Discussion on "Reply to Gary Morriso

Hello, Heinz!

Unfortunately I don't know German, but I would like to share with you the
article by Pierce, Roberts, and Matthews in _Harmony and Tonality_
(proceedings of the Royal Swedish Academy of Music, edited by J. Sundberg).
Other articles in the book mention your scale. Randy Winchester has done a
good job composing/improvising in it. I don't think he uses square waves,
but Enrique Moreno and I agree that this doesn't matter as much as Pierce
first thought it would. (Did you discuss overtone structure in your original
article?) Manfred Schroeder describes "Pierce's scale" alongside "Bach's
well-tempered scale" in his truly wonderful book, _Fractals, Chaos, Power
Laws_, and the footnote is to the article "Theoretical and experimental
explorations of the Bohlen-Pierce scale." J. Acoust. Soc. Am. 84, 1214-1222.

Before I knew of these scales, I had recognized 7-limit chords such as 3:5:7
as consonant and found a scale (based on normal octaves) from which they
could be derived. This is described in a paper I am currently completing and
which will appear in Xenharmonikon 17. I don't believe that major or minor
thirds were heard, even unconsciously, as anything other than the dissonant
intervals they were in the early and middle Middle Ages. I do believe,
however, that triadic harmony makes the diatonic scale easier to use and
understand, since three (not necessarily all major) complete consonant
triads do give you the whole scale. My scales have this property as well,
using complete consonant tetrads . . .

Heinz, what subset of the 13 notes do you feel is the best analogy to the
major scale? Pierce, et al describe the mode 0 1 3 4 6 7 9 10 12 (13). Did
you come up with this?

-Paul


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