57ed6: Difference between revisions

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{{Infobox ET}}
'''[[Ed6|Division of the sixth harmonic]] into 70 equal parts''' (70ED6) is very nearly identical to [[22edo|22 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 2.75 [[cent]]s [[stretched and compressed tuning|compressed]] and the step size is about 54.4203 cents. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch|zeta peak]] around 27 is located at 22.025147, which has a step size of 54.483 cents, making 57ed6 close to optimal for 22edo.


== Harmonics ==
{{Harmonics in equal|57|6|1|prec=2|columns=15}}
[[Category:Edonoi]]

Revision as of 14:16, 6 September 2024

← 56ed6 57ed6 58ed6 →
Prime factorization 3 × 19
Step size 54.4203 ¢ 
Octave 22\57ed6 (1197.25 ¢)
Twelfth 35\57ed6 (1904.71 ¢)
Consistency limit 12
Distinct consistency limit 8

Division of the sixth harmonic into 70 equal parts (70ED6) is very nearly identical to 22 EDO, but with the 6/1 rather than the 2/1 being just. The octave is about 2.75 cents compressed and the step size is about 54.4203 cents. The local zeta peak around 27 is located at 22.025147, which has a step size of 54.483 cents, making 57ed6 close to optimal for 22edo.

Harmonics

Approximation of harmonics in 57ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) -2.75 +2.75 -5.51 -10.88 +0.00 +5.23 -8.26 +5.51 -13.63 -15.38 -2.75 +21.93 +2.48 -8.13 -11.02
Relative (%) -5.1 +5.1 -10.1 -20.0 +0.0 +9.6 -15.2 +10.1 -25.1 -28.3 -5.1 +40.3 +4.6 -14.9 -20.2
Steps
(reduced)
22
(22)
35
(35)
44
(44)
51
(51)
57
(0)
62
(5)
66
(9)
70
(13)
73
(16)
76
(19)
79
(22)
82
(25)
84
(27)
86
(29)
88
(31)