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#1484019 - 07/29/10 05:53 PM Re: How to tune Tempered Octaves ? [Re: BDB]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Folks, changing the definition of cent is not going to change any tuning any more than measuring a string length in inches instead of centimeters alters its pitch.

Kees

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#1484036 - 07/29/10 06:18 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
Olek Offline
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Registered: 03/14/08
Posts: 7904
Loc: France
As long as you agree that a spreadsheet cannot tell how a tuning sound, I will agree with you. !

did you check the pitch difference heard between a plucked string and the same played by the hammer ? which is the real pitch ?
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#1484040 - 07/29/10 06:24 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
The difference doesn´t matter per se. What is important is the concept.

Before iH was discovered, tuners were able to tune correct octaves, in the low bass and in the high treble. To speak of tempered octaves was nonsense.

Now that we are aware of iH we tune the same correct octaves but we can better understand the behavior of octaves in the high treble compared to the low bass. And now speaking of tempered octaves makes sense.

We can no more believe we tune Pithagoras's octaves where the fundamentals are in a 2:1 ratio, that model doesn't work for pianos.

So the model you choose makes a difference!


Edited by Gadzar (07/29/10 06:25 PM)
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#1484105 - 07/29/10 08:14 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
pppat Offline
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Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Originally Posted By: DoelKees
Folks, changing the definition of cent is not going to change any tuning any more than measuring a string length in inches instead of centimeters alters its pitch.

Kees


Originally Posted By: Gadzar
The difference doesn´t matter per se. What is important is the concept.

Before iH was discovered, tuners were able to tune correct octaves, in the low bass and in the high treble. To speak of tempered octaves was nonsense.

Now that we are aware of iH we tune the same correct octaves but we can better understand the behavior of octaves in the high treble compared to the low bass. And now speaking of tempered octaves makes sense.

We can no more believe we tune Pithagoras's octaves where the fundamentals are in a 2:1 ratio, that model doesn't work for pianos.

So the model you choose makes a difference!


smile I kind of agree with both of you. Kees is right on his idea of scaling/measurement. The problem is that it's a slippery son of a… target.

It touches something I've thought quite a bit about. Just where does the need for stretch come into play? We like to measure it by the octave, but guess what - that octave isn't really there. Or, at least, it can be measured from 12 different angles.

As long as we are limited to any known scale (yes, even a logarithmical one - they are hopelessly symmetrical, too) the best we can do is to establish it, and give offsets/deviations. This is what any ETD will be capable of, and even though it is a crippled reading, it is all we've got for now.
_________________________
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Senior Lecturer (jazz piano, composition, music theory, conducting) @ Novia University of Applied Sciences, Jakobstad, Finland
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Dedicated to learning the craft of tuning. Getting better.

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#1484118 - 07/29/10 08:33 PM Re: How to tune Tempered Octaves ? [Re: pppat]
BDB Offline
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Registered: 06/07/03
Posts: 21926
Loc: Oakland
It gets to what I was asking: What is the frequency of a piano note? Do you measure it from peak to peak or from zero to zero? The wave put out by a piano is not periodic, and the two measurements are different.

Remember the old joke about the mathematician, the physicist, and the engineer, where they are put at one end of the room and a pile of money is at the other end of the room? They are told that they can have the money if they get to it obeying one rule: After they go half the distance to the money, they need to stop, wait a minute, and repeat until they get to the money. The mathematician thinks about it and walks away. The physicist walks halfway to the money, waits a minute, walks halfway again, waits a minute, thinks about it and walks away. The engineer walks halfway to the money, waits a minute, walks halfway again, waits a minute, walks halfway again, waits a minute, walks halfway again, waits a minute, walks halfway again, waits a minute, walks halfway again, waits a minute, walks halfway again, waits a minute, walks halfway again, waits a minute, says "That is close enough!" and grabs the money and leaves.
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#1484126 - 07/29/10 08:47 PM Re: How to tune Tempered Octaves ? [Re: Olek]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: Kamin

not much to do with a pure 3:2 or a pure 6:4 It is something that sound acoustically just, thats all.

