But is 14/11 so different from 9/7?

Replying to Charlie Jordan's reply from Digest 1577 from Nov. 10:

>Date: Sun, 01 Nov 1998 23:12:26 +0000
>From: Harold Fortuin
>Subject: LA/San Diego visit

>I work
>out new functional harmonies by modelling the voice-leading with these
>ratios above 1/1:
>7/6, 6/5, 11/9, 5/4, 9/7 (the five kinds of thirds)

If 11-limit just intervals are acceptable, how about 14/11 at 417.51
cents?

HF: I'm not thinking in terms of limits as usually used on this list.
Instead, some time ago, I asked myself, "Which ratios correspond closest
to PERCEPTUALLY DISTINCT qualities?" (in a harmonic context based on
existing Western tonal practice)

I listened to a large number of ratios one after another, alone and in
chords (using harmonic timbres), and concluded that for root position
3-6 tone tertian harmony, the intervals I listed, including the 3rds
above, provide the necessary model for an extension of tonal practice.

We can label these qualities according to accepted terms:

7/6 subminor 3rd
6/5 minor 3rd
11/9 neutral 3rd
5/4 major 3rd
9/7 supermajor 3rd

In this view, 14/11 will be heard either as a supermajor or major third,
so it's not a perceptually distinct quality.

It's also true that one must create certain musical contexts to enable
the listener to distinguish certain of these thirds from others--for
example, it's easy to make a neutral third have the quality of 'major'
if it isn't surrounded by a pair from the remaining 3rds, built from one
of the 'minors' and one of the 'majors'.


>7/5, 3/2 (fifths)

Is there some reason you prefer 7/5 over 10/7?

HF: 7/5 is the first 'diminished fifth' quality in the harmonic series,
and is found in the 5:6:7 diminished triad.

As mentioned already, these ratios can be used to model aspects of
voice-leading in JI as well as various ETs--thus, I'm not tied to one
system, but do have a consistent model for voice-leading across them.

The best way to make sense of all this is to try it out yourself. For
example, recreate this V-I four-part harmony cadential pattern (ratios
built on the same tone until the final chord):

8 18 7 10
6 15 6 8
5 12 5 8
4 10 4 4
------ --
V I (obviously a 3/2 distance between V and I)

Happy listening.

If you live in southern CA, contact me now if you'd like to try and meet
(if you haven't already).

With intent to generate discussion
(but remember I'll be cut off from e-mail 'til Thanksgiving now),
Harold Fortuin
www.wavefront.com/~hfortuin