131edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''131EDT''' is the [[EDT|equal division of the third harmonic]] into 131 parts of 14. | '''131EDT''' is the [[EDT|equal division of the third harmonic]] into 131 parts of 14.5187 [[cent|cents]] each, corresponding to 82.6520 [[edo]] (similar to every third step of [[248edo]]). It is notable for consistency to the no-evens 25-[[odd limit#Nonoctave equaves|throdd limit]]. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore [[262edt]], which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19. | ||
131EDT is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]]. | 131EDT is the 16th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]]. | ||
Revision as of 04:36, 21 September 2024
| ← 130edt | 131edt | 132edt → |
131EDT is the equal division of the third harmonic into 131 parts of 14.5187 cents each, corresponding to 82.6520 edo (similar to every third step of 248edo). It is notable for consistency to the no-evens 25-throdd limit. Furthermore, several higher primes, including 29, 31, 37, 43, and 53, lie at close to halfway between 131edt's steps; therefore 262edt, which doubles it, improves representation of a large spectrum of primes, though it loses consistency of a few intervals of 19.
131EDT is the 16th no-twos zeta peak EDT.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.06 | +0.00 | +1.28 | -0.48 | +1.04 | +2.21 | +2.38 | -1.44 | +1.73 | +6.96 | -6.87 | +6.23 | +2.74 | -7.12 | -1.40 | -6.14 |
| Relative (%) | +34.8 | +0.0 | +8.8 | -3.3 | +7.2 | +15.2 | +16.4 | -9.9 | +11.9 | +47.9 | -47.3 | +42.9 | +18.9 | -49.1 | -9.7 | -42.3 | |
| Steps (reduced) |
83 (83) |
131 (0) |
192 (61) |
232 (101) |
286 (24) |
306 (44) |
338 (76) |
351 (89) |
374 (112) |
402 (9) |
409 (16) |
431 (38) |
443 (50) |
448 (55) |
459 (66) |
473 (80) | |