Try to tune a pure 5 with a 3:2 partial match on an EDT, then try the same by ear , and listen to wich you prefer.

one will have some added "light" due to a good coupling, the other will tone constrained and flat.


I prefer something which is between a 3:2 and 6:4 fifth. It has nothing to do with light, it just minimizes the maximum of the 3:2 and 6:4 beat rates.

Kees

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#1484134 - 07/29/10 09:05 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: BDB
"That is close enough!" and grabs the money and leaves.


Right!

The same is true for Kamin. The good sounding octave won't be 3:2 nor 6:4.

There is an interference between the two of them. If they are close enough they act on the other to produce a one unique sound.

Like unisons. When the frequence of one string approaches the other there is a range in which it acts on the other string and makes it vibrate at the same frequence and they fall into the unison.
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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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#1484135 - 07/29/10 09:05 PM Re: How to tune Tempered Octaves ? [Re: BDB]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: BDB
It gets to what I was asking: What is the frequency of a piano note? Do you measure it from peak to peak or from zero to zero? The wave put out by a piano is not periodic, and the two measurements are different.

Neither, there are various algorithms to measure the fundamental, all very accurate. More accurate than anyone can tune.

Kees

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#1484151 - 07/29/10 09:31 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Originally Posted By: DoelKees
Originally Posted By: Gadzar

Can you please give me the definition of a cent?

cents = 1200*log2(F'/F)
Originally Posted By: Gadzar

Please, don't tell me that
cents = 1200*log2(F'/F)
If so then you are using the model of 12th root of 2.


That is nonsense. It's like saying that because Americans measure the price of gas per gallon, they must therefore drink a gallon of Coca Cola a day.

Anyways this thread is supposed to be about octaves. Why don't you read the tread about mathematics? Once you understand what was discussed there we can talk more.

Kees


Rafael, Kees is making a point. If anybody want a new scale instead of cents, they have to implement it. But why? The octave will be whatever you want it to be. Why not stick to cents and play around with F' ? smile


Edited by pppat (07/30/10 05:08 PM)
Edit Reason: correcting "double octave" to what I meant, ie "octave".
_________________________
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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#1484152 - 07/29/10 09:32 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21926
Loc: Oakland
Originally Posted By: DoelKees
Originally Posted By: BDB
It gets to what I was asking: What is the frequency of a piano note? Do you measure it from peak to peak or from zero to zero? The wave put out by a piano is not periodic, and the two measurements are different.

Neither, there are various algorithms to measure the fundamental, all very accurate. More accurate than anyone can tune.

Kees


What are those algorithms? What does "accurate" mean in this case? What definition of frequency are you using?
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#1484162 - 07/29/10 09:46 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
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Registered: 12/15/06
Posts: 1910
Loc: Mexico City
I liked very much the joke refered by BDB. "Close enough to grab the money"

Close enough to achieve a good tuning.

Here is an extract of the book by C.Chang. "Fundamnetals of piano practice"

