126edo: Difference between revisions
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The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63. | The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit [[Diaschismic_family#Srutal-11-limit|srutal temperament]]. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63. | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 18:54, 4 October 2022
| ← 125edo | 126edo | 127edo → |
The 126 equal temperament divides the octave into 126 equal parts of 9.524 cents each. It has a distinctly sharp tendency, with the 3, 5, 7 and 11 all sharp. It tempers out 2048/2025 in the 5-limit, 2401/2400 and 4375/4374 in the 7-limit, and 176/175, 1331/1323 and 896/891 in the 11-limit. It provides the optimal patent val for 7- and 11-limit srutal temperament. It also creates an excellent Porcupine [8] scale, mapping the large quills to 17 steps, and the small to 7, which is the precise amount of tempering needed to make the 3rds and 4ths equally consonant within a few fractions of a cent. It has divisors 2, 3, 6, 7, 9, 14, 18, 21, 42, and 63.