78edo: Difference between revisions
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Wikispaces>MasonGreen1 **Imported revision 585778963 - Original comment: ** |
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The 78 equal division divides the octave into 78 equal parts of size 15.385 [[cent|cent]]s each. It tempers out 2048/2025 in the [[5-limit|5-limit]]; 875/864 and 2401/2400 in the [[7-limit|7-limit]]; and 100/99, 385/384 and 1375/1372 in the [[11-limit|11-limit]]. It provides the [[Optimal_patent_val|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 | 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|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. | ||
[[Category:edo]] | |||
[[Category:keen]] | |||
[[Category:theory]] | |||
Revision as of 00:00, 17 July 2018
The 78 equal division divides the octave into 78 equal parts of size 15.385 cents 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 keen temperament.
Much like 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 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.