62edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-05-27 13:57:31 UTC.
- The original revision id was 339876836.
- The revision comment was:
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Original Wikitext content:
62edo divides the octave into 62 equal parts of 19.355 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone|hemimeantone]] temperaments. It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a "false" quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7\31, which is a good generator for [[Orwell]]. This makes 8\62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.
Original HTML content:
<html><head><title>62edo</title></head><body>62edo divides the octave into 62 equal parts of 19.355 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> <br /> It is also strong as an 1/8-tone Armodue-Hornbostel system, with the 6th being 35 steps. However, 31 is a "false" quarter-tone system with respect to the same temperament since the Armodue-Hornbostel whole tone is simplest when achieved by a chain of 5 of the septimal minor third at 7\31, which is a good generator for <a class="wiki_link" href="/Orwell">Orwell</a>. This makes 8\62 an Orwell whole tone as well, so 62 is twice an 1/8-tone system; but this is no real surprise since 1/8-tone systems will have 40 to 80 divisions in the octave as a matter of course.</body></html>