d. Sympathetic Vibrations. The accuracy required to bring two strings into perfect tune is so high that it is a nearly impossible job. It turns out that, in practice, this is made easier because when the frequencies approach within a certain interval called the "sympathetic vibration range", the two strings change their frequencies towards each other so that they vibrate with the same frequency. This happens because the two strings are not independent, but are coupled to each other at the bridge. When coupled, the string vibrating at the higher frequency will drive the slower string to vibrate at a slightly higher frequency, and vice versa. The net effect is to drive both frequencies towards the average frequency of the two. Thus when you tune 1 and 2 unison, you have no idea whether they are in perfect tune or merely within the sympathetic vibration range (unless you are an experienced tuner). In the beginning, you will most likely not be in perfect tune.
Now if you were to try to tune a third string to the two strings in sympathetic vibration, the third string will bring the string closest to it in frequency into sympathetic vibration. But the other string may be too far off in frequency. It will break off the sympathetic vibration, and will sound dissonant. The result is that no matter where you are, you will always hear beats -- the tuning point disappears! It might appear that if the third string were tuned to the average frequency of the two strings in sympathetic vibration, all three should go into sympathetic vibration. This does not appear to be the case unless all three frequencies are in perfect tune. If the first two strings are sufficiently off, a complex transfer of energy takes place among the three strings. Even when the first two are close, there will be higher harmonics that will prevent all beats from disappearing when a third string is introduced. In addition, there are frequent cases in which you cannot totally eliminate all beats because the two strings are not identical. Therefore, a beginner will become totally lost, if he were to try to tune a third string to a pair of strings. Until you become proficient at detecting the sympathetic vibration range, always tune one string to one; never one to two. In addition, just because you tuned 1 to 2 and 3 to 2, it does not mean that the three strings will sound "clean" together. Always check; if it is not completely "clean", you will need to find the offending string and try again.
Note the use of the term "clean". With enough practice, you will soon get away from listening to beats, but instead, you will be looking for a pure sound that results somewhere within the sympathetic vibration range. This point will depend on what types of harmonics each string produces. In principle, when tuning unisons, you are trying to match the fundamentals. In practice, a slight error in the fundamentals is inaudible compared to the same error in a high harmonic. Unfortunately, these high harmonics are generally not exact harmonics but vary from string to string. Thus, when the fundamentals are matched, these high harmonics create high frequency beats that make the note "muddy" or "tinny". When the fundamentals are de-tuned ever so slightly so that the harmonics do not beat, the note "cleans up". Reality is even more complicated because some strings, especially for the lower quality pianos, will have extraneous resonances of their own, making it impossible to completely eliminate certain beats. These beats become very troublesome if you need to use this note to tune another one.


I wonder if the same phenomenom is present when tuning near pure intervals,other than unisons, I mean octaves, 12ths and 5ths.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1484177 - 07/29/10 10:05 PM Re: How to tune Tempered Octaves ? [Re: BDB]
DoelKees Offline
1000 Post Club Member

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

What are those algorithms? What does "accurate" mean in this case? What definition of frequency are you using?


That would become too technical. "Pitch detection" and google/wikipedia should get you going here if you're interested.

The best method that I know of to find all partials and their decay rates is described in this paper

Kees

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#1484181 - 07/29/10 10:09 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Kamin:

In Cordier tuning do you get enough stretch in the bass? Are the pure fifths (3:2/6:4 equal beating I think) continued all the way to the bottom?

Kees

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#1484223 - 07/29/10 11:04 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
DoelKees Offline
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Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Here are some plots of the sizes of various intervals for Cordier tuning, which I interpret as equal beating 3:2/6:4 fifths (i.e., minimizing the maximum bps for those two partials). The first plot is for my Heintzmann upright, the second for a Steinway D. I used tunelabs modification of Young's model for inharmonicity.


Heintzmann


Steinway

For the upright Cordier seems about equivalent to 6:3 octaves throughout.

For the Steinway everything is stretched. (Note the P5 data are based on 3:2.)

So that answers my question to Kamin from a theoretical point of view. Kamin, do you observe this also in practice, i.e., Cordier on uprights in about the same as tuning 6:3 octaves, but on grands it stretches way more?

Kees

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#1484226 - 07/29/10 11:09 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21926
Loc: Oakland
Originally Posted By: DoelKees
Originally Posted By: BDB

What are those algorithms? What does "accurate" mean in this case? What definition of frequency are you using?


That would become too technical. "Pitch detection" and google/wikipedia should get you going here if you're interested.

