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#609541  01/13/09 07:31 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

I have some ideas how I would go about it, but have never tried. I am in love with 4:2 octaves in the mid section.
If no one else posts how to tune it aurally, I will share my ideas in a day or two.
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#609542  01/13/09 07:43 AM
Re: Stoppers temperament

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Registered: 09/20/04
Posts: 1778
Loc: Massachusetts

Originally posted by Erus: [QUOTE] Having *A* measurement that is good enough doesn't mean the theory is wrong. [/b] Oh, yes it does. The article claims that any such measurement can't be done in that amount of time, but it canover and over. Your appeals to the sampling theorem also do not dispute my counter example. Counters running at 10 megahertz, 100 megahertz or whatever, can be used to measure the period of middle C. That sample rate greatly exceeds the Nyquist criterion, so the sampling theory agrees that my example method is valid. Finally, and most importantly, the article used the energy of a photon to purportedly prove a claim about measuring the frequency of musical tones. Using the energy of a photon may well make a valid proof about measuring the frequency of light, but unless someone can explain what the energy of photons has to do with measuring the frequency of sound waves or vibrating strings, then my conclusion is once again that the article is pseudoscience.

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#609544  01/13/09 01:28 PM
Re: Stoppers temperament

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The formulas in that article are not using the speed of a photon (quote): "the formula can be transformed into the relation between time and frequency of waves". Then, it is transformed and even marks: "...Here, there is no 'h'... The position and momentum of a wave in space have been changed in form to the time and frequency of a wave..." Plank's constant is out and the connection with the electromagnetic world is gone. The inequations he uses deal only with time and frequency, which can be used for sound. The speed of a photon is not being used there. I mentioned NyquistShannon because you said "I believe by precision, he means resolution". The NyquistShannon theorem is about sampling (it is relevant to resolution), and it is not being discussed here. Sampling frequency is no substitute to longer measurements according to the article being discussed. That's why I mentioned it, because you are talking about something else, not about uncertainty. I know counters that run at high frequencies, how they work and what they can do. They work great (as in "good enough" taken to amazingly high standards), and that is not being discussed. That article is not about electronics, but about a physical limitation that can't be overcome. The point of the article is not that those counters don't exist or don't work. It's point is: "If you want to get the exact Middle C, you need an infinite time and a continuous wave of C." If time increases, you can get a closer approximation, with shorter measurements you can't be that approximate. It doesn't matter what you use to make those measurements. *Exact* is the keyword here. You cannot get exact measurements, period. What you can get is approximations. We can currently have great approximations, "good enough" for A LOT of applications. There are devices that give AMAZING measurements, but that doesn't mean exactness. We can make a lot of things to try to get as close as possible, but that doesn't mean being exact. I am not saying we cannot measure a frequency. I'm saying we cannot measure it and be 100% sure we are 100% right. I am saying we can have very good estimations and things work great: my computer works, ETD's work, software based ETD's running in PDA's/phones/laptops and what not work great, but are not exact (they are much more precise than we, humans, can be). I have no elements to prove that point discussed in the article is wrong, but am not saying it can't be proven wrong. It could indeed be utterly rubbish, but so far I have no elements to prove it is. To prove it is wrong, you need to show the maths are wrong, or that some physical principle is wrong or incorrectly applied. This kind of thing goes beyond current technology, because the article deals with a physical limitation and you want to use technology that has ITS OWN limitations. You need to overcome the limitations of that technology to attempt to prove the physical limitation discussed in the article. To prove it wrong by making measurements you need to aim for *exact* repeatable measurements with current technology. Is that possible? http://en.wikipedia.org/wiki/Measurement_uncertainty

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#609545  01/13/09 04:27 PM
Re: Stoppers temperament

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Registered: 09/20/04
Posts: 1778
Loc: Massachusetts

Originally posted by Erus: "the formula can be transformed into the relation between time and frequency of waves". Then, it is transformed and even marks: "...Here, there is no 'h'... The position and momentum of a wave in space have been changed in form to the time and frequency of a wave..." [/b] He eliminates 'h' by using the energy of a photon, which contains 'h'. In so doing, he ends up an 'h' on both sides of the equal sign, and he is thus able to divide it out. Without using the energy of a photon, the 'h' is NOT eliminated. That is the whole point of what I've been saying. His derivation relies on sticking in the energy of a photon, and then, with no explanation or justification, claiming that the result is valid for any kind of wave. Unless you or anyone else can give us valid reasons why using the energy of a photon in this context is valid, his thesis is just so much bologna. Look carefully at his equations and you'll see his slight of hand. I have no interest in discussing this any more. I think I have clearly stated the flagrant problem with the author's derivation. The math doesn't lie. This is not an argument about what precision or exactness meanswhat's at issue is ONLY the author's mathematical derivation. I'm done.

