57ed6: 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 [[22edo|22 EDO]], but with the [[6/1]] rather than the 2/1 being just. The octave is about 2. | '''[[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 2.754{{c}} [[stretched and compressed tuning|compressed]] and the step size is about 54.4203{{c}}. 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{{c}} and an octave of 1198.63{{c}} (which is compressed by 1.37{{c}}), making 57ed6 very close to optimal for 22edo. | ||
== Harmonics == | == Harmonics == | ||
Revision as of 14:18, 6 September 2024
| ← 56ed6 | 57ed6 | 58ed6 → |
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 2.754 ¢ compressed and the step size is about 54.4203 ¢. The local zeta peak around 27 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 57ed6 very close to optimal for 22edo.
Harmonics
| 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) | |