RE: definition of JI

I guess it's pretty well accepted that JI tuning is tuning using
small whole number frequency ratios. The difficult part is
defining small.

I guess no one would be surprised that my approach to the matter
is based, in part, on the Least Common Multiple. The other part
is absolute frequency.

The LCM of tones sounded simultaneously, together with the
absolute frequency determine the length of patterns in the sound
in the time domain.

I think the ear/brain as the ability to remember what is heard
for a certain length of time and remember it in great detail.
When the patterns in the sounds are comfortably within that
length of time, the ear/brain experiences the "pleasure" of
easily decoding the patterns.

As length of time it takes to reapeat the sound patterns
approaches the capacity of the sound memory, the ear/brain has
difficulty decoding the patterns, and we register that difficulty
as distress, or dissonance.

Some patterns actually take a very long time to repeat, but
include smaller patterns that are not actually alike, but are
very nearly alike. The ear can decode these patterns easily, and
also registers the fact that they are not exactly alike. This,
of course, is a description of tempered music.

But here we have a possible physiological basis for a definition
of small. Small would be when the ear can easily decode the
pattern. Large would be when the ear can't decode the pattern.

Marion

Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 14 Nov 1995 18:55 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id IAA19575; Tue, 14 Nov 1995 08:54:57 -0800
Date: Tue, 14 Nov 1995 08:54:57 -0800
Message-Id: <199511141625.RAA18992@musik.auc.dk>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

I'd be willing to bet that the ancient Greeks knew well of the similarity
between the syntonic and pythagorean commas, because I know that they were well
aware of the syntonic comma. But I don't know for certain that they used that
chord structure.

By the way, Bill Wesley (from the San Diego vicinity) has built ... three I
think ... instruments that use this principle profusely. They could perhaps be
described as "megakalimbas" in that they use metal tynes on a wood soundboard.
Form a quick look about two years ago, I would guess that they had about 150
tynes or so.


Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Wed, 15 Nov 1995 03:01 +0100
Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id RAA29858; Tue, 14 Nov 1995 17:01:45 -0800
Date: Tue, 14 Nov 1995 17:01:45 -0800
Message-Id: <199511150101.RAA04426@ella.mills.edu>
Errors-To: madole@ella.mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu