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#1294218 - 10/26/09 04:33 PM Re: Nikiforoff Temperament summary [Re: UnrightTooner]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2330
Loc: Niagara Region, On. Canada
Tooner, I think how well each of us can discern changes in beat rates in both SBI's and RBI's has much to do with the time spent listening for them. Coming from a background more in line with a modified Braid White temperament I pretty well found a M3rd in the F4-A4 region almost useless, kind of like a revving chainsaw. Some people find it useful as the upper end of CM3rds and such but perhaps they spent a lot of time working in the +12 bps range. As a chromatic progression I think anything above 12 bps is not reliable....for me at least.
_________________________
Piano Technician
George Brown College /85
Niagara Region

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#1294602 - 10/27/09 07:29 AM Re: Nikiforoff Temperament summary [Re: Emmery]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Well said!
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1294942 - 10/27/09 04:39 PM Re: Nikiforoff Temperament summary [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1432
Loc: Mexico City
Tooner,

Of course I can answer.

When tuning CM3s you can set these five notes (F3, A3, C#4, F4 and A4) in a way that every major third beats faster than its contiguous lower major third. And you can easily hear a deviation of 0.3 cents in the tuning of F3. Not because you can estimate its beat rate all by itself, but because of the way the progression of CM3 is affected by such a deviation. Remember that when you move F3 you have to readjust F4, so the beat rates of the three M3s: F3-A3, C#4-F4 and F4-A4 are all affected simultaneously and that changes the hole progression in a way that lets you detect the right spot for F3 with an acuracy of 0.3 cents.

That precision in the tuning of the CM3s makes unecesary any further testing. With these five notes tuned with that acuraty you can tune the rest of the temperament octave or tenth, and then you can refine the tuning in order to have an even chromatic progression of all the intervals (M10ths, 8ves, M6ths, P5ths, P4ths, M3rds).
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1294954 - 10/27/09 04:47 PM Re: Nikiforoff Temperament summary [Re: Gadzar]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1432
Loc: Mexico City
BTW,

Do you think 0.3 cents is not enough precision?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1295278 - 10/28/09 08:01 AM Re: Nikiforoff Temperament summary [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Gadzar:

We can look at this both subjectively and objectively.

Subjectively, you seem to be able to hear a very slight difference in the progression of CM3s. Objectively, a change of +0.3 cents on C#4 of a perfect, theoretical set of CM3s will change the CM3 ratio from 3.97:5 to 4.15:5. That is not very much.

Subjectively, I do not hear small differences in the progression of CM3s. I do hear any slight difference in SBIs, though. And I can hear whether chromatic RBIs are in even progression easier than I can hear CM3s. Objectively, it requires greater accuracy to tune progressive chromatic M3s than it does to tune progressive CM3s.

No, 0.3 cents is not enough accuracy to guarantee progressive M3s and M6s, although progressive M3s and M6s can be tuned with errors greater than 0.3 even up to 0.9 cents. (I think this is part of the reason for the 0.9 cent allowable error on the PTG exam.)

I am pretty sure that you understand math enough to follow this. A M3 is 13.7 cents wide of just. If a sample M3 beats 8 bps at 13.7 cents, it will beat 16 bps at 27.6 cents. Twice as fast for twice as wide, same as if the M3 was an octave higher. This means that the 12th root of two can be used to determine how much a M3 (or any other interval) can be changed before it beats the same speed as the interval chromatically higher. So for the sample M3 to beat the same speed as the next higher M3 (8 bps * 1.059 = 8.472 bps) the interval would need to be widened to 14.5 cents, or 0.8 cents wider than theoretical (13.7 * 1.059 = 14.51 cents). But if we start with perfect theoretical ET and flatten the lower note of a M3 0.8 cents and sharpen the upper note 0.8 cents, then the interval will have a beat speed as fast as the interval two semi-tones higher. A tolerance of +/- 0.4 cents is not accurate enough either, because one M3 could be widened by 0.8 cents and the next narrowed by 0.8 again causing the beat rates to be unprogressive. Although a tolerance of 0.2 cents can allow some chromatic M3s to beat at the same speed, they would not be unprogressive. So I believe to guarantee that all M3s and M6s to be progressive requires a tolerance of +/- 0.2 cents, although +/- 0.4 cents will usually result in progressive M3s and M6s (but I have not used statistical analysis to work out a bell curve.) If you choose, you can work out the allowable tolerance for a progressive set of CM3s in the same way.

The reason I chose M3s instead of M6s for calculating the allowable tolerance is because M6s are 2 cents further from just intonation than M3s, and do not require as close a tolerance for progressiveness. The closer to just intonation, the closer the tolerance that is required. This is an objective reason for using SBIs. Since they are 7 times more just than M3s, when they are out of progression, they show an error seven times smaller than M3s would. In a typical piano, this is a smaller tolerance than the pin and string can be reliably set.

