79ed12

From Xenharmonic Wiki
Jump to navigation Jump to search
← 78ed12 79ed12 80ed12 →
Prime factorization 79 (prime)
Step size 54.4551¢ 
Octave 22\79ed12 (1198.01¢)
Twelfth 35\79ed12 (1905.93¢)
Consistency limit 11
Distinct consistency limit 8

79 equal divisions of the 12th harmonic (abbreviated 79ed12) is a nonoctave tuning system that divides the interval of 12/1 into 79 equal parts of about 54.5⁠ ⁠¢ each. Each step represents a frequency ratio of 121/79, or the 79th root of 12.

79ED12 is very nearly identical to 22 EDO, but with the 12/1 rather than the 2/1 being just, resulting in octaves being compressed by about 1.99 ¢. The local zeta peak around 22 is located at 22.025147, which has a step size of 54.483 ¢ and an octave of 1198.63 ¢ (which is compressed by 1.37 ¢), making 79ed12 very close to optimal for 22edo.

Harmonics

Approximation of harmonics in 79ed12
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) -1.99 +3.97 -3.97 -9.10 +1.99 +7.39 -5.96 +7.95 -11.09 -12.73 +0.00 +24.79 +5.40 -5.13 -7.95
Relative (%) -3.6 +7.3 -7.3 -16.7 +3.6 +13.6 -10.9 +14.6 -20.4 -23.4 +0.0 +45.5 +9.9 -9.4 -14.6
Steps
(reduced)
22
(22)
35
(35)
44
(44)
51
(51)
57
(57)
62
(62)
66
(66)
70
(70)
73
(73)
76
(76)
79
(0)
82
(3)
84
(5)
86
(7)
88
(9)