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Doelkees: Excellent. Thanks for the quick response.
I think you meant an iH delta of .025 per semi-tone, n'est-ce pas?

The theoretical values are : less half a tone = -12% iH

Seem to agree with the numbers you find.

Changing pitch a little strong (444 Hz) show a very small lowering, but audibly the difference in tone quality is evident.

.025 per semitone, indeed. And I get 11% for the theoretical value.

Kees

I have never heard the inharmonicity change while tuning. The tension changes we make while tuning are a thousand fold or more below what would appreciably change the frequency relations amongst the partials. Unison coupling CAN change the energy distribution (Olek I think you use the term "spectra' for this), amongst the partials.

It would seem that the amount of stretch one chooses to use, in the upper octaves particularly, would affect the iH, which would in turn affect the required stretch to make an effective tuning. This iterative process would, in theory, converge on an optimal stretch for a given temperament. I would argue therefore in this case, that the stretch used would be different for different temperaments.

Aren't these two statements saying the opposite of one another?

This is what I love about piano technology...

So much more still left to be discovered.

Well, DoelKees' test implies that iH changes with a change in tension (all other variables unchanged), and Isaac has anecdotal evidence of the same result. It would seem logical, therefore that a well tuned piano will exhibit different iH across its compass than an out of tune piano, and it would seem wise to do several passes in order to converge on the best overall sound.

That's true that some pianists like their pianos tuned a certain way but many tuners are called upon to tune a piano without an interview with the pianist. That tuner would be wise to tune the piano to ET with perfect unisons. Aren't we splicing hairs here on my point though?

I don't think you appreciate the smallness of the effects involved.

Kees

So if my assumption that very fine tuning in the A440 area accuracy is less than 0.5cent difference between strings that sound perfectly in tune-that is a .025cent tolerance. That makes the inharmonicity difference between the perfectly tuned string and the nearly perfectly tuned string 0.00025cent. I can't hear that! And no one else can either.

It has long been suggested that when using a calculated program, to recalculate after a pitch correction. I have noted different values upon recalculating sometimes, sometimes not. I am still one that believes that the inharmonicity that a piano has depends upon the diameter of the wire, the speaking length and the pitch. If the pitch is altered significantly, then the inharmonicity may change accordingly. Whatever temperament may be used is too small of a difference to be significant. That much makes sense. Otherwise, the inharmonicity does not change significantly, only the readings of it may.

On another note, I was listening to the recording I made on March 9 in my car yesterday. With the way I had the tone set mostly for talk radio, (+2 treble, -2 bass and +2 front and -2 rear speakers), I had concentrated so much on pure unisons and with the tone controls set the way I had them, the compression of the final audio product and the temperament that was so maxed out equalized, the piano sounded more like a digital piano than a real one!

It was truly a case of a piano that sounded so in tune that it was terrible!

Who's going to break this news to Isaac?

x

Nobody told that this was heard as an inharmonicity change. (in unison)
I hear a small straightening of the spectra when the piano is tuned high pitched, but saying I hear an iH change there is , I admit exaggerated, as the power output is larger too.

What I mean is that iH is a part of tone quality, that it is not directly perceived, but at last in its effect to the spectra.

Pianos tuned lower than their pitch have a less well defined spectra, may be also for iH reasons.

Scaling is supposed to provide a smooth slant of iH, but many old scales do not.
Also the last treble section is often using a different octave progression, hence a differnt iH if the point is not corrected.
That way we find pianos that have "inverted" iH in the high treble (inverted in regard of the progression from mediums)

It happened me for a long time when I was using ETD, there is a tendency to make the tone "purer " and purer.

That is why I say we need a slighly different way of apprehending the tone, so to have it as pure as possible, without breaking the tone building"

One have to learn to be able to control the acoustical coupling at partials level (the iH part of the tone" vs the coupling at fundamental level, to keep the control on his job.

This was a huge problem when I was tuning in concert.

I noticed that your unison are sounding way different than some years before, they share a "construction" .

But you could deal with tone projection more than with beat fighting, at some point the energy provided by the strings follows its own path and it is useless to try to push it too much where it does not want to go.

It is not a question of leaving some sort of very slow beat, not at all, this is the way the energy is parsed, how long doe sit take to have anything put at its preferred loctation.

I seem to see that many tuners here believe that we tune some kind of moaning unison in order to have some "life" in the tone.
It have nothing to do with that.

I even feel that the sooner the tone is regulated after the initial hammer "crash" the more stable the tone is in the long run (while I may try to obtain a more or less rounded tone by enlarging the delay the crash take to stabilize in musical tone)

In the end the quality of tone that is changing the most is the tone projection, the ability to fulfill the room and to be heard with some clarity at some distance.

If the tone is not "build" that way, chances are the tuners will tend to rely on hammer dope and hardening, to get some support of the top spectra that is left too inconsistent if not.

The way the pianist use the piano makes a huge differnce of course, I remind a piano tuned for a concert.
In those times I was often anxiously wondering if I did make a good tone construction, as I noticed that with ear fatigue I had a tendency to clean so much the spectra it was getting lifeless at some point (and I could not really analyse that clearly)

The first pianist have a sort of hard touch and the piano make her no gift at all. All the nervous stress was heard, and I thought I had totally missed the tuning, it almost sounded false for so much unnatural precision.
Then another pianist played, with a better touch and more talk (more things to say with the music)

The piano then sounded bright but neutral and well tuned. no more roughness perceived.
But in that case he had to use more the sustain pedal he would if the tone had been less hard.

The difference between and optimal strong tone and a hard very clean tone is in the end relatively large.

One have to cool his ears to listen, and let the piano guide him.
The ETD are almost a difficulty in that context, anyway for me it was.

When tuning on stage, or in a romm with enough reverberation, I like to hear how the tone returns from the walls.

But when it is not possible being able to analyse the unison is a big help.

That said, only pianos with a sufficient level of iH allow to be at ease mastering the tone. Low iH pianos oblige you to straighten the tone, very little rounding of the fundamental is possible.

The iH differnce is absolutely not perceived in the unison, I do not understand what you mean there.
Pitch differnces in "almost perfectly tuned (make me smile) string may vary from 0.4 to 2 cts.
Very difficult to "measure" with ETD due to the coupling from the other strings, and the up and down motions of pitch in time.

Ih is used to obtain more power or more sustain, that's all.

as with the Bluethner and the aliquot 4th string, that is there to cause trouble to the unison.
That way it is colored.
If the ballast string was tuned perfectly straight with the others, it would just rob energy from them.

That subject is sensitive as no tuner want to be accused of making "Honky tonk tunings" that are often the sign of poor pin setting/stabilisation.

Also in my opinion, as Isaac reports and suggests, it won't be only tuning... meaning that correct frequencies (which would make a piano sound "in tune") should go along with tone quality (read color) and energy circulation (resonance).

Think of a singer: he/she might be "perfectly" in tune and yet sound terrible... Pro-singers normally depart from an amateur approach and start a process that goes far beyond their (perhaps natural) talent, they will learn how to manage their spectral content and their own flows of energy, so I do not think we can separate these three issues, again pitch, color and energy: taken individually, every single issue might reduce performances, but these issues all together can achieve the best performance.

Then I too would suggest to evaluate iH fluctuations (approximations) and influence also in consideration of other factors that apparently contribute to shaping the tone and making energy flow, all factors being related: active-pin//active pin-block//string-3-lenths-tensions//loads//and all the other details that produce the sound, hammers and dynamics of the piano action.

From the field: I recently tuned a baby-G for a colleague, so that in real time he could follow his ETD and record the job. I can confirm that the ETD was not sensible to some variations, both on single string's pitch and unisons, that for my ear would be determinant. To be clear, in order to manage and control partials, I - surely like others - will have to take into account infinitesimal variations that were far beyond the performance of that ETD, perhaps differences that we believe to be "...too small of a difference to be significant".

In this sense, I would not take the worse of what theory, maths and "science" can offer, for instance I would not confuse ETDs figures, how exact they seem to be, with the exactitude needed and that we are able to achieve aurally.

Regards, a.c.
.

Loren's prediction in the original post seems to have become true. I'm finding this discussion quite entertaining.

Can I call 'em or what?!

I do appreciate the smallness. However, I am a literalist, and if a claim is made that iH doesn't change with a small pitch change, and then is found in fact to do so, I am interested in that, regardless of the order of magnitude. Thanks again for your test.