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I spent some time reading the cached pianotech archives.

There were posts from Mr. Stopper mentioning how the temperament is set by listening to the 12th along with other notes that are a 5th from one of the notes that make up the 12th. There are certain ratios that these notes are tuned to. I am guessing that this is the process of using “SuperSymmetry”. I am also guessing that for different scalings, that the 12th may not be a beatless 3:1 or 6:2 or whatever, but a compromise in order for these tuning ratios to work out as good as possible.

This seems very plausible to me, being a fourths and fifths tuner. I have never been completely satisfied with the idea of picking an octave width or type and going on from there, even though that is what I do. Wouldn’t there be a best octave width or type for a particular piano? Why not pick one so that the fourths, fifths, octaves and twelfths sound best? This may be what Stopper is doing. Whether tempering this way is also best to the extreme ends of the piano is another matter.

Yes! ! !

I've been wondering how to interject this into the discussion. Not only a "best" octave width, but a "best" 12th. I'm only guessing, because I haven't had a chance to hear or analyze a Stopper tuned piano...

During the work I did years ago on alternate temperaments, there was a group of us communicating and creating, tweaking, spreadsheeting and learning. The graphs that most of us have seen focus on the widths in cents of the major thirds and other intervals. While helpful, these graphs just weren't showing what I was hearing. We went back to predicting beat rates... still wasn't what I was hearing. Not until we got to the point of realizing that in a chord there is a major third and a minor third stacked - and that the ratio between the beats in these two intervals might have more to do with the feeling of a tuning than the width of the octave.

We found that in equal temperament the ratio (m3/M3) is the only thing that stays constant. Robert Wendall (who has WAY more math ability than I) was able to construct a fairly strong temperament that had equal ratios. The people that played it thought it too bland or equal...

Which brings us to the subject at hand - I believe that while listening for the octave/doubles/triples/12ths... the individual partial matches (2:1/4:2/6:3..) aren't nearly as important as we may believe. It is the blend of all, and how the beat rates interact for the "syncronous" effect.

There's always been a bit of "voodoo" around Stopper's ideas - probably because he is trying to keep parts secret so that he can market it... I've only heard one report about someone that has used the software, and I haven't seen any evidence that it repeats what he does aurally. Until there is more solid information, we're all just guessing.

Ron Koval

Ron:

Thanks so much for joining in.

“We found that in equal temperament the ratio (m3/M3) is the only thing that stays constant.” I think this would be because the test for a 6:4 fifth is the m3-M3 test. I have been pooh-poohed here for using this as a test to set my fifths, and the M3-M6 test to set my fourths. On challenging pianos this results in a more even color across the break even though the M3s jump in beat rate.

This settles it. I’m going to make a 12th spanner and see what happens.

Jeff, Ron said it better than I could have. Thanks, Ron. I explained to Gadzar in a private post that in usual ET, each octave size is actually different, not all exactly the same in any one part of the piano, even the temperament octave. Different, yes but very close to each other. I gave the example of a set of hammers or a loaf of Italian bread, take your pick.

Each hammer (or slice of bread) is a slightly different size. If you switched any two of them, you could tell the difference but if you went up or down several pieces and switched them, you could. Certainly, if you took one from the end and switched it from one in the middle, there would be a large difference.

So, when tuning ET aurally, the best way to get the temperament "equal" is to insure that the F3-F4 and A3-A4 octaves are *within* 0.5 cents of each other. (Sometimes, making them numerically exactly the same doesn't quite work but anything more than 0.5 cents doesn't work either).

When I tune the EBVT, I have some 5ths that are pure, some barely tempered and some tempered more than in ET. This causes me to tune a variety of differently sized octaves outside the temperament and up and down the piano. When I get to the point where I have a double octave, I compare it with the octave and 5th (12th) and make the two equal beating. However, in normal practice, I start favoring the 12th after about a half octave (going up) and then tune pure 12ths but at the very top, I expand both intervals.

So, I can well imagine that while Bernhard calls the idea pure 12ths, what he really does is tune the 12th pure in part of the piano, maybe a good part of it but at some point he goes beyond that. Perhaps in the middle on some pianos, those 12ths are somewhat but just very slightly contracted.

I talked to him personally about it but left with more questions than were answered. Steinway tuners in NYC for example are well known for stretching the temperament octave enough so that the 12ths are pure. "It is not the same thing" was the answer.

Bill:

Again the question arises: Is what Stopper is doing different in approach or different in result? If more than two notes are listened to when tuning, as he says they are when tuning aurally, then I would say both.

Not sure what Ron said better than you could have. Was it the word “Yes! ! !” ? ? ?

Here's my guess at what's different.

1. I don't remember how he sets the octave+5th temperament - do you remember reading about that? I've played with Tunelab enough to know it's pretty easy to set up a curve for one partial to end up with that width. The question then becomes which partial??? (It's a whole 'nuther discussion to notice the differences between smooth-curve tunings of different partials on the same piano.)

2. Once the "temperament" section is set, it should be pretty easy to expand the tuning outwards using the 12th spanner. The idea sounds similar to tuning a unison... You've got two tuned notes - the octave - add the untuned 12th, listening to all three together. Go slightly above, and slightly below to listen for the "best", or "least bad" spot and call it done.

While I find it hard to believe that the beats cancel out, I don't have any problem with the idea that there is a "best" spot that our ears find to place the 12th.

I seem to remember that part of Stoppers first writings had something about:

When tuning the octave and octave+fifth the goal is to find the placement where the sum of the beats of all matching partials is minimized.

So if I remeber correctly, he wasn't concerned with any particular partial match, rather ALL of the possible (audible) partial matches - and how they sound together.

Ron Koval

Ron:

Here is A Link to a Cached Pianotech Archive.

These paragraphs lead me to believe that three notes are played together and the best blend, perhaps without the 12th being pure (note the tildas ~) is the goal:

Bernhard Stopper has recently discovered, that only in this tuning solution,
all beat ratios of octaves and fifths are symmetric to the interval ratios,
that means they have also ratios of 1/1, 3/1, ~2/1 and ~3/2 and multiples
of
them like the interval ratios.

Beside the mathematical mysteries, this fact is responsible for the
phenomene, that in every three-note interval combination consisting of an
octave and a fifth, the beats are phased out to a pure state in the
stopper-tuning (there are six such three-note combinations in a perfect
twelfth who have all a pure state in the Stopper Tuning).

This is correct.

The "sweet spot" can be achieved when the duodecime tuning tool (as shown on a photograph on my homepage) is used, to tune the duodecime aurally pure. (I prefer the term duodecimo because many technicians still think a twelfth is an octave)

Here is the link to the duodecime tuning tool photograph:
http://www.piano-stopper.de/html/stopper-stimmung.html

This approach is slightly different from listening the 3rd partial of the lower note together with the first partial of the upper note, (what is probably in use by some tuners, like NY Steinway tuners, as Bill mentioned).

To listen to the 3/1 partials is like tuning a 2/1 octave. By using the duodecime tuning tool, one gets the "sweet spot" duodecime, which is slightly beyound the 3/1 duodecime.

As i published the method with the duodecimo tuning tool in euro-piano twenty years ago, it woud also not be surprinsing, if there are some tuners around using the duodecime tuning tool method already.

The goal is to keep the symmetry present in this temperament also under presence of nonlinearity, to produce the special acoustic effects. There is no voodo or quantum mechanic calculations in my software, (which deals the nonlinearity in the background). There is only heavy math. Although the discovered inherent symmetry sometimes appears to me like voodo, in fact it´s just beauty.

My statements about the uncertainity principle were contributed to the problem of real time frequency measurement in extreme accuracy. There is a limit of precision, the shorter the time interval is. We (as tuning professionals) do not have the time to measure about a second or two to evaluate the frequency to get it accurate enough, then turn the lever and measure again, that´s all about that.

As there are always experts around who do not hesitate to throw around with their titles, i want to provide another link about the matter from a scientific source, what simply figures out what uncertainity principle is (a principle, nothing else):

http://www.math.ntnu.no/~yura/Projects/uncert_project.pdf

I rarely jump into forum discussions, I apoligize for that.

Bernhard Stopper

Mr. Stopper:

Thank you for joining in.

When I started contributing to this topic, I was very careful to talk about beatless 12ths as separate thing from your tuning because I was not sure that they were the same thing. It appears that I was right; they are not the same thing.

I understand what you mean by a “sweet spot” and it should be easier to tune a twelfth this way than an octave because of the fewer coincident partials. But what about the other notes that must be tuned to form the temperament? From the Pianotech archive, I understand that octaves and fifths within the 12th are listened to, made beatless as possible, and the temperament proceeds around the circle of fifths. I imagine that on some pianos the twelfth’s “sweet spot” might need to be compromised for the other intervals to sound more pure.

I plan on making a twelfth “spanner” and giving this a try. I use the Braid White sequence and am very comfortable with it. Do you have any tips on setting the temperament with your method?

