source file: mills2.txt Date: Thu, 19 Oct 1995 10:37:43 -0700 Subject: Meantone & kleisma From: COUL@ezh.nl (Manuel Op de Coul) Here are two meantone scales where the kleisma is made away. I haven't seen them before, so they are probably of theoretical interest only. The kleisma is 15625/15552 or about 8.1 cents and the difference between five fifths and six major thirds plus an octave. The first is almost indistinguishable from 1/5-comma meantone. 1: 16384/15625 82.11775 2: 194.891 cents 194.8910 3: 307.664 cents 307.6641 4: 389.782 cents 389.7821 5: 502.555 cents 502.5552 6: 584.672 cents 584.6723 7: 697.445 cents 697.4453 8: 779.563 cents 779.5633 9: 892.336 cents 892.3364 10: 1005.109 cents 1005.109 11: 1087.227 cents 1087.227 12: 2/1 1200.000 1: 16384/15625 82.11775 2: 207.153 cents 207.1530 3: 289.271 cents 289.2711 4: 371.388 cents 371.3881 5: 496.424 cents 496.4242 6: 578.541 cents 578.5413 7: 703.576 cents 703.5762 8: 785.694 cents 785.6943 9: 910.729 cents 910.7294 10: 992.847 cents 992.8474 11: 1074.965 cents 1074.965 12: 2/1 1200.000 The first is also close to 74 and 117-tET and the second to 29-tET. Equal temperaments wherein the kleisma disappears are 15, 19, 23, 30, 34, 38, 49, 53 and more. 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; Thu, 19 Oct 1995 22:01 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id NAA11714; Thu, 19 Oct 1995 13:01:03 -0700 Date: Thu, 19 Oct 1995 13:01:03 -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