TUNING digest 1188

Just a note to alert harmonic scholars out there of an excelent new book by
W. A. Mathieu called "Harmonic Experience". The stated purpose of the book
is to reconcile the phenomenon of 12-ET with the actuality of just
intonation. It is a fantastic addition to the literature that is
breathtaking in its depth and clarity.

Harmonic experience: tonal harmony from its natural origins to its modern
expression...

ISBN 0-89281-560-4

publisher:
Inner Traditions International
One Park Street
Rochester, Vermont 05767

www.gotoit.com


Scot Gresham-Lancaster
< Neo-Luddite Technology Victim >
ph: 510-885-3150
fax: 885-3461
www: http://tesla.csuhayward.edu/~scot/sglbio.html



SMTPOriginator: tuning@eartha.mills.edu
From: Peter.Blasser@oberlin.edu
Subject: et fretting question
PostedDate: 25-09-97 17:05:35
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On Thu, 25 Sep 1997 Peter.Blasser@oberlin.edu wrote:
> Why does everyone use 22tet instead of 24tet frets on their instruments?
> It seems to me, after testing it out on a spreadsheet program, that 22tet
> does not imitate 4/3, 16/9, even 9/8 well enough. I do see a better
> imitation or ability to play 7/4, 5/4 and quarter tone tetrachords. has
> anyone heard a 22tet compared to a 24tet? Is there a noticeable
> difference? I guess what it all boils down to, is, what sounds best?

The reasons for this are based in a concept for which Paul Erlich coined
the term "consistency". Paul E. and I had a lengthy discussion on this
some time back in which some variations and extensions of the concept
also came up, but in brief an ET is consistent within a given harmonic
limit if the ET's approximation of harmonic intervals within that limit
is distributive. Example: 12TET is consistent within the 5-limit
because 5/4 is approximated by 4 steps, 6/5 is approximated by 3 steps,
and their product 3/2 is approximated by 7 steps.

To get back to the question, 22TET is consistent up to the 11-limit,
while 24TET is only consistent to the 5-limit. (In this respect it is
actually worse than its subset 12TET, which is consistent to the
9-limit.)

Peter, if you are interested I could dredge up some of the messages from
the last time we discussed this. (Hey, is the list archived anywhere?)

--pH http://library.wustl.edu/~manynote <*>
O
/\ "Well, so far, every time I break he runs out.
-\-\-- o But he's gotta slip up sometime . . . "



SMTPOriginator: tuning@eartha.mills.edu
From: flynn@mills.edu
Subject: w.a. mathieu's _harmonic experience_
PostedDate: 25-09-97 19:46:14
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>Why does everyone use 22tet instead of 24tet frets on their instruments?
>It seems to me, after testing it out on a spreadsheet program, that 22tet
>does not imitate 4/3, 16/9, even 9/8 well enough.

"Well enough" is of course relative. If my memory serves, 22TET's
fifths and fourths are about as far off as 19TET's, although in the
opposite direction. And again, if memory serves 22TET does a pretty good
job of approximating 7:6, 6:5, and 5:4.

22TET also has a syntonic pseudocomma, which can be cumbersome at first,
but opens you to some intriguing, sneaky musical effects.

Ivor Darreg's main reason for pursuing 22TET separately from
quartertones and 19TET, was that it has a "restful" mood compared to 19TET
having "lots of zonk", and 24TET having 12TET's 'restless" mood.



SMTPOriginator: tuning@eartha.mills.edu
From: mr88cet@texas.net
Subject: Re: 22tet and 24tet
PostedDate: 27-09-97 18:20:02
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