source file: mills2.txt Date: Thu, 11 Jul 1996 06:39:20 -0700 Subject: Consistency limits From: COUL@ezh.nl (Manuel Op de Coul) I have created a list of equal temperaments up to about 650 tones per octave with their consistency limits as was explained by Paul Erlich's post of 13 June 1996. However it's not restricted to integer divisions, all scale step sizes that give a different consistency limit were calculated. Initially I thought this could make a nice graph, step size horizontally, limit vertically, but the function behaves very wildly and there are very many points. Not included in the file are points where both left and right side limits are smaller than 5. This is the filename: ftp://ella.mills.edu/ccm/tuning/papers/consist_limits.txt Another larger file ftp://ella.mills.edu/ccm/tuning/papers/cons_limit_bounds.txt contains the step size bounds for each consistency limit of 3 to 18, also up to 650-tET. The first list looks like this: Limit at right side (larger step) Step size in cents Number of tones per octave Limit at left side (smaller step) Uniqueness limits for this temperament 4 589.572 2.03537 5 3 2 5 543.415 2.20825 2 3 2 2 422.656 2.83918 5 4 4 5 413.594 2.90139 6 4 4 6 387.530 3.09653 7 4 4 7 371.508 3.23007 4 4 4 3 320.000 3.75000 7 3 2 7 308.735 3.88682 8 3 2 8 295.424 4.06195 5 3 2 5 293.296 4.09142 4 3 2 4 242.288 4.95278 9 4 4 9 241.594 4.96699 10 4 4 10 233.004 5.15010 6 4 4 6 229.774 5.22251 5 4 4 5 228.571 5.25000 3 4 4 2 200.205 5.99383 5 4 4 5 200.126 5.99622 8 4 4 8 199.770 6.00691 7 4 4 7 199.218 6.02355 3 4 4 3 177.777 6.75000 5 5 4 5 177.254 6.76992 6 5 4 6 168.867 7.10616 4 5 4 4 150.611 7.96752 6 4 4 6 149.050 8.05098 7 4 4 7 145.454 8.25000 3 4 4 4 135.917 8.82887 7 6 6 7 135.843 8.83369 8 6 6 8 132.110 9.08328 6 6 6 6 131.998 9.09104 5 6 6 5 131.169 9.14848 2 6 6 2 122.706 9.77941 5 5 4 5 121.645 9.86475 8 5 4 8 119.717 10.0236 9 5 4 9 118.566 10.1209 4 5 4 3 110.676 10.8423 6 5 4 6 110.375 10.8719 4 5 4 4 101.320 11.8436 6 6 6 6 100.562 11.9329 10 6 6 10 99.2594 12.0895 11 6 6 The second list runs like this: 3 2400.00 0.50000 - 1403.91 0.85475 3 1267.97 0.94639 - 800.000 1.50000 3 760.782 1.57732 - 543.415 2.20825 3 480.000 2.50000 - 467.970 2.56426 3 422.656 2.83918 - 345.810 3.47011 3 342.857 3.50000 - 292.608 4.10104 etc. 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, 11 Jul 1996 17:01 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id IAA20802; Thu, 11 Jul 1996 08:01:41 -0700 Date: Thu, 11 Jul 1996 08:01:41 -0700 Message-Id: <73960711145837/0005695065PK2EM@MCIMAIL.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu