Reply to Peter Blasser and Carl Lumma

Peter Blasser wrote,

>Why does everyone use 22tet instead of 24tet frets on their instruments?

Everyone? Wow, I thought I was the only one! (I did see a few in
Experimental Musical Instruments once). Considering the amount of
electric Arabic pop music I hear these days, I suspect there are a lot
more 24-tet guitars than 22-tet. Actually, I did inspire a guy (Steven
Rezsutek) on this list to refret his guitar to 22-tet, after he
independently came up with a lot of the same ideas as I did.

Let's say you're trying to play a 4:5:6:7 chord. In cents this is 0 386
702 969. In 24-tet, you'd start with 0 400 700. If you used 1000 (as in
12-tet) for the top note, your 7:6 would be 33 cents out-of-tune. If you
used 950, your 7:5 would be 33 cents out-of-tune. Both are pretty bad.
In 22-tet, using 0 382 709 982 has a maximum error of 17 cents (in the
7:5). That's about the same as the maximum error of a triad in 12-tet
(16 cents). Not too bad! (The same goes for 1/7:1/6:1/5:1/4).

Another reason I like 22-tet is certain scales it contains. The
pentatonic scale is a nice source for 3-limit harmony and is OK in 7-tet
but almost perfect in 12-tet. The meantone diatonic scale is a nice
source for 5-limit harmony and is OK in 12-tet but better in 19, 31, or
50-tet. I discovered/invented some nice scales for 7-limit harmony and
their optimal tuning is very close to a subset of 22-tet.

Carl Lumma wrote,

>If we can agree that there is a difference between re-tuning music made for
>100 cent equal, as powerful a model and good-sounding a tuning as it is, and
>playing music made for 7+ limit Just Intonation, however embellished,

I agree! That's why I'm more interested in 22-tet than 19, 31, or
50-tet.

>then
>maybe we can be free to appreciate the excellent musicianship that thrives
>in every idiom the world over.

Whoops! I lost your train of thought.



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From: Peter.Blasser@oberlin.edu
Subject: Re: 22tet and 24tet
PostedDate: 25-09-97 23:14:29
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On Thu, 25 Sep 1997 Peter.Blasser@oberlin.edu wrote:
> After testing 22tet and 24tet on a spreadsheet application, I must ask why
> 22tet is better at imitating 11 limit ratios. [snip]

You can't just consider the intervals in isolation. Consider how 5/4
and 7/4 are represented in 24TET. The closest approximation to 5/4 is 8
steps. The closest approximation to 7/4 is 19 steps. But the closest
approximation to 7/5 is 12 steps, which doesn't equal 19 minus 8. So
how are you going to tune a 4:5:7 triad in 24TET?

--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 . . . "



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From: neuwirth@smc.univie.ac.at
Subject: Re: TUNING digest 1189
PostedDate: 26-09-97 14:16:14
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Many others, including Wendy Carlos, Yunik & Swift, etc. etc. have
evaluated tunings on the basis of how well they approximate several just
intervals, without bothering to check if these approximations are
consistent with each other. So, Peter Blasser, you're in good company. I
don't think the consistency idea is published anywhere; I came up with
it in 1991, posted some tables based on it to Tuning Digest [7-8]??,
John Chalmers presented it at some conference, and Paul Hahn had been
independently playing with similar ideas. The idea is useful only for
ETs with enough notes to offer accurate approximations (e.g., the fact
that 5-tet is 9-limit consistent is not particularly meaningful) but few
enough notes so that for any just interval, only one tempered interval
is an acceptable approximation of it (e.g., 35-tet has two acceptable
approximations of the 3:2, so restricting all chords to contain the
better of the two is not really fair).



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From: clumma@nni.com
Subject: Misc
PostedDate: 26-09-97 23:15:34
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>After testing 22tet and 24tet on a spreadsheet application, I must ask why
>22tet is better at imitating 11 limit ratios.

I personally think that 11-limit ratios would not be the reason. Better
reasons would be the sorts of things I mentioned earlier: Its syntonic
pseudocomma and different mood.



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From: mr88cet@texas.net
Subject: Re: 22tet and 24tet
PostedDate: 27-09-97 18:20:56
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>You can't just consider the intervals in isolation.

Bingo!

Knowing what JI interval approximations are available is a useful first
step, but it is only that. The next step for me (usually) is to see how
they group into potential scales (aka "modes") and chords. An immediately
interesting question is whether those especially-well-represented intervals
appear as primaries or chromatics in an interesting-sounding scale.



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From: gbreed@cix.compulink.co.uk
Subject: Re: Sysex vs. Pitch Bend
PostedDate: 27-09-97 18:32:24
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