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#609546  01/14/09 09:04 AM
Re: Stoppers temperament

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Registered: 12/10/03
Posts: 787
Loc: Cincinnati, Ohio

Besides arguments about the theory behind the tuning, I still am curious about the tuning software. It's hard to get any information. There is virtually no information on his website. When I contacted Mr. Stopper a few weeks ago, he emailed back and just said to read the mailing lists and forum. That was it. Well, the PTG archives have been down. You can find some cached pages. There must have been some high praise on the PTG lists that he is banking on. There are no trial versions of the software available, so you can't try it out.
The basic concept of what he is trying to do has potential. If he says that the program doesn't use memory, I think he just means that it doesn't stored calculated tunings. If the program has one set stretch standard, this simplifies calculations, doesn't it? It wouldn't have to take measurements and do calculations before you start. It could be doing calculations in the background as you tune and it gathers information. It obviously would use some memory to run the program. It must take some sort of reading, and maybe it reads inharmonicity as you tune. But, since there doesn't seem to be a way to get information on this, we are left to guess.

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#609547  01/14/09 09:47 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Since no one has posted on how to aurally tune beatless twelfths I will give it a try, even though I have never tuned it. I choose to refer to this tuning as beatless twelfths rather than the “Stopper” or “OnlyPure” method. I am not sure what those are and do not want to give out misinformation on Mr. Stopper’s work.
Since this is based on beatless twelfths, it seems that it should only be used with Equal Temperament. Otherwise, any key color will shift by a fifth for each twelfth of the piano's scale. A full keyboard arpeggio would progress through many tonal colors.
When tuning perfect twelfths there is a stretch added beyond what is required by inharmonicity for beatless 2:1 octaves. The additional stretch is 2 cents per 19 semitones, or 0.1 cent per semitone. So an octave will have 1.2 cents, a fifth 0.7 cents and a fourth 0.5 cents of additional stretch. The fifths will beat one third slower and the fourths one quarter faster than they would when tuning with beatless 2:1 octaves.
The A3A4 octave should be wide by one beat in three seconds. When this is established, a check of octave type can be used as a reference to tune other octaves until sufficient notes are tuned to allow beatless twelfths to be tuned. The m6M3 test for 8:4 octaves may be helpful.
An RBI test for the beatless 3:1 twelfth is the M6M17 test. Example: F2D3 beats the same speed as F2A4
A SBI test for a beatless 3:1 twelfth would be the P5P8 test. Example: D3A3 beats the same as A3A4.
Since the twelfth uses the low partials of 1 and 3, but RBIs use the higher partials from 3 thru 6, a sudden change in RBI beat rates can be expected across the tenor break on smaller pianos.
A tool that spans a twelfth on the keyboard is probably a good idea, especially at the extreme ends of the piano.
I skipped the math, but if someone asks, I will provide it.
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#609548  01/14/09 10:00 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

RoyP:
I suspect, but do not know, that Stopper’s tuning device tunes to theoretical pitches based on the 19th root of 3 and does not measure inharmonicity.
This could be a melodic model of the human ear and the best compromise between pianos. In other words, this may be the pitches that people want to hear and also may be a great way to tune pianos with different scales so that they sound good together.
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#609549  01/14/09 10:26 AM
Re: Stoppers temperament

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Registered: 12/15/06
Posts: 2519
Loc: Mexico City

It is clear that what you say is correct. But it is not enough to tune the Streched ET of Mr. Stopper.
How do you set the 19 notes in the temperament 12th? A la Braid White? You tune from the A4 note by fifths, expanded fifths, until you reach the 12th to check if it closes the circle of 12ths?
Or can you proced with another scheme a la CM3rds, that is: tune A4 to 440 Hz, then D3 a pure 12th below and from that point subdivide this 12th in smaller intervalls in order to tune the 19 notes that build up your 12th?
The problem here is that 19 is a prime number, it is not divisible, so you can't construct the 12th adding smaller similar intervalls, you can't subdivide the 12th in smaller similar intervalls.
You only can estimate expanded octaves,fiths, fourths, etc. to try to build up your pure 12th. And this estimations may be wrong and uneven, ruining the "expanded ET".
No, I was wondering, hearing Jurgen's words and Stopper's claims about Onlypure tuning, if there was a procedure to tune a circle of "tonicfithoctave" notes in which you obtain the cancelation of beats. I guess that it is this cancellation of beats that can help to be sure you are on the right way when setting the 19 notes of the temperament 12th.
Hasn't Mr. Stopper published a book or article about the Onlypure method?

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#609551  01/14/09 10:51 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Gadzar:
I think that any method of tuning ET could be used. As the twelfths are tuned, it would be corrected and refined by using the usual chromatic tests.
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#609553  01/14/09 11:46 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Gadzar:
I respect your prerogative to believe that this is something different.
I think this is only a stretched ET. By ET I mean that there is no difference in key color.
If D3A3A4 is an example of the “tonicfifthoctave” that is being mentioned, then it is the same as the P5P8 SBI test for a beatless 3:1 twelfth. It does not matter where the middle note is, within reason. The fifth and the octave will have the same beat rate. This may be why I like 4:2 octaves so much. The fourth beats the same as the fifth in the P4P5 test.
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#609555  01/14/09 01:43 PM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Gadzar:
Thanks for continuing this. I am really enjoying it.
Because of inharmonicity, the 19th root of 3 will not produce beatless twelfths any more than the 12th root of 2 will produce beatless octaves. Only by tuning so that the partials match can an interval be beatless.
Any note can be tuned so that there is a beatless 12th above or below it. The other notes do not matter. And as long as the test note for the P5P8 test is reasonable there will be equal beating within the “tonicfifthoctave”. The P5 could even be wide with a narrow P8! To also have progressive beat rates, then the fundamental frequencies must also increase at steady rate, something a little greater than the 19th root of 3 due to inharmonicity.
The above paragraph could be reworded and still be valid when using the 12th root of 2 and any chosen octave type, or even the 7th root of 1.5 and the M6M10 test for beatless fifths.
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#609556  01/14/09 11:48 PM
Re: Stoppers temperament

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Registered: 12/15/06
Posts: 2519
Loc: Mexico City

Originally posted by UnrightTooner: Only by tuning so that the partials match can an interval be beatless. Any note can be tuned so that there is a beatless 12th above or below it. The other notes do not matter. And as long as the test note for the P5P8 test is reasonable there will be equal beating within the “tonicfifthoctave”.[/b] That's the point! I am not talking about a beatless interval nor equal beating intervals. I am talking about a beat in an interval that cancels a beat in another interval when sounded together. Furthermore this two beats have not the same rate. For example in A3E4A4 the 2:1 octave A3A4 beats at +0.31 BPS, the 3:2 fifth A3E4 beats at 0.47 BPS (minus sign for narrow interval, positive numbers for wide)and the fourth E4A4 beats at +1.88 BPS. The amazing is that when the three notes are sounded together you hear no beats, they cancell each other. That's unique to this tuning, no other temperament does that. If you calculate de deviation in cents from ET you'll find that Onlypure tuning has an increasing deviation from 0 cents for A4 to 4.94 cents for A0 and to +4.01 cents for C8. As it is an expanded ET the amount of deviation in cents increases constantly as you get far from A4. In that aspect it is also unique! No other temperament or tuning system has this characteristique. In all octave based temperaments the deviation of a given note remains constant no matter what octave it is in. For example in Bill Bremmer's EBVT the notes C0, C1, C2, C3, C4, C5, C6, C7 and C8 all have the same amount of deviation of +3.8 cents from ET. So when aurally tuning this temperament you can't simply use the same techniques or tests you use in ET. This temperament behaves differently. You know I am an ETD oriented tuner. I am not able to program Onlypure tuning in my ETD, because I can not set the 12 figures it asks to set a temperament. In Onlypure system there are no 12 figures, there are 88 figures. Even if I try to make measured tuning (interval tuning) with my ETD, I can't because I don't know how wide the interval must be and which partials are involved in. The same thing happens when I try to tune it by ear, I don't know what to listen to! Except for the initial pure 12th D3A4. I hope you can understand what I am trying to explain, my bad english poses me strong limitations.

