22-tone exhortations

I wrote:

>}I haven't investigated Paul Erlich's decatonic
>}modes enough to decide if they can be treated as 10 pitch classes.
>}I don't like the theory because it clings to the idea of diatonic
>}harmony -- that all notes used in harmony must belong to the same key.
>}I'd rather work out a chord sequence, and fit a melody to it. Or,
>}define a melodic mode, write a tune in it, and harmonise it
>}chromatically.

and Paul replied:

>You can't deny that most Western music derives much of its beauty and
>contrapuntal versatility from having both vertical and horizontal sonorities
>taken from the same pitch set. These pitch sets have characteristic dissonant
>intervals which allow a "tonic" to be defined and when the pitch set changes,
>so does the tonic. In this way non-diatonic notes can anticipate a change of
>tonality before that tonality also arrives.

Actually, my statement looks stronger than I intended. There are
a number of reasons for which I like Paul's theory, and some for
which I don't. I mentioned diatonic harmony (is there a better
term that doesn't imply a 7-note scale?) because it's an assumption
that isn't explicitly justified in the paper. I'm no expert on
Western classical music, but I don't feel full blown tonality is
for me. There are a number of personal reasons for this. I like
the idea of decentered harmony in a post-relativistic world. I
feel that harmony, which grew out of modality, is mature enough to
stand on it's own.

Now I've been put on the spot, I suppose I'll have to justify my
other objections, so here goes ...

The criteria under "scale structure" are dispensable, but do have
some value.

I'd rather the scale worked with triads, as even just 4:5:6:7
chords aren't consonant enough for me to use as a tonic. This
means the tonic has to be a 5-limit chord, as septimal diminished
triads don't work that well either, and other 7-limit chords
will tend to share their root with a 5-limit one.

I don't like more than 7 notes in a key. I can accept additional
chromatic notes, but 10 is too many for me as the reference against
which the chromaticism is added.

I expect the scale, in its consonant limit, to be significantly
_better_ than 12 equal in the 5-limit. To my ears, a 5-limit
chord progressing to a 7-limit one will almost always sound like
an increase in dissonance in 22 equal, although the 7-limit chords
are still tuned well enough to be contrasted against stronger
dissonances.

With these restrictions, I don't think 7-limit tonality will work.
The best theory we have is that of the decatonic modes, and there
is the potential for some great music to be written using it.
It just won't be written by me.


SMTPOriginator: tuning@eartha.mills.edu
From: gbreed@cix.compulink.co.uk (Graham Breed)
Subject: Reply to Gregg Gibson
PostedDate: 17-12-97 20:31:49
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