70ed6: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''[[Ed6|Division of the sixth harmonic]] into 70 equal parts''' (70ED6) is very nearly identical to [[27edo|27 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 3.5316 [[cent]]s stretched and the step size is about 44.3136 cents.
'''[[Ed6|Division of the sixth harmonic]] into 70 equal parts''' (70ED6) is very nearly identical to [[27edo|27 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 3.5316 [[cent]]s [[stretched and compressed tuning|compressed]] and the step size is about 44.3136 cents. The local [[The_Riemann_zeta_function_and_tuning#Optimal_octave_stretch|zeta peak]] around 27 is located at 27.086614, which has a step size of 44.3071 cents, making 70ed6 very close to optimal for 27edo.


==Harmonics==
==Harmonics==

Revision as of 17:30, 13 May 2024

← 69ed6 70ed6 71ed6 →
Prime factorization 2 × 5 × 7
Step size 44.3136 ¢ 
Octave 27\70ed6 (1196.47 ¢)
Twelfth 43\70ed6 (1905.49 ¢)
Consistency limit 10
Distinct consistency limit 8

Division of the sixth harmonic into 70 equal parts (70ED6) is very nearly identical to 27 EDO, but with the 6/1 rather than the 2/1 being just. The octave is about 3.5316 cents compressed and the step size is about 44.3136 cents. The local zeta peak around 27 is located at 27.086614, which has a step size of 44.3071 cents, making 70ed6 very close to optimal for 27edo.

Harmonics

Approximation of harmonics in 70ed6
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -3.53 +3.53 -7.06 +5.45 +0.00 -0.99 -10.59 +7.06 +1.91 +14.16 -3.53
Relative (%) -8.0 +8.0 -15.9 +12.3 +0.0 -2.2 -23.9 +15.9 +4.3 +32.0 -8.0
Steps
(reduced)
27
(27)
43
(43)
54
(54)
63
(63)
70
(0)
76
(6)
81
(11)
86
(16)
90
(20)
94
(24)
97
(27)