1001edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
1001edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[19/1|19]], and [[23/1|23]], making it suitable for a 2.9.7.11.13.19.23 [[subgroup]] interpretation, with an optional addition of either [[5/1|5]], or [[15/1|15]]. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. | |||
Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
{{ | {{Harmonics in equal|1001}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1001 factorizes as | Since 1001 factorizes as {{factorization|1001}}, 1001edo has subset edos {{EDOs| 7, 11, 13, 77, 91, and 143 }}. | ||
Latest revision as of 22:56, 20 February 2025
| ← 1000edo | 1001edo | 1002edo → |
1001 equal divisions of the octave (abbreