Re: Digest Number 304

> Message: 6
> Date: Sat, 4 Sep 1999 20:55:00 -0700 (PDT)
> From: "M. Schulter" <mschulter@value.net>
> Subject: Re: Digest Number 303
>
> > Interval JI5 pyth JI7
> > --------------------------------------------------------------

> min7 9/5 16/9 7/4
> 17.6c 4.1c -31.2c

Hello, there, and please note that under Pythagorean or 3-limit JI, the
difference from 12-tet should be -4.1c. Maybe this illustrates the dangers
of writing plus or minus values, where it isn't too hard to get the signs
wrong, without specifying the actual value of about 996.09 cents -- 4.1
cents _less_ than the 1000 cents (10/12 octave) of 12-tet.

Incidentally, in reply to a later comment, I might add that Pythagorean is
not too far from 12-tet in some ways: it has quite active thirds and
sixths (more so than 12-tet) and pure fifths, fourths, major seconds, and
minor sevenths.

Whether a bare Pythagorean 16:9 is more or less concordant than a bare 9:5
may be an open question; the latter interval is closely approximated by
the Pythagorean "pentatone" (fifth whole-tones, or an augmented sixth,
e.g. Eb-C#). I'd tend to say that the 16:9 may be milder, although as
someone else mentioned, the pure 9:12:16 sonority (two pure fourths), e.g.
G-C-F, brings out the concordant size of this Pythagorean ratio.

Most respectfully,

Margo Schulter
mschulter@value.net