The best method that I know of to find all partials and their decay rates is described in this paper

Kees


Well, there comes a point where you have to define the pitch of a piano note well enough so that you can distinguish between 440*2^(1/12) = 466.163761518 and 440*3^(1/19) = 466.191468485 on a piano, otherwise there is no point in discussing it at all. I am not certain it can be done. I do not believe that a piano note's pitch is that well defined.
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#1484233 - 07/29/10 11:18 PM Re: How to tune Tempered Octaves ? [Re: BDB]
DoelKees Offline
1000 Post Club Member

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

Well, there comes a point where you have to define the pitch of a piano note well enough so that you can distinguish between 440*2^(1/12) = 466.163761518 and 440*3^(1/19) = 466.191468485 on a piano, otherwise there is no point in discussing it at all. I am not certain it can be done. I do not believe that a piano note's pitch is that well defined.

That would be a beat rate of 2/min, which can not be distinguished electronically or aurally.

However your premise that "you have to define the pitch of a piano note well enough so that you can distinguish ..." is unclear to me. Why would you come to this point? Maybe you should argue with Alfredo instead of me.

Kees

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#1484248 - 07/29/10 11:39 PM Re: How to tune Tempered Octaves ? [Re: DoelKees]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Kees,

your graphs look the way I hear it. Have you input (and posted) a similar graph for Stoppers pure 12th tuning? If you have so, please forgive me, I had summer vacation and the weather is unusually hot here... wink

And (withdrawn from the same vacation account) - which program did you use for the graphs?
_________________________
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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#1484256 - 07/29/10 11:59 PM Re: How to tune Tempered Octaves ? [Re: pppat]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1766
Loc: Vancouver, Canada
Originally Posted By: pppat
Kees,

your graphs look the way I hear it. Have you input (and posted) a similar graph for Stoppers pure 12th tuning? If you have so, please forgive me, I had summer vacation and the weather is unusually hot here... wink

And (withdrawn from the same vacation account) - which program did you use for the graphs?


Here it is for 3:1 12ths across the board:


Heintzmann


Steinway

I used my own program, described in the "tuning math" thread.
(Again P20 should read P22, forgot to fix it.)

Kees

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#1484260 - 07/30/10 12:04 AM Re: How to tune Tempered Octaves ? [Re: DoelKees]
pppat Offline
1000 Post Club Member

Registered: 08/09/08
Posts: 1195
Loc: Jakobstad, Finland
Great stuff, and very useful and logical layout! Thanks, I'll check into the math thread.
_________________________
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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#1484444 - 07/30/10 07:59 AM Re: How to tune Tempered Octaves ? [Re: pppat]
UnrightTooner Offline
4000 Post Club Member

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

My, it was a busy evening!

Cents are very handy as a measuring tool because it always means cents from something else. But contrary to Gadzar’s belief, I do not calculate in cents, I calculate and analyze in the aural tuners measuring device of bps which results in Hz. Then where appropriate, I display results in cents deviation from theoretical pitches. Unlike Kees’ fine graphs, I prefer the y-axis to be in bps. That has more meaning to me.

Looking at Kees’ graphs solidifies something that has been developing in my mind. How do we determine what is considered a high, medium or low iH piano? Even with an ETD taking the iH reading of one note does not mean much. The slope of the iH curve is important, too.

On the graphs, any curve could be straightened into a line resulting in the other curves changing their shape. The ones that interest me most, lately, are the 12th and the 4:2 octave. Particularly at what point going up the scale does the 4:2 give the same stretch as the 12ths, or in other words, where 4:2 octaves produce pure 12ths.

For an aural tuner, this is one way to determine the iH (high, med, low) of a piano. I would say high is when this happens below the temperament, medium in the temperament, and low above the temperament. So looking at Kees’ fine graphs and noting where the 12ths line crosses the 4:2 curve the Hientzman could be considered medium iH and the Stienway D low iH.

So taking what Gadzar said about real vs simulated pianos to heart and keeping in mind what Pat correctly mentioned about being stubborn (my choice of word) during a discussion, I meticulously tuned my Charles Walter Console (the scaling is more of a Studio with #1 being 48 inches) with 4:2 octaves until pure 12ths were produced and continuing with twelfths from there. My simulator predicted that pure 12ths would be produced at the C4-G5 12th, but in reality this happened about an octave higher. I have no explanation just an observation. Perhaps the iH curve that I use is not the same as my particular piano.

