78edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author MasonGreen1 and made on 2016-06-18 10:43:29 UTC.
- The original revision id was 585778963.
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Original Wikitext content:
The 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent]]s each. It tempers out 2048/2025 in the [[5-limit]]; 875/864 and 2401/2400 in the [[7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit]]. It provides the [[optimal patent val]] for 11-limit [[Diaschismic family|keen temperament]]. Much like [[100edo|100bddd]], the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning|tuned in tritones]]. The appeal of this scale is that it is less xenharmonic than [[22edo]] is, for listeners accustomed to 12edo. In particular, the 163.6¢ "flat minor whole tone" of 22edo is now 169.2¢, making it more clearly a //whole// tone (albeit noticeably flat), rather than a neutral second.
Original HTML content:
<html><head><title>78edo</title></head><body>The 78 equal division divides the octave into 78 equal parts of size 15.385 <a class="wiki_link" href="/cent">cent</a>s each. It tempers out 2048/2025 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 875/864 and 2401/2400 in the <a class="wiki_link" href="/7-limit">7-limit</a>; and 100/99, 385/384 and 1375/1372 in the <a class="wiki_link" href="/11-limit">11-limit</a>. It provides the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for 11-limit <a class="wiki_link" href="/Diaschismic%20family">keen temperament</a>.<br /> <br /> Much like <a class="wiki_link" href="/100edo">100bddd</a>, the 78ddd val can be used to construct an alternative to 22edo for pajara. The large and small step sizes in this case have ratio 4:3. The width of the tempered perfect fifth is 707.7 cents. The major third is 384.6 cents; less than two cents flat of just. The harmonic seventh is 984.6 cents, or about 15.8 cents sharp; hence this tuning prioritizes the 3- and 5-limits over the 7-limit, while still ensuring that no basic 7-limit intervals other than the tritones are more than 16 cents off. The 22-note 2MOS generated in this way could be used to build straight-fretted guitars that would be <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow">tuned in tritones</a>. The appeal of this scale is that it is less xenharmonic than <a class="wiki_link" href="/22edo">22edo</a> is, for listeners accustomed to 12edo. In particular, the 163.6¢ "flat minor whole tone" of 22edo is now 169.2¢, making it more clearly a <em>whole</em> tone (albeit noticeably flat), rather than a neutral second.</body></html>