Re: [MMM] Re: pythagorean approximation to quartertones (was: Ives' quartertones)

monz wrote:

> (I guess it was habit: i usually do list pitches in
> descending order. It makes sense to me to see the highest
> pitch at the top of the list and the lowest at the bottom.
> Alas, no one else seems to agree with me ...)

The ancient Greeks and Byzantines would.

> Anyway, since i mentioned Scala, i thought i might as
> well make a .scl file of it:
>
> -------------------------------------------------------
> ! monzo_pyth-quartertone.scl
> !
>
> 24
> !
> 46.92002
> 90.22500
> 156.98998

[...]

That's very similar to what I came up with; actually, it was a 17-tone scale inspired by Ibn Sina's tetrachord, but the remaining five tones were easy to add. Only three pitches are different than yours: I have 360.89998 for E half-flat, 1024/729 (598.26999) for F sharp/G flat, and 1062.85498 for B half-flat. (1/1 is C, for the record.)

The pattern, if the scale is thought of as a subset of 53-tone, is 0-2-4-7-9 for the whole tones C-D, D-E, F-G, G-A and A-B, and 0-2-4 for the semitones E-F and B-C.

~D.