Beats vs cycles vs cents

[Don A. Gilmore]

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