C4 beats 4 times.

F3 from C4 so that F3-C4 beats 2 times when G3-C4 beats 3 times.
At this time i could check with the M3-M6 test (F3-A3 = 7bps F3-D4 8bps)
Then i tuned:

A#3 from F3 about 0,7 bps, checked so that F3-A#3 beats 4 times compared to F3-C4
At this time i could also check that F3-A3 , F3-D4 and A#3-D4 all are accelerating.

D#4 from, A#3. a bit faster than A3-D4.

G#3 from D#4 a little faster than G3-D4 and G#3-D#4 should beat 3 times compared to A#3-D#4. G#3-C4 should beat about 1 bps slower than A#3-D4.

C#4 from G#3. A3-C#4 should fit inbetween A#3-D4 and G#3-C4. C#4-G#3 should also fit in between G3-C4 and A3-D4.

F#3 from C#4 a little bit slower than G3-D4 but faster than F3-C4. F#3-A#3 should be 0,5 bps faster than F3-A3.
F#3-C#4 should beat 2 times compared to G#3-C#4 3 times.
again the M3-M6 test.

B3 from F#3. a little faster than F3-A#3. F#3-B3 should beat 4 times compared to F#3-C#4. at this time G3-B3 should fit inbetween F3-A3 and A3-C#4 and progress evenly.

The last note is E4 which is tuned from A3 and B3. B3-E4 should beat 3 times when E4-A3 beats 2. C4-E4 should also beat a little faster than B3-D#4. E4-B3 beats 4 times compared to F#3-B3.

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

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#1673287 - 05/07/11 11:06 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
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. This is something I can do very accurately. Then I tune the 4ths and 5ths making up F3A3, first C4 to F3 then D4 to A3 then fit in G3 to make G3C4 and G3D4 be "correct". I can do this very accurately too. At this point I have F3 G3 A3 C4 and D4 solidly in place and just tune by 4ths and 5ths checking any RBI's that become available and if tests failed I listen to the 4ths and 5ths again and usually discover a problem.

With the contiguous M3 method I have problems placing C#4 as the A3C#4 and C#4F4 beats are sometimes very hard to hear.

I guess there'r many ways to skin a cat.

Kees

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#1674082 - 05/09/11 12:53 AM Re: Tuning Circle of Fifths [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
Originally Posted By: Bill Bremmer RPT
Originally Posted By: mstore
I can´t believe that you did that so fast, I think i tried tuning by fourths and fifths maybe 50 times and didn´t get it even once... I have been trying bills sequences now for a while and i think i´m starting to get deacent results now...


Touché!


Then I guess I won't bother telling about some really amazing things I have done, like herding bear.


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

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#1674230 - 05/09/11 08:47 AM Re: Tuning Circle of Fifths [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3191
Loc: Madison, WI USA
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.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1674386 - 05/09/11 01:42 PM Re: Tuning Circle of Fifths [Re: Bill Bremmer RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
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

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#1674433 - 05/09/11 03:12 PM Re: Tuning Circle of Fifths [Re: Ron Voy]
mstore Offline
Full Member

Registered: 04/01/11
Posts: 36
Whatif you use a hybrid version where the F3-A3 is set by tuning the first set of contigous thirds?, then you would have a frame for tuning the rest of the notes, C4-G3-D4 between F3-A3 and F#-B3-E4 between A3 and C#4 and finally G#3-D#4-A#3 between C#4 and F4...

Martin

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#1674661 - 05/09/11 09:52 PM Re: Tuning Circle of Fifths [Re: DoelKees]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3191
Loc: Madison, WI USA
Originally Posted By: DoelKees

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 am not even thinking about theory! I am a seat-of-the-pants type guy. When I regulate, I never measure anything! I let the dimensions find themselves. So, why impose an arbitrary beat rate of which you can never be certain? Let the beat rate find itself!

If you have not had success with my descriptions, try investigating what Jack Stebbins RPT (long term primary instructor at the North Bennett Street School and three decade PTG tuning examiner) says in his material on "Let the piano tell you!"
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

Top
#1674677 - 05/09/11 10:19 PM Re: Tuning Circle of Fifths [Re: mstore]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3191
Loc: Madison, WI USA
Originally Posted By: mstore
Whatif you use a hybrid version where the F3-A3 is set by tuning the first set of contigous thirds?, then you would have a frame for tuning the rest of the notes, C4-G3-D4 between F3-A3 and F#-B3-E4 between A3 and C#4 and finally G#3-D#4-A#3 between C#4 and F4...

Martin


There seems to be something very intelligent coming out of Finland these days! If you can get the series of contiguous thirds from A3 to A4 and verify that both octaves, F3-F4 and A3-A4 are at least similar in size, everything else will work, no matter how you go about it. Tune all the 4ths & 5ths you want after that until kingdom come and you will be able to correct yourself, now matter how you go about it.

I refuse to believe that people "cannot hear" the F4-A4 M3! If you say that you cannot, then you must do as I said, practice moving F4 against A4 until you can. Surely, you will be able to hear when you have a slow beat. Flatten F4 when you do hear it as you hear the speed increase to beyond the point of discernibility. You will hear it if you try.

There must always be an interaction and cross check between SBIs and RBIs in ET. Leaning too heavily on 4ths & 5ths will almost always result in Reverse Well, especially if you try to count 7 beats per second for the F3-A3 M3. That is a quick and easy recipe for Reverse Well.

Leaning too much on RBIs easily results in a Marpurg type quasi ET. The RBIs sound good but the 4ths & 5ths are all over the place.

Equal Temperament means exactly what it says: all intervals are tempered equally.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

Top
#1674684 - 05/09/11 10:29 PM Re: Tuning Circle of Fifths [Re: Bill Bremmer RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1701
Loc: Vancouver, Canada
Originally Posted By: Bill Bremmer RPT
Originally Posted By: DoelKees

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 am not even thinking about theory! I am a seat-of-the-pants type guy. When I regulate, I never measure anything! I let the dimensions find themselves. So, why impose an arbitrary beat rate of which you can never be certain? Let the beat rate find itself!

If you have not had success with my descriptions, try investigating what Jack Stebbins RPT (long term primary instructor at the North Bennett Street School and three decade PTG tuning examiner) says in his material on "Let the piano tell you!"


Well I find just about any recipe to set the ET temperament works for me, so I just like to play around with different methods.

What I like about setting the beat rate of F3A3 and taking it from there is that I can, if appropriate, set it to a low value (like 4bps), tune the 4ths and 5ths that span it proportionally, and then deal with the rest as I please to make up any unequal temperament I like.

Kees

Top
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