Re: [Common Cents?]

"Brian Thomson, London UK" <bnt@email.com> wrote:
> From: "Brian Thomson, London UK" <bnt@email.com>
>
> Hi, folks. I have a concern which I'm going to have a go at answering
myself:
>
> I've noticed on this list that most posts can be divided into roughly two
topics: a) variations on 12-tone scales, and b) non-12-tone scales.
>
> What concerns me slightly is the use of "cents" in both cases to describe
scale intervals. It seems to me that a) cents only really fit 12-tone scales,
and b) cents are a linear "difference" of what is actually a geometric
relationship - they don't scale correctly for higher octave divisions.

A cent is just a conviently small interval with a frequency ratio of
2^(1/1200), which is about the minimum difference limen (MDL) of human
perception of pitch. Any interval in any scale structure can be expressed in
n cents as Interval (frequency ratio) = 2^(n/1200). Thus, it is _not_ a
linear measurement of frequency, but a linear measurement of pitch which is
(approximately) log frequency. It is true that the selection of 1200 cents
per octave does historically derive from the 12-et scale, but changing the
reasonably smallest interval to a "mil", 2^(1/1000), or a "bil", 2^(1/1028),
would just fly in the face of centuries of convention.

Fred Reinagel

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