source file: mills2.txt Date: Wed, 21 Feb 1996 04:51:09 -0800 Subject: All proper modes of ET From: COUL@ezh.nl (Manuel Op de Coul) On Brian's request I have written a computer program for finding 5-, 6-, 7-, 8-, and 9-note modes of equal temperaments with fifths less than 21 cents away from 3/2 and the fifth degree relatively prime to the number of notes. I have restricted the list to proper and strictly proper modes and didn't go beyond 31- to 53-tET as Brian wanted, because that would yield a very very long list. The ET's are: 5, 7, 12, 17, 19, 22, 26, 27, 29 and 31. Most of the cyclic and inversely identical modes were left out, but not all because otherwise the program would need to run a fortnight. This is the file, compressed by 83% to 84 Kb: ftp://ella.mills.edu/ccm/tuning/papers/modes5-9.zip These are the results of 7 and 12. The strictly proper modes are indicated with an asterisk. A mode is called proper when all intervals of an interval class are not smaller than those of lower interval classes. It is called strictly proper when all intervals of an interval class are larger than the ones of lower classes. Number of notes: 7 Selection of 5: 1 1 2 1 2 Selection of 6: 1 1 1 1 1 2 Selection of 7: * 1 1 1 1 1 1 1 Number of notes: 12 Selection of 5: 1 2 3 3 3 1 3 2 2 4 1 3 2 3 3 1 3 3 1 4 1 3 3 2 3 1 3 3 3 2 1 4 1 3 3 1 4 2 2 3 2 1 3 3 3 2 2 2 2 4 2 2 2 3 3 2 2 2 4 2 2 2 3 1 4 * 2 2 3 2 3 2 2 3 3 2 2 2 4 1 3 2 2 4 2 2 2 3 1 3 3 2 3 1 4 2 * 2 3 2 2 3 * 2 3 2 3 2 2 3 3 1 3 2 3 3 2 2 Selection of 6: 1 2 2 2 2 3 1 2 2 2 3 2 1 2 2 3 1 3 1 2 2 3 2 2 1 2 3 1 2 3 1 2 3 1 3 2 1 2 3 2 1 3 1 2 3 2 2 2 1 3 1 2 2 3 1 3 1 2 3 2 * 1 3 1 3 1 3 1 3 1 3 2 2 1 3 2 1 2 3 1 3 2 1 3 2 1 3 2 2 1 3 1 3 2 2 2 2 2 1 2 2 2 3 2 1 2 2 3 2 2 1 2 3 1 3 2 1 2 3 2 2 2 1 3 1 2 3 2 1 3 1 3 2 2 1 3 2 1 3 2 1 3 2 2 2 2 2 1 2 2 3 2 2 1 2 3 2 2 2 1 3 1 3 2 2 1 3 2 2 2 2 2 1 2 3 2 2 2 1 3 2 2 2 2 2 1 3 * 2 2 2 2 2 2 Selection of 7: 1 1 2 2 2 2 2 1 2 1 2 2 1 3 1 2 1 2 2 2 2 1 2 1 3 1 2 2 1 2 2 1 2 1 3 1 2 2 1 2 2 2 1 2 2 1 3 1 2 1 2 2 2 1 2 2 1 2 2 2 2 1 2 Selection of 8: 1 1 2 1 2 1 2 2 1 1 2 1 2 2 1 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2 1 2 1 2 1 1 2 1 2 2 1 2 1 1 2 2 1 2 1 2 1 2 1 1 2 2 * 1 2 1 2 1 2 1 2 Selection of 9: 1 1 1 2 1 1 2 1 2 1 1 1 2 1 2 1 1 2 1 1 2 1 1 1 2 1 2 1 1 2 1 1 2 1 1 2 Manuel Op de Coul coul@ezh.nl Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 21 Feb 1996 15:49 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA24713; Wed, 21 Feb 1996 06:48:28 -0800 Date: Wed, 21 Feb 1996 06:48:28 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu