87edo
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- This revision was by author genewardsmith and made on 2011-01-22 02:26:27 UTC.
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Original Wikitext content:
The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so. 87et tempers out 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29|, the misty comma, <26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103. Some 13-limit rank two temperaments supported by 87et are these: tritikleismic 72&87 <<18 15 -6 9 42 ... || rodan 41&87 <<3 17 -1 -13 -22 ... || mystery 29&58 <<0 29 29 29 29 ... || countercata 34&87 <<6 5 -31 32 14 ... || luna 31&87 <<15 -2 -5 22 -23 ... || 87 can serve as a MOS in these: 270&87 <<24 -9 -66 12 27 ... || 494&87 <<51 -1 -133 11 32 ... || 224&87 <<27 8 -67 -1 5 ...|| 87et is a particularly good tuning for [[Gamelismic clan|rodan temperament]]. The 8/7 generator of 17/87 is a remarkable 0.00062 cents sharper than the 13-limit [[POTE tuning|POTE]] generator and is close to the 11-limit POTE generator also. Also, the 32/87 generator for [[Kleismic family|clyde temperament]] is 0.04455 cents sharp of the 7-limit POTE generator. Music By Gene Ward Smith http://www.archive.org/details/Pianodactyl
Original HTML content:
<html><head><title>87edo</title></head><body>The 87 equal temperament, often abbreviated 87-tET, 87-EDO, or 87-ET, is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 cents. It is solid as both a 13-limit (or 15 odd limit) and as a 5-limit system, and of course does well enough in any limit in between. It represents the 13-limit tonality diamond both uniquely and consistently, and is the smallest equal temperament to do so.<br /> <br /> 87et tempers out 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29|, the misty comma, <26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103. <br /> <br /> Some 13-limit rank two temperaments supported by 87et are these:<br /> <br /> tritikleismic 72&87 <<18 15 -6 9 42 ... ||<br /> rodan 41&87 <<3 17 -1 -13 -22 ... ||<br /> mystery 29&58 <<0 29 29 29 29 ... ||<br /> countercata 34&87 <<6 5 -31 32 14 ... ||<br /> luna 31&87 <<15 -2 -5 22 -23 ... ||<br /> <br /> 87 can serve as a MOS in these:<br /> <br /> 270&87 <<24 -9 -66 12 27 ... ||<br /> 494&87 <<51 -1 -133 11 32 ... ||<br /> 224&87 <<27 8 -67 -1 5 ...||<br /> <br /> 87et is a particularly good tuning for <a class="wiki_link" href="/Gamelismic%20clan">rodan temperament</a>. The 8/7 generator of 17/87 is a remarkable 0.00062 cents sharper than the 13-limit <a class="wiki_link" href="/POTE%20tuning">POTE</a> generator and is close to the 11-limit POTE generator also. Also, the 32/87 generator for <a class="wiki_link" href="/Kleismic%20family">clyde temperament</a> is 0.04455 cents sharp of the 7-limit POTE generator.<br /> <br /> Music<br /> By Gene Ward Smith<br /> <!-- ws:start:WikiTextUrlRule:25:http://www.archive.org/details/Pianodactyl --><a class="wiki_link_ext" href="http://www.archive.org/details/Pianodactyl" rel="nofollow">http://www.archive.org/details/Pianodactyl</a><!-- ws:end:WikiTextUrlRule:25 --></body></html>