source file: mills2.txt Date: Wed, 15 Nov 1995 10:28:52 -0800 Subject: Re: TUNING digest 559 From: marcus@fa.disney.com Regarding Mclaren's post: > In fact one could just as easily "modulate" between different > modes of vibration of a sphere: zonal harmonics, torsional > vibrations, etc., each giving rise to a different non-just > non-equal-tempered scale. > This is a process conceptually akin to "modulation" in > JI and equal temperament, but more complex: for the > subinharmonic series formed on a given n-j n-e-t are, > as we have seen, in general not as closely related to > the vertical structures formed from inharmonic series > as is the minor triad to the harmonic series of the major > triad in traditional Western harmony. > Regardless, this set of posts may have given a glimpse > of the universe of new harmonies and melodies awaiting > the composer adventurous enough to dare composing > in non-just non-equal-tempered tunings. Okay, I got the glimpse, and I'm completely excited. But I'm missing a few pieces. Can someone help? The 12 tone equal temperament scale is derived from the overtone series of a vibrating string. Unfortunately for me, my only reference on the derivation is Hindemith's Craft Of Musical Composition. If any of you have read his work, you'll all groan with me. It's not helpful. Apparently, this scale is generate by using 6 overtones, and then a few approximations, which is where I get lost. I'd be very interested in hearing someone concisely construct the scale in this forum. I think this will help me attempt to construct other scales from other vibrational modes, i.e., a cylinder, a rod, a sphere, etc. (a friend pointed out that a cylinder would have two fundamentals...any comments on that?) Thanks all. I loooove this list. Marcus Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 16 Nov 1995 05:48 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id TAA22112; Wed, 15 Nov 1995 19:48:06 -0800 Date: Wed, 15 Nov 1995 19:48:06 -0800 Message-Id: <951115223813_23763864@emout06.mail.aol.com> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu