From rockkey@sbcglobal.net Tue Dec 04 05:51:04 2012
Subject:Re: 30 yr old Korg BX3 question-Hammond Tuning-Piano Stretch

Tuning on a real Hammond is a fairly close approximation of ET. Here are the offset values in cents:
A 0.0
A# -.28
B -.58
C -.57
C# -.67
D +.20
D# -.08
E -.13
F -.67
F# +.03
G +.02
G# -.70

A fine ear can of course detect the difference but as a point of reference, up to fairly recently, a typical inexpensive electronic chromatic or guitar tuner had an accuracy of plus or minus 3 cents. So that's a total deviation of 6 cents. Many people were happy with that even though it was potentially fairly coarse. In contrast, you see the deviations from Equal Temperament on the Hammond are all less that 1 cent.

Stretch tuning, IMHO is misunderstood even by some piano tuners. Stretch tuning is done in response to the inharmonicity of highly tensioned, stiff piano strings (actually hardened steel wires). Every individual piano will have a different (range of) stretch required due to the length, diameter and tension of the strings (called the piano scale).

The range of stretch on a given piano is due to the choices of octave tuning by the tuner. An octave can be tuned in many ways. Some examples are 2 to 1 where the 2nd partial (harmonic) of the high note is tuned to the 1st partial (harmonic) of the low note. 4:2, 6:3, 4:1, 8:1 are some other examples. Compromises are possible too so there can be many "correct" stretches depending on taste although some are better than others.

Basically, ALL (acoustic) PIANOS REQUIRE STRETCH TUNING, PERIOD. Sorry to yell but that's the bottom line and you can take it to the bank. If a piano is not stretched tuned i.e. if inharmonicity is not considered or taken into account, the piano will not be in tune. Like I said earlier, there is a range depending on the choices of octave tuning so one stretch may be wider than another for the same piano.

Cheers,
Rock

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