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#609557  01/15/09 08:27 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Gadzar:
I think your English is good, better than Jerry’s. How about an English as Second Language Story to lighten things up? On one particular ship I had a helmsman that was from Honduras. (All the Hondurans I’ve met were fine people.) Anyway, his English was adequate. One day a messman came up to the bridge to blab a while with the helmsman, but the helmsman did not say much. Later I asked him why. He said “Mate, I know just little English. (holding his fingers up about an inch apart) I do not want to waste it”
Did you actually hear the intervals that you mention and hear the resulting effect? Or are these beat rates what you calculated and are assuming that they will sound a certain way from what others have described? Also, I thought that we were talking about the P5P8 intervals not the P5P4 intervals. We seem to have been discussing different things. Glad you made this clear.
The idea of equal beating intervals “cancelling each other out” always bothered me. I know now that is not what you are talking about, but I thought I would mention it. Since the beats are in phase, they would reinforce each other, not cancel each other out. But since they are equal beating, the sound would be more pure because there would not be the sum and difference of the two beat rates confusing the sound. I suppose it is just semantics.
I don’t know much about ETDs so I can’t say whether my suggestions will work for tuning perfect twelfths. But if one of the “octave types” that can be selected is 3:1, then this should produce beatless twelfths. Or you could tune a beatless twelfth, measure the frequencies, do the math, tune the other notes and then tune beatless twelfths by measuring the third partial (direct comparison). Another possibility is to calculate the frequency for A3 so that the A3A4 2:1 octave beats +0.31 bps, determine the octave type, enter this octave type into the ETD, and then tune the notes in this octave. Direct comparison can than be used for tuning the twelfths.
Looking at this mathematically I see it as a cut and dried interpolation / extrapolation problem.
The beat rate numbers that you gave brings up a problem. The numbers you give may be for a particular piano scale, or may be theoretical, but they could not possibly be for all piano scales. So, if these beat rates do produce a certain effect, it would not be for all piano scales due to differing iH.
You mention that beatless twelfths are unique: “As it is an expanded ET the amount of deviation in cents increases constantly as you get far from A4.” Any octave tuning scheme that accounts for iH will have this effect. This is shown with the Railsback Curve.
I guess you didn’t find any math errors in my earlier post. I used some “rules of thumb” and did it in my head.
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#609558  01/15/09 09:43 AM
Re: Stoppers temperament

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Posts: 2002
Loc: Murphys, Ca

Too bad the archives for the PTG lists have been lost by the new server. Stoppard did reply. He said it is not 19th root of 3. Very close. Fred Sturm from the U of T Austin covered that. I don't know enough of what he said to relay it here.
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#609559  01/15/09 09:54 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Thanks Keith. I will continue to refer to beatless twelfths and not "Stopper's" or "OnlyPure".
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#609562  01/15/09 01:09 PM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Gadzar:
I think tuning the A3A4 as a wide 2:1 octave so that it beats once in every three seconds will be as close to ideal as can be tuned anyway. The iH is already incorporated into this interval. And until all twelve notes (or with beatless twelfths all nineteen notes) are tuned along with a number of octaves, can the progressive beating of all the intervals be tested which is the proof of ET. Any errors should be apparent as the twelfths are tuned and other intervals are checked.
Even with a perfect set of CM3s, there is guess work in getting the fourths and fifths correct. Why would tuning beatless twelfths aurally be any different?
If your ETD can give an accurate reading of the third partial of A440, divide it by 440 and find the 19th root of the result. By applying this to A440 you can calculate the frequencies to tune as long as there are no changes in the rate of change of iH in the scaling.
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#609563  01/15/09 01:16 PM
Re: Stoppers temperament

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Posts: 5628
Loc: Bradford County, PA

Jurgen:
Please don't think that I am trying to degrade the value of this tuning, which I admit I have not heard. I am only discussing how beatless twelfths may be tuned, which I also admit may not be the Stopper or the OnlyPure Tuning. No one else has offered to try, so I am.
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#609564  01/17/09 01:24 AM
Re: Stoppers temperament

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Registered: 09/22/08
Posts: 1011

Originally posted by Roy123: Originally posted by Coolkid70: I looked into it a little more, and it does indeed seem that the Heisenberg Uncertainty Principle does have an effect on reading the vibrations of a string. The main result is that the longer you attempt to read the frequency, the easier it will be to determine. An informal discussion can be found here: http://www.geocities.jp/imyfujita/wtcuncertain.html [/b] Please, anyone, correct me if I'm wrong, but I believe the mathematical derivation that purports to show that the uncertainty principle applies to musical waves is utter hogwash. The derivation starts with the formulas for the uncertainty principal and for energy, but on the 6th line of the math, the author introduces the energy of a photon, and uses that to derive the result. What does the energy of a photon have to do with measuring the vibration of a sting? Rightnothing. Plus, one can disprove his theory practicallyone can measure the frequency of an electronic signal with extreme accuracyaccuracy that is far better than his supposed proof indicates. Bah, humbug! [/b] You're quite right. Quantum mechanics has no place at all in piano tuning. There's no uncertainty about this. Indeed, there's much certainty ... The goof who's perpetrating this crap CERTAINLY has no idea what he's talking about. (My qualifications: BS degree in Physics and Mathematics)