Once I understood all this, including my personal abilities and limitations to hear RBIs and SBIs, the choice for me was obvious. I choose to tune with intervals that have a tolerance greater than I can actually tune. It is like doing carpentry work that requires +/- 1/8 inch tolerances. I want a tape measure with 1/16 inch marks, not ¼ inch marks.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1296479 - 10/30/09 07:42 AM Re: Nikiforoff Temperament summary [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1432
Loc: Mexico City
You understand nothing!

You seem to ignore what I say, as always.

I'll put it in numbers to show you how a deviation of 0.3 cents in the tuning of F3 can alter the progression of the CM3s.

I'll make the calculations without iH. I leave to you the work to put iH into play with your brand new database.

The frequences in hz. are:

F3=174.61
A3=220
C#4=277.18
F4=349.23
A4=440

The beat rates in bps of CM3s are:

F3-A3 = 6.93 (4*220-5*174.61)
A3-C#4 = 8.73
C#4-F4 = 11.00
F4-A4 = 13.86

The ratios of the progression:

A3-C#4/F3-A3 = 8.73/6.93 = 1.26 aprox 5:4
C#4-F4/A3-C#4 = 11.00/8.73 = 1.26 aprox 5:4
F4-A4/C#4-F4 = 13.86/11.00 = 1.26 aprox 5:4

Now if we detune F3 by an amount of 0.3 cents flat we have:

F3=174.58
A3=220
C#4=277.18
F4=349.17 (F4 is adjusted to 2*F3)
A4=440

F3-A3 = 7.08
A3-C#4 = 8.73
C#4-F4 = 10.76
F4-A4 = 13.86

A3-C#4/F3-A3 = 1.23 between 6:5 and 5:4
C#4-F4/A3-C#4 = 1.23 between 6:5 and 5:4
F4-A4/C#4-F4 = 1.32 almost 4:3


And now you see that the ratio of the latest is 4:3 instead of 6:5-5:4 of the two preceding ratios. That is a very easy to hear difference: F4-A4 beats 4 times for 3 beats of C#4-F4!

In simple words F4-A4 beats too fast and you can distinctly hear the uneveness in the progression!

You need no much training in apreciating the difference between 5:4 and 4:3 ratios. Remember that you are hearing and comparing these ratios, you are not trying to estimate a single 5:4 ratio, you are evaluating the whole progression.

Of course it is not possible to distiguish the change in the beat rate of F3-A3 from 6.93 to 7.08. But after you adjust F4 and you play the four CM3s, you can easily detect the uneveness at F4-A4 which will beat too fast compared to the other CM3s.

In the same way, if F3 was tuned 0.3 cents sharp then you will find that F4-A4 will beat too slow in the progression.

Could you please borrow an ETD, or install the trial version of Tunelab for free in your computer and give it a try?

You will change your mind if you do!

You'll see that your ear is accurate enough to detect that 4:3 to 6:5-5:4 ratio difference and you can tune F3 with an accuraty of 0.3 cents.

About 0.3 cents being enough acuraty, please read my words: 0.3 cents in the tuning of F3 from A3. That means just that. A3 is tuned to A4 and F4 is tuned to F3 with the precision you can achieve in tuning your octaves.

That doesn't mean you can have F3 0.3 cents flat with A3 0.3 cents sharp, that would be a "mathematical" conception of acuraty, based on random errors, which is not the case.

And you seem to ignore consistently that this is only the beggining part of the sequence, after that you will refine the tuning of your temperament and correct notes testing all other kind of intervals.


Edited by Gadzar (10/30/09 07:48 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1296495 - 10/30/09 08:38 AM Re: Nikiforoff Temperament summary [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Gadzar:

I posted: “Objectively, a change of +0.3 cents on C#4 of a perfect, theoretical set of CM3s will change the CM3 ratio from 3.97:5 to 4.15:5. That is not very much.”

Objectively, our math agrees: 4.15:5 is the same ratio as 4.98:6.

Subjectively, our opinions differ. I do not think this is much of a difference. And btw 3.97:5 is the same ratio as 4.76:6, not far at all from 5:6 and also the same ratio as 3.18:4 not far at all from 3:4.

Although I used to do things a little differently, I now prefer to use each new note that I tune in order to refine the others already tuned, and not wait until the end for refinement. A fourth and fifth sequence is great for this.

I consider much of this to be in the realm of personal abilities and preferences. I do not feel a need for us to agree. Do you?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1296923 - 10/30/09 10:51 PM Re: Nikiforoff Temperament summary [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1432
Loc: Mexico City
No, I don't feel the need to agree.

But, if you can not hear the difference between CM3s with a beat ratio of 4:3 instead of 5:4, then I can not see how you can tune a piano by ear!

I wish I could hear a piano tuned by you in ET.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1297045 - 10/31/09 06:11 AM Re: Nikiforoff Temperament summary [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4789
Loc: Bradford County, PA
Gadzar:

Progressive, chromatic RBIs is the proof of ET, not CM3 ratios. How they are achieved does not matter.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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