source file: mills2.txt Date: Mon, 29 Jul 1996 11:09:03 -0700 Subject: Re: Non-octave scales; monkeys banging o From: PAULE 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. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 29 Jul 1996 20:13 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA00053; Mon, 29 Jul 1996 11:13:39 -0700 Date: Mon, 29 Jul 1996 11:13:39 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu