source file: mills2.txt
Date: Sun, 29 Jun 1997 20:13:28 +0200

Subject: Re: Partch Limit vs Prime Limit

From: mr88cet@texas.net (Gary Morrison)

>I have always used the term "limit" as if it were really "prime
>limit", and I think I am probably not the only person who sees
>things this way.

   I too am inclined to see it as primes rather than odds, although I don't
claim to but a little bit of experimental basis for that.

   The underlying principle for using odds, as I understand it (this is
coming from Dave Hill who changed his opinion from primes to odds), is that
octaves duplicate harmony, so anything that doesn't involve a factor of two
will produce a nonduplicate harmony.

   That makes sense under the assumption that there are no recognizable and
compoundable qualities of 3, 5, 7, or other primes.  That is to say that,
for example stacks of 3:1s or of 5:1s, do NOT have distinctive properties
of their own other than the duplication property of two.  I think they do
based upon 27:16 compared to 5:3:  27:16, to my ears, still has the steely
cold, brazen sensation of a fifth or fourth, whereas 5:3 has a genuine
sweetness to it.

   But I personally am not very firmly commited to that premise.  I think
it's quite clear that two other qualities of an interval are much more
significant than this prime- or odd-number basis idea:
*  The size of the interval.  No matter factors you put into a major sixth
   they'll all be much more alike than any tritone for example.
*  The simplicity of the frequency relationship (ratio) they come closest to.

   And "closest to" here is another question, and a complex one.  It
harkens WAAAAAAYYY back to a conversation on the list a long time ago
shortly after I joined, about how far off you can be from a given ideal
ratio before it becomes clearly something else in its own right rather than
a "bad" version of that interval.

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