What I am going to be playing with is the relationship between a tempered F3-C4 fifth, a 4:2 C4-C5 octave, and an F3-C5 12th to get an idea of the iH of pianos as I tune them.
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#1484462 - 07/30/10 08:53 AM Re: How to tune Tempered Octaves ? [Re: DoelKees]
UnrightTooner Offline
4000 Post Club Member

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

I used tunelabs modification of Young's model for inharmonicity.

.....


So what is this modification???
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1484528 - 07/30/10 10:51 AM Re: How to tune Tempered Octaves ? [Re: DoelKees]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7904
Loc: France
Kees I have not been trained to tune Cordier. Seem to me that they use a standardized beat set, supposed to fit on every piano (which it does more or less well for what my colleagues have told me)
It have surprized me, but they use double octaves beat rates to avoid to extreme tunings.
the 5th having some stretch latitude , they aim for even beating of sixth and tenth eventually min 3d and M 3d.
That tuning absorb iH, the large semi tone is appreciated by the ear, but at some point the tone can sound as the first digital organs piano tone (Bontempi tone)

I have noticed that sometime, the tuner have to lower the strech of the high treble to avoid the63 cts us you tell about. I also find that the basses does tone a little compact, but it sound Ok with the mediums.

In any case, on a piano like Yamaha Gh1B a highly open tuning is natural to the tone, it "seats" in the iH quite well.

Btw the experiments on differen scales ET, Zarlino, Pythagore, where conducted in the 40s by different searchers, in America and France.
Van Esbroek & Monfort
They prooved than violonists tend to use Pythagorean justness more than Zarlin , the same in singing (large M3d, )

See Johnn Backus (acoustical fundation in music)1970
JG Roederer : Introduction to Physics and Psychophysics (1974)


Too difficult for me to resume, some of those work showed that justness is contextual, that intervals are raised, not lowered, and that more in the treble, orchestra raise from 10 to 20cts some notes when it makes sense harmonically.
People tend also to prefer Et justness, unless the 5th is played as a chord and isolated. ther, the pure 5th is prefered

also, they noticed that a small octave (1comma) is noticed as false by all listeners, wwhile a large one by the same amount sound just to thelisteners
(panel and statistical analysis done with organ tones)
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#1484538 - 07/30/10 11:04 AM Re: How to tune Tempered Octaves ? [Re: Olek]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7904
Loc: France
about Cordier I said a "standardized" double octave beat rate.

But then, in usual tuning, the 17th beat rate can also be used in the same way.
If a piano is tuned with a progressive beat rate of those intervals, whatever the shape of the progression is, the ear will catch that logic as "justness"

any logic, I belive, Btw. an ET with all octaves smaller than 1:2 by the samme amount will certainly sound less out of tune than one belive.
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#1484602 - 07/30/10 12:16 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: UnrightTooner
Originally Posted By: DoelKees
.....

I used tunelabs modification of Young's model for inharmonicity.

.....


So what is this modification???



Here it is. It was taken from the Tunelab documentation. Notice that Tunelab manages iH in a slightly different way than Young's approach. Here the fundamental is the reference from whom the iH of the other partials is measured, thus the iH for the fundamental is always 0 cents.

Inharmonicity

Complex sounds, such as those from a piano, are composed of many component frequencies. These frequencies generally fail into the pattern of being multiples of the lowest, or fundamental, frequency. But due to the nature of stiff piano wire, these components (called partials) are not exact multiples of the fundamental. Inharmonicity refers to the degree to which the frequencies of the partials deviate from being exact multiples of one fundamental frequency. This is important in piano tuning because how a note sounds when played with other notes is dependent on the frequencies of the different partials.

There are various ways of reporting inharmonicity. One is to report the deviation in cents for each partial frequency from its corresponding exact multiple of the fundamental. For example, if the fundamental of A4 is 440 Hertz and the second partial is 881 Hertz, then, according to tile formula for cents, the second partial deviates from its exact multiple of the fundamental (880 Hertz) by 1.97 cents.

