Well, that's a good point. But the cent system and ET are still based on a doubling in frequency for every octave (hence the base 2 in the equation) and twelve notes in each octave (hence the 12 in the exponent), regardless of the detuning required by aural tuning. If the strings of a piano produced pure sine wave fundamentals, you wouldn't have inharmonicity. You could just as well base a musical system on 15 notes per octave using 2^(1/15) But it would probably sound like hell. The 12-note octave was invented way before ET came along and was based on sonorous ratios, like 3:2, 4:3, etc. ET just evens it all out. Don ----- Original Message ----- From: "Kent Swafford" <kswafford@earthlink.net> To: "Pianotech" <pianotech@ptg.org> Sent: Monday, March 15, 2004 6:45 PM Subject: Re: Beats vs cycles vs cents > Well stated. > > Of course, on a piano that is finely tuned in Equal Temperament, you'll > find few, if any, half-steps that are tuned exactly 100 cents apart. Or > are cents redefined for pianos to allow for the vagaries of > inharmonicity? :) > > Kent Swafford
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