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#609565  01/18/09 09:24 AM
Re: Stoppers temperament

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Registered: 04/02/08
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Loc: Niagara Region, On. Canada

If you were using an optical device to measure the string frequency the photon might come into play. Is it possible this is the connection?
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#609566  01/18/09 10:05 AM
Re: Stoppers temperament

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Registered: 09/20/04
Posts: 1778
Loc: Massachusetts

Originally posted by Emmery: If you were using an optical device to measure the string frequency the photon might come into play. Is it possible this is the connection? [/b] No, because you'd be using an enormous number of photons to measure movement that's huge relative to quantum dimensions. Quantum mechanics is fascinating and somewhat disturbing. I say disturbing because it describes how tiny particles behave in ways that defy any logic. Yet, the behavior described and predicted by quantum mechanics has been verified and measured to astonishing accuracy so we know that it is a successful theory. According to legend, even Einstein was upset with quantum mechanics, and said, "God doesn't play dice with the universe," or something like that. I don't know if he really said that, but it has been widely reported that he did.

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#609567  01/19/09 08:28 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Originally posted by Keith Roberts: Too bad the archives for the PTG lists have been lost by the new server. Stoppard did reply. He said it is not 19th root of 3. Very close. Fred Sturm from the U of T Austin covered that. I don't know enough of what he said to relay it here. [/b] Thanks, Keith: I was able to get some posts from Fred Sturm on the subject by googleing “site:ptg.org stopper fred sturm” and then clicking on “Cached” for the desired link. No, it would not be the 19th root of 3, but something a little larger for instruments with iH. And when tuning aurally, it probably won’t be beatless 3:1 12ths, but rather a blend of nearly beatless 3:1, 6:2, 9:3, etc 12ths. I may try beatless twelfths on the High School’s Baldwin R. They recently bought a 7 ft Boston and I expect the R will need extra stretch to blend well. I know that they will be using them together.
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#609568  01/19/09 09:21 AM
Re: Stoppers temperament

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Registered: 08/21/02
Posts: 3844
Loc: Madison, WI USA

At the convention last year, I attended Bernhard's class and heard the piano tuned the way he does and it sounded remarkably clear. There was even an element of the "pipe organ effect" that I get with the way I tune. I asked the question, "Couldn't the same effect be had by simply tuning ET within a wider than usual octave, such as a 6:3 or perhaps even a bit wider, so that the 12ths outside the initial temperament octave would end up being beatless?"
The answer was "No!" The reason given was that the temperament was not based on equal divisions of the octave in 12 parts but equal divisions of the 12th into 19 parts. I'm sorry but I still don't get it. Wouldn't an initial octave made wide enough end up producing the very same thing? If not, why not? It seems to me that many technicians do that very thing, including very well know technicians such as Jim Coleman, Sr. RPT and Virgil Smith RPT.
There is no question that a wider or narrower octave makes ET sound differently and there can be a certain "magic" when a certain "sweet spot" is found.

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#609569  01/19/09 09:34 AM
Re: Stoppers temperament

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Registered: 05/04/04
Posts: 2002
Loc: Murphys, Ca

He must be using the 12th to determine stretch instead of the octave. Tune the 12th pure and make all the 5ths the same. Then the octave falls where it does. All the ETD has to do is listen for the 3rd partial and calculate the tuning.
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#609570  01/19/09 10:22 AM
Re: Stoppers temperament

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Registered: 11/13/08
Posts: 5628
Loc: Bradford County, PA

Bill & Keith:
This is scary… We seem to be agreeing with each other!
If a particular octave type produces beatless twelfths in the mid section, and beatless twelfths are tuned outwardly from there, I don’t see how there could be a difference.
I think the practical way to aurally tune this is with a wide 2:1 octave that beats once in 3 seconds, set the temperament in whatever manner is customary, and when the beatless twelfths are tuned, make adjustments as needed to even out the progression of M6s and M10s (never just one or the other.)
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