According to one theory, the inharmonicities of the various partials of a simple bare piano wire compared to the fundamental are related by the formula

IH(n)=B*(n*n-1)

Where n is the partial number (1 for the fundamental) and B is called the inharmonicity constant for the particular wire. TuneLab Pro uses the following modification of this model. Empirical data has shown that the inharmonicity of each partial is more accurately described by

IH(n)=B*(C[n]-1)

where C[n] is given by the lookup table

n C[n]
1 1.00
2 4.00
3 8.45
4 13.18
5 19.72
6 27.27
7 35.53
8 46.25
9 57.12
10 69.43
11 83.22
12 96.60
13 109.8
14 125.4
15 139.5
16 156.1



The value of B is given by the program when you measure a note. It measures the offsets of partials and calculates a constant that best fits them.


Edited by Gadzar (07/30/10 12:19 PM)
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#1484604 - 07/30/10 12:18 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
BDB Offline
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However, there are other things that affect the apparent pitch of the string besides inharmonicity.
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#1484609 - 07/30/10 12:23 PM Re: How to tune Tempered Octaves ? [Re: BDB]
Gadzar Offline
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Oh yes, indeed.

But I am afraid here they (me included frown ) are talking about numbers no notes.
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#1484657 - 07/30/10 01:34 PM Re: How to tune Tempered Octaves ? [Re: Gadzar]
UnrightTooner Offline
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Registered: 11/13/08
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Loc: Bradford County, PA
Originally Posted By: Gadzar
I liked very much the joke refered by BDB. "Close enough to grab the money"

Close enough to achieve a good tuning.

Here is an extract of the book by C.Chang. "Fundamnetals of piano practice"

d. Sympathetic Vibrations. The accuracy required to bring two strings into perfect tune is so high that it is a nearly impossible job. It turns out that, in practice, this is made easier because when the frequencies approach within a certain interval called the "sympathetic vibration range", the two strings change their frequencies towards each other so that they vibrate with the same frequency. This happens because the two strings are not independent, but are coupled to each other at the bridge. When coupled, the string vibrating at the higher frequency will drive the slower string to vibrate at a slightly higher frequency, and vice versa. The net effect is to drive both frequencies towards the average frequency of the two. Thus when you tune 1 and 2 unison, you have no idea whether they are in perfect tune or merely within the sympathetic vibration range (unless you are an experienced tuner). In the beginning, you will most likely not be in perfect tune.
Now if you were to try to tune a third string to the two strings in sympathetic vibration, the third string will bring the string closest to it in frequency into sympathetic vibration. But the other string may be too far off in frequency. It will break off the sympathetic vibration, and will sound dissonant. The result is that no matter where you are, you will always hear beats -- the tuning point disappears! It might appear that if the third string were tuned to the average frequency of the two strings in sympathetic vibration, all three should go into sympathetic vibration. This does not appear to be the case unless all three frequencies are in perfect tune. If the first two strings are sufficiently off, a complex transfer of energy takes place among the three strings. Even when the first two are close, there will be higher harmonics that will prevent all beats from disappearing when a third string is introduced. In addition, there are frequent cases in which you cannot totally eliminate all beats because the two strings are not identical. Therefore, a beginner will become totally lost, if he were to try to tune a third string to a pair of strings. Until you become proficient at detecting the sympathetic vibration range, always tune one string to one; never one to two. In addition, just because you tuned 1 to 2 and 3 to 2, it does not mean that the three strings will sound "clean" together. Always check; if it is not completely "clean", you will need to find the offending string and try again.
Note the use of the term "clean". With enough practice, you will soon get away from listening to beats, but instead, you will be looking for a pure sound that results somewhere within the sympathetic vibration range. This point will depend on what types of harmonics each string produces. In principle, when tuning unisons, you are trying to match the fundamentals. In practice, a slight error in the fundamentals is inaudible compared to the same error in a high harmonic. Unfortunately, these high harmonics are generally not exact harmonics but vary from string to string. Thus, when the fundamentals are matched, these high harmonics create high frequency beats that make the note "muddy" or "tinny". When the fundamentals are de-tuned ever so slightly so that the harmonics do not beat, the note "cleans up". Reality is even more complicated because some strings, especially for the lower quality pianos, will have extraneous resonances of their own, making it impossible to completely eliminate certain beats. These beats become very troublesome if you need to use this note to tune another one.


