Non-octave scales; monkeys banging o

Gary M. wrote:

>Paul E indirectly mentioned in his post why octave-equivalence makes
>nonoctave tunings valuable: In an octave-based tuning, each octave's span
>provides octave-equivalents of the same basic harmonies, whereas in a
>nonoctave
>tuning, each octave's span gives you an all new set of harmonies.

That's right! I thought I was being too obtuse for anyone to get this
message, but it's true. As usual, the results of an ill-conceived
matho-musical concept, that of tritave equivalence in this case, are
musically very interesting even though they do not corroborate the original
premises of the theory. What I did in my post was take the theory completely
at face value, and work out its consequences within the framework of the
faulty premise. The music will have a lot of interesting features as a
result of the tritave structures, but near-octaves will take on the
character of equivalence and the effect will be, as Gary pointed out, that
of entirely new harmonies within each octave span.

> So the almost universal perception and agreement on the idea of octave
>equivalence bodes well for nonoctave tunings, because it ensures that they
>provide more harmonic variety than octave-based tunings (for a given
>scale-step size).

Whether this means an increase in harmonic variety, I don't know, because
(octave) inversions and extensions are very valuable in organizing harmonies
into coherent progressions. Perhaps it's an increase in variety, but at the
expense of unity.


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