Answers to Chris Palmer

> First, do any of you have any ideas on how to notate scales that divide
> the octave into more or less than 12 steps? The standard 5-line system
> doesn't really do it for me.

Many tunings can function quite well for traditional musical frameworks, and
as such traditional notation is a reasonable possibility. The traditional
notation of these tunings still allows you to convey many of their
nontraditional effects too. Tunings of this sort include 19TET (TET="Tone Equal
Temperament"), 17TET, most meantone- and well-temperaments, and some of the more
traditional Just tunings (with adaptions to show changes of tuning reference).
Examples of tunings that aren't generally amenable to traditional notation are
10TET, 15TET, 16TET, 22TET, 24TET, 31TET, and most nonoctave tunings, although
24 and 31 require only the addition of quarter-accidentals.



> Second, being new to this tuning thing, are there any books that will
> explain the concepts?

Libraries worth! Neil Haverstick just announced that he has completed his
street-wise musicians' guide to 19TET. A number of people have said that they
like my EPS Xenharmonic Scales Disk documentation as a general introduction.
But most of the commercially-available books out there concentrate on one or two
types of tunings. Fewer are truly general in nature.

But that is certainly not to suggest for a moment that they're not valuable
books. David Doty's Just Intonation Primer, for example, is said to be one of
the most definitive and easy-to-understand books on JI. (I personally haven't
had a chance to read it, but have heard nothing but good reports about it.)
Bill Sethares is probably about 3/4 of the way done with what I strongly suspect
will become one of the great landmark books in the field, exploring the
interactions of tuning and timbre - why certain tunings sound good and bad in
certain instrumental timbres, and the reverse. (I'm helping review the
manuscript for him, so this one I can vouch for from first-hand experience!)

And then there are the venerable old books: Partch's Genesis of a Music,
Rameau's Treatises, James Tenney's and Barbour's books, for example. And, down
in the nuts and bolts, there are lots of books and magazine articles on
Psychoacoustics. Brian McLaren has read a lot of them, and can probably make
some suggestions if you're interested in them.


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> to my ear, Blackwood's
> comment that a diatonic scale will sound "recognizable" if it follows the
> standard pattern of 2 large intervals, one small, three large, and one small
> seems correct.

Certainly that's more true in a melodic perspective than harmonic. Diatonic
melodies, even rhythmically simple ones, are very easily recognizable on
shrunken or stretched interval sizes. Try for example tuning up a synthesizer
to 12 steps per 3:2 and play some familiar melodies. You'll definitely
recognize them. They're even recognizable if the "coefficient" is negative as
well as fractional or mixed. In other words, melodic inversion works!

But it's also very easy to see that diatonic harmony is instantly destroyed
by doing this.


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