I wonder if the same phenomenom is present when tuning near pure intervals,other than unisons, I mean octaves, 12ths and 5ths.

I wonder how much of this is really true.

Certainly two strings tuned to slightly different pitches can couple and vibrate at the same pitch, for a while. But what circumstances could exist where the left and center string couple, but the right cannot?

Perhaps there is a very narrow range that the tuner must leave the right string at if the frequencies of the left and middle are barely able to couple. But then what are the chances of the right string being tuned to that very narrow range when it is tuned separately to just one of the strings that can barely couple?

I think the first place to look when a unison won’t tune easily, and there are not false beats, is hammer mating. If the strings start in phase, they are more likely to stay in phase.

But your question of other intervals coupling does make me wonder. Sometimes when I am using a three note technique for tuning 4:2 octaves (C3-F3-C4) it works best by listening to the 2:1 match. The M3-M10 test then shows a better 4:2 octave. Perhaps the relative frequencies of the partials are being changed by a strong sympathetic vibration. I don’t know. I do know that partials can be ghosted and often notice when tuning an upper octave that some string down lower will start “humming the same tune”. The damper is not completely seated due to the temperament strip misaligning the outside strings of the unison.
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#1484663 - 07/30/10 01:43 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
UnrightTooner Offline
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Registered: 11/13/08
Posts: 4980
Loc: Bradford County, PA
Gadzar:

Thanks very much!

I wonder why I did not notice such a difference in the upper partials when I was analyzing the verituner files. And I wonder why Mr. Scott did not mention this when discussing and confirming Young’s equations in previous posts.

???

[Edit:] This is disturbing. Still, inharmonicity is a factor, just not quite as much as it may seem. It would explain the difference between what I actually tuned compared to what the simulator predicted. Hmmm... So Dr. White was more correct than it may have seemed when Young's paper first became popular....


Edited by UnrightTooner (07/30/10 02:25 PM)
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#1484760 - 07/30/10 04:31 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Those are only approximations, very crude approximations, of the real world which is much more complex than that.

I think CHAS and ONLYPURE are much better models. At least closer to the real world.

For what I know about the bearing plan outlined by Braid White in 1917, it gives theoretical figures to tune fifths and fourths and also for the rare thirds and sixths used as checks. These figures do not take iH into account.

Table III, page 87, gives theoretical frequencies and beat rates.
Table IV, pages 108 and 109, sumarizes the bearing plan and also give theoretical figures for the beat rates in the tests.

Dr. Albert Sanderson has discovered much more than Braid White about iH in pianos. And he has designed an instrument to measure it with accuraty.

You are aware of all that I suppose, aren't you?.


Edited by Gadzar (07/30/10 04:32 PM)
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#1484789 - 07/30/10 05:15 PM Re: How to tune Tempered Octaves ? [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1910
Loc: Mexico City
Originally Posted By: UnrightTooner
I wonder why I did not notice such a difference in the upper partials when I was analyzing the verituner files. And I wonder why Mr. Scott did not mention this when discussing and confirming Young’s equations in previous posts.


Verituner does not use calculated but measured partials.

Mr. Scott (TunLab's designer/owner) has nothing to do with Verituner which was designed by Dave Carpenter.


Young's equations are the responsability of only one person: Young him self.

But, that is interesting: So you have observed discrepancies between what you actually tune and what your simulator predicts, don't you?



Edited by Gadzar (07/30/10 05:19 PM)
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