72-Eq notation (Sims)

[Erlich, TD 79:]
> 72-tET, besides being consistent through the
> 17-limit, has unique (max. error 4 cents)
> representations of all 11-limit intervals.
> (I mean odd limits here.)

[Dan Stearns, TD 80:]
> I have used a variant of Ezra Sims' notation
> that adds a crosshatch to the existing
> ('arrow', 'half-arrow', and 'square root')
> symbols. <snip>...
>
> While I believe that these 144tET symbols
> would accomplish that end...[etc.]

[Monzo, TD 83:]
> Sims does not need a notation more complex
> or more accurate than his 72-Eq to get close
> enough (to the JI results he's looking for)
> to satisfy him.

I "just" ran across a parenthetical statement
in an article Sims wrote for _1/1_, "A 72-Tone
Just Computer System" [v 5, no 1, Winter 1989]
that pertained to this thread, particularly
those comments above:

[Sims:]
> Identifying the 13th harmonic [= 841 cents]
> with the sixth-tone-high minor 6th [= 2^(50/72)
> = 833 cents = the 8-cent error in this scale
> pointed out by Erlich] causes a bit of inconvenience
> at times. But to have done better by it would
> have required a notation for and a chromatic
> of 144 tones [i.e., Stearns's notation],
> which, it seemed to me, would introduce
> more inconvenience than the slight inaccuracy
> seemed likely to do. I'm not convinced that
> we need the 13th harmonic yet, anyhow, or
> that our performers are ready for it.

I wish to emphasize that last sentence, because
Sims considers his "basic scale" to represent
harmonics as high as the 37th! And when determining
his upper harmonies by summation tones of the
lower notes in the chord, he sometimes goes far
higher in the odd/prime series than that. But
here he is stating quite matter-of-factly that
he doesn't expect performers to acheive an accuracy
beyond the 11-limit, and implying that listeners
can't tell the difference anyway. (remember,
11-limit worked for Partch!)

This article, BTW, is a very thorough explanation
of how Sims uses 72-Eq to represent JI.
Recommended for all those who like 72-Eq notation.
(I do.)

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html
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