FWIW:

I made the tool and tuned my CW Console to beatless 12ths, but did not care for the sound. I did learn some things that will be useful, though. I’ll give details if anyone is interested.

Hey Jeff - onward to experimentation!

Now take a step back - you tried what the Stopper tuning is NOT... We know for sure that he's been very clear that his tuning is not a beatless 12ths tuning - because he's said as much many times.

A little detective work:
(from the cache you linked)

"For inharmonicity related
instruments, pure means the state, where the sum of the beats is minimal."

"that in every three-note interval combination consisting of an
octave and a fifth, the beats are phased out to a pure state"

"pure 3-note
combinations of octaves an fifths, and there are four different combinations
of them, (an octave and a outer upper fifth, an octave and a outer lower
fifth, an octave and a inner upper fifth, and an octave and a inner lower
fifth)"

"It is not possible to reach this precision with the usual electronic tuning
devices or the usual two-note aural bearing plan techniques"


So where does that leave us? Usually confused...

Most of us in North America, with the aural tradition strongly influenced by the machines and the reliance on coincedent partials get caught up in the goal of beatless intervals. This detour of the tuning world has led to a much higher level of precision than was possible before, yet may lesson the accuracy of the goal of a musical result...

If I read/interpret the above properly, it seems to say that every octave-fifth (inside and outside) is tuned so that the sum of all of the sounding beats is minimized. Nothing there indicates that the goal is beatless 3:1 or 6:2 octaves...

That would mean that after setting A4, A3 and D3 are manipulated to find the minimal beating loctation when all three notes are played together. Then that D3-A4 temperament is divided into the 19 steps. After that, every note to be tuned is moved as part of an octave-fifth triad, as opposed to a two-note interval as we are used to using.

Make any sense?

Ron Koval
(tuning sleuth)

Ron:

The example of A4, A3, D3 is perfect. What will result from tuning these so that they are as beatless as possible? A beatless 3:1 12th, a beatless 2:1 octave, and a beatless 3:2 fifth. Easy, but try to make an equal temperament out of it!

I understand that Mr. Stopper tunes the twelfth to be a compromise between 3:1 and 6:2. This is very, very close to being beatless 12ths unless this is not what Mr. Stopper actually does. I could hear enough difference between the 3:1 and 6:2 to make a compromise in the lower bass, but nowhere else. Elsewhere, tuning the 12ths was much like tuning a unison; there was only one place that was correct. It was very different than tuning an octave where there is a window that the octave can be in, and seem to be beatless.

Analyzing the 12th is interesting. If you take the two end notes and tune octaves within the 12th in order to have intervals for ET, this forms a P5 a P4 and another P5. The upper two intervals are a P4-P5 test for a 4:2 octave and the P4 must beat faster than the P5 for beatless 12ths. The bottom P5 must beat slower than the upper P5. The upper octave will beat the same speed as the lower P5 as this is the test for a 3:1 12th. And the upper octave will beat faster than the lower octave. The challenge is getting the P4 to the correct beat rate to create an ET.

"That would mean that after setting A4, A3 and D3 are manipulated to find the minimal beating location when all three notes are played together."

Ah ha! The "sweet spot"! When all of the slowly beating intervals, octaves, 4ths, 5ths *and* all of their multiples tend to cancel out each other's beating, you find a remarkable clarity across the whole piano.

When I do this withe the EBVT and play that long C Major arpeggio, the CE M3 is only half the speed that it is in ET and its M3 and M6 are also equal beating and thus cancel each other out. The arpeggio played and held has everything tempered but all you hear is a very slow wave that seems to pass up and down the whole piano. The strings from the lower and middle parts of the piano's higher partials match the fundamentals of the notes in the 7th octave and thus reinforce them and keep them ringing in sympathy. They sound like the tiny pipes that do not decay but keep playing constantly as the organist slowly lets up on the volume pedal until the whole chord fades out. It works on the the finest grand on down to Whitney spinets.

Bernhard's tuning, as I heard it at the convention in Anaheim, had much of that same effect except, of course that the C Major chord did not have the same M3-M6 tempering as the EVBT has. Yet, the manipulation of the octaves, 4ths and 5ths had much of the same canceling out effect.

In my view, he looks far beyond the narrow focus that most tuners have of tuning one interval at a time and trying to make each interval be the best it can be while ignoring what happens with the whole rest of the piano with respect to inharmonicity. This is where Brade-White and all of the other early tuning books fail us today. Even the PTG "Master Tuning" for the exam fails to do that (in a rather big way).

That is why I have always looked at that that theoretical way of tuning as just that, theoretical, not for public consumption and I never tune that way for any customer for any reason. There is always something better than that even though I acknowledge that most technicians believe it to be the end all, the "holy grail" of tuning.

Never be completely satisfied that what you have learned or been taught is the one and only correct way to do anything with the piano, tuning, regulation, hammer or part choice, you name it. Study all of the sources available to you and form your own set of experiences and conclusions. I know that is what Bernhard has done. I am SO looking forward to meeting him again and having a fine dinner with him in Grand Rapids. I am working on a way to have a piano tuned in the EBVT at the convention and will let everyone know when and where to find it when those plans are in place. Bernhard will likely do the same.

Ron, I think you are 100% right about Stopper's temperament. It consists of tuning three notes chords and not two notes intervalls.

Once you have the first 3 notes D3-A3-A4, or what ever they are, the point is to subdivide the 12th into 19 equal steps by tuning three notes chords. How? I don't know.

(Maybe we'll need a third hand with a second tuning hammer in order to tune two notes at the same time. . Plus, of course, the tool made by Unright to play the 12th intervall and the third note with the other hand.)

Unright:

I think you don't get the entire picture, you strive to tune beatless or whatever intervalls between a pair of notes. You talk about 3:1, 6:2 12ths, compromises between different coincident partials, 4:2 octaves, upper octaves beating faster than lower octaves, etc.

All that stuff is what all of us were, and are still, doing for decades.

I think Mr. Stopper goes a step forward. Listen to Stopper's words:

"It is not possible to reach this precision with the usual electronic tuning devices or the usual two-note aural bearing plan techniques"

underline:

"It is not possible to reach this ... ...with the usual... ...two-note aural bearing plan"

So it is not only a matter of tuning a given kind of intervall...

If anyone wants to really understand what I am saying, try it for yourselves. Make a spanner. I used 1/2 inch dowels 10-3/8 inches apart glued into a piece of wood with some action cloth glued to the ends of the dowels. Then tune A3 and D3 to A4 until the sound is as beatless as possible. I expect you will have the same results as I did. The three notes played together will form just intervals with each other. What could be more beatless than that? Now try to make an ET from these 3 just intervals.

O.K. Unright, I'll try it. I guess the sequence is something like that:

Tune
A4 to fork as usual
D3 to A4 around pure, only an approximation
A3 to [D3/A4] adjust D3 to get to the sweet point

from here, all the notes are tuned as 3 notes chords striving for the sweet point.

D4 to [D3/A4]
G3 to [D3/D4]
G4 to [G3/D4]
C3 to [G3/G4]
C4 to [C3/G4]
F3 to [C3/C4]
F4 to [F3/C4]
A#3 to [F3/F4]
A#4 to [A#3/F4]
D#3 to [A#3/A#4]
D#4 to [D#3/A#4]
G#3 to [D#3/D#4]
G#4 to [G#3/D#4]
C#3 to [G#3/G#4]
C#4 to [C#3/G#4]
F#3 to [C#3/C#4]
F#4 to [F#3/C#4]
B3 to [F#3/F#4]
E4 to [A3/A4]
E3 to [A3/E4]

The rest of the piano can be tuned by 12ths with an embedded octave.

What tests to use?

I never understood why a spanner would be necessary when the Sostenuto pedal is already there for just such a purpose. If there is none or it doesn't work which may very often be the case, the damper pedal may also be used in the same way the Sostenuto pedal is used. That is; play the notes first, then press the pedal. There will, of course, be a little extraeneous noise but the beats you want to hear will still clearly be heard.

Yes Bill, but then you have to use both hands to play the notes.

With the use of a spanner you can leave one hand on the tuning hammer while playing the notes with the other hand. It's easyer to tune that way.

Thanks Jim for the clip from the archives.

This:
3. F21 to D30 (sixth) with the same beatrate.This will result the 3. harmonic of this D30 to the same pitch as the A49 =440 Hz, the 12th is set now.

Seems to suggest that in 2004, Stopper WAS just setting a beatless 3:1 - as opposed to the onlypure definition of sum of the beats of 3 notes minimized...

Again, my perception is that the result is not that far from what a lot of us do with other methods. It IS however, often that last, tiny little bit that makes the difference between something good and something special. From Virgil Smith's "resonance" to Bill Bremmer's "pipe organ" to Bernard Stopper's "just beauty" - I think it is finding a way to make the whole piano work together the best way possible.

Ron Koval