source file: m1438.txt
Date: Sat, 6 Jun 98 09:04 BST-1

Subject: Re: magic chord

From: gbreed@cix.compulink.co.uk (Graham Breed)

Paul Erlich wrote:

> Here's my problem with that: the 28:25 is represented in 31TET by 193.5
> cents, and that interval by itself doesn't really evoke a consonant 9:8.
> If one really hears intervals at the 9-limit or higher, then both 9:8
> and 10:9 must be considered consonant, and there should be a dissonant
> point about halfway between them.

I don't agree with this reasoning.  Is the 22-equal 7/5 similarly
at a dissonant point?  Or is the just 11/9 at a dissonant point
between 6/5 aand 5/4?

> There are many chords in 31TET where the 9:8 is clearly
> evoked, because other ratios are supporting that interpretation. But in
> this chord, that doesn't happen.

Granted, the 9/8 isn't "clearly evoked" but it can still function
as a 9-limit consonance.  Besides, how do the other ratios
support 10/9???


For the record, 28/25 vanishes in almost all meantone and schismic
temperaments.  Exceptions are 26- and 118-equal.  Diaschismic
scales generally express it, the exception here being the
remarkably economical (if not so accurate) 22-equal.