99edo
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- This revision was by author genewardsmith and made on 2011-03-23 01:34:04 UTC.
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Original Wikitext content:
The //99 equal temperament//, often abbreviated 99-tET, 99-EDO, or 99-ET, is the scale derived by dividing the octave into 99 equally-sized steps, where each step represents a frequency ratio of 12.1212 cents. It is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far of the mark. It tempers out 3136/3125, 5120/5103, 6144/6125, 2401/2400 and 4375/4374, and supports hemififths, amity, parakleismic, hemiwuerschmidt and ennealimmal temperaments, and is pretty well a perfect tuning for hendecatonic temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7. Using the [[patent val]], <99 157 230 278 342|, 99 is the [[optimal patent val]] for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the <99 157 230 278 343| val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of [[Breedsmic temperaments|hemififths temperament]]. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way. ===Music in 99edo=== [[http://www.archive.org/details/NonagintaEtNovem|Nonaginta et Novem]] by [[Gene Ward Smith]]
Original HTML content:
<html><head><title>99edo</title></head><body>The <em>99 equal temperament</em>, often abbreviated 99-tET, 99-EDO, or 99-ET, is the scale derived by dividing the octave into 99 equally-sized steps, where each step represents a frequency ratio of 12.1212 cents. It is a very strong 7-limit (and 9 odd limit) temperament, but extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far of the mark. It tempers out 3136/3125, 5120/5103, 6144/6125, 2401/2400 and 4375/4374, and supports hemififths, amity, parakleismic, hemiwuerschmidt and ennealimmal temperaments, and is pretty well a perfect tuning for hendecatonic temperament. It has a sound defined by the slight sharpness (1.075, 1.565, 0.871 cents) of its 3, 5, and 7.<br /> <br /> Using the <a class="wiki_link" href="/patent%20val">patent val</a>, <99 157 230 278 342|, 99 is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank four temperament tempering out 121/120; zeus, the rank three temperament tempering out 121/120 and 176/175; and hitchcock (11-limit amity), the rank two temperament which also tempers out 2200/2187. Using the <99 157 230 278 343| val, 99 tempers out 896/891, 243/242, 441/440 and 540/539, and is an excellent tuning for the 11-limit version of <a class="wiki_link" href="/Breedsmic%20temperaments">hemififths temperament</a>. Hence 99, in spite of the fact that it tunes 11 relatively badly, is an important 11-limit tuning in more than one way.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h3> --><h3 id="toc0"><a name="x--Music in 99edo"></a><!-- ws:end:WikiTextHeadingRule:0 -->Music in 99edo</h3> <a class="wiki_link_ext" href="http://www.archive.org/details/NonagintaEtNovem" rel="nofollow">Nonaginta et Novem</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a></body></html>