On Aug 21, 2021, at 9:21, Bruce Wahler via <
bw@...> wrote:
> Other harmonic-based tunings don’t need this – or at least have enough other problems to not turn to Stretch for their solution.
I think this might be the crux of the situation.? Equal Temperament is very close to an ideal choice, but tuners noticed that following the rules of tuning exactly didn't end up with the best end results, at least, to the ear.
But the string issue is real:? the windings do not track the center core perfectly, and the issue grows over the distance from the reference string -- in our case, usually Middle C.? So, it becomes a choice:? do we follow the mathematical model -- which results in the same beating between intervals of the *fundamentals* across the keyboard -- or do we focus on the beating between harmonics by stretching the tuning?? Since a piano is harmonic-rich, the answer seems to be the latter.
As you have written in previous message, harmonics are not problem, but inharmonicity of piano sound. And a certain role can play also psychoacoustics and pitch perception - it “seems” to our hearing that stretched tuned piano sounds better.
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But I still wonder if the process applies to digital piano samples; or to non-string instruments like the Rhodes.? It's difficult to answer, because any reference piano is only going to remain perfectly tuned for a very short time.? Within minutes, string tension and temperature/humidity changes conspire to alter the pitch of each string.? So, one cannot compare a grand piano vs. a sample (or modeled) piano and make strong conclusions about frequency relations, unless its possible to do all the analysis within minutes of a piano tuner's work.
Maybe it has some sense to use stretched tuning for well done piano samples of each note with many velocity layers, or modeled piano. But I don’t think there’s hardly any reason in using stretched tuning on FM simulated piano sound (which is far from real piano sound) or on Rhodes or Wurlitzer. But it is good that Yamaha used it on vintage CP series of electro-acoustic pianos with strings.
That said, sometimes adding a little imperfection improves the overall sound, even if the results aren't 100% accurate.?
Exactly, maybe that’s the reason for permanent interest in analog synthesizers (or recent boom of interest about modular synths), with all their pitch inaccuracies caused by unstable voltage control or oxidized key contacts.. And a good reason for the implementing various Random Pitch algorithms and functions in some digital instruments (including DX7 II D and its relatives).
Daniel Forro
