Limits, Octave equivalence

Two things recently discussed on the list have taken me by surprise, and I'd
like to see more general discussion of them (or perhaps someone could point
me to an earlier thread or two?).

First, it seems that some prefer odd-limits while others prefer only prime
limits. Is there some controversy here? Both ideas strike me as equally
valid and useful concepts- simply different.

Second, some of us evidently don't believe that octave equivalence (2:1, give
or take a few cents :-) should be taken for granted, but is a merely
culturally-instilled idea. Holy cow! Have you never seen pictures of
waveforms? E.g., given two waves, one of which has a frequency at a
power-of-two of the other, the lower one will cross the zero point (volage-
or SPL-wise) only at points at which the higher one is crossing as well.
This is a unique property of frequencies related by powers-of-two; they
have, then a special relationship of some kind, no? The higher one is
repeating at the same frequency as the lower one, as well as at its own
nominal frequency. They can, then, in a very real and physical sense, be
considered to be the same note; i.e., the same "pitch" but in different
registers.

David J. Finnamore
Just tune it!

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>I have recently joined this group,

Welcome aboard!



>1) Well Temperament arose in the latter half of the 17th century and
>... the further a piece�s key is removed from C, the stranger it>will sound to the modern ear,

Actually, no. The entire point of well temperaments is that they are
about equally well in tune in all keys.

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