Re: towards a Hyper MOS

Hi Paul,

> Three specific interval sizes for each generic interval size! Wow! Is this a
> mode of any previously identified 17-tone scale?

I've just done a search of the SCALA archive, using FTS search capability to order the archive by number of notes in the
scales, and numbers of steps of each size.

It's a mode of

wilson_17.scl | Wilson's 17-tone 5-limit scale

1/1 135/128 10/9 9/8 1215/1024 5/4 81/64 4/3 45/32 729/512 3/2 405/256 5/3 27/16 16/9 15/8 243/128 2/1

steps 135/128 256/243 81/80 135/128 256/243 81/80 256/243 135/128 81/80 256/243 135/128 256/243 81/80 256/243 135/128 81/80 256/243

Compare new scale:

1/1 135/128 2187/2048 9/8 1215/1024 5/4 81/64 45/32 729/512 3/2 405/256 27/16 3645/2048 15/8 243/128 2/1

steps 135/128 81/80 256/243 135/128 256/243 81/80 135/128 256/243 81/80 256/243 135/128 81/80 256/243 135/128 256/243 81/80 256/243

Easiest to compare if one uses L M S notation:

wilson_17.scl
L M S L M S M L S M L M S M - L S M
new scale:
L S M L M S L M S M L S M L M S M
(- = point at which new scale begins in wilson_17.scl)

> I'd certainly say so . . . though your construction seemed kind of haphazard
> . . . can you think of a more systematic way of describing the construction
> of hyper-MOS scales? And what happened to the Tribonacci-like sequence we
> were expecting?

See the end of digest 967 for first attempt at conjecture to clarify ideas of
how they are constructed.

Not much sign of the Tribonacci-like sequence yet, but it is early days,
and there can be lots of ways of looking at the data.

Robert