source file: mills2.txt Date: Sun, 21 Jan 1996 04:53:03 -0800 Subject: Re: Manuel Op de Coul's list From: brg@netcom.com (Bruce R. Gilson) COUL@ezh.nl (Manuel Op de Coul) wrote: >Your presumption that all of the modes in the list are selections from >ET scales is wrong. Many of them can indeed be but for most it is >not a requirement. If I have been vague about it, I apologise. The notation seemed to imply it. When you give only a "number of steps in an octave" and the number of steps between consecutive notes in the scale [as 2 2 1 2 2 2 1 for a standard major scale] you have something well-defined only in ET. >Messiaen's modes work best in equal temperament. The Indian modes >aren't necessarily used in just intonation, take the popular harmonium >for instance, which is tuned more or less equally. >The Arabic 17-tone modes are to be taken from this scale: > 256/243 65536/59049 9/8 32/27 8192/6561 81/64 4/3 1024/729 262144/177147 3/2 > 128/81 32768/19683 27/16 16/9 4096/2187 1048576/531441 2/1. All the scales that are based on ration- al frequency ratios need such a chart in addition to the list you provide in order to be useful. >The modes of the Indian shruti scale are also not for ET, though the >theory of shrutis is not universally accepted among Indian >musicologists and you see different proposals for the frequency >ratios. I suppose that what I'm looking for is something that would enable me to re- liably reproduce any scale that has a name. Your chart, for equal-tempered scales, does that (for the ones you provide, but obviously any you've missed can be added). But for non-equal scales, it still misses the one thing that makes it useful to my purpose, the precise ratios that the 12, or 14, or however many, steps are supposed to mean. I like your format, and I'd like a table such as yours to serve as a base for what I'm trying to do. Bruce R. Gilson brg@netcom.com Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 21 Jan 1996 14:56 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id FAA01181; Sun, 21 Jan 1996 05:56:46 -0800 Date: Sun, 21 Jan 1996 05:56:46 -0800 Message-Id: <0099CB98E5E81BF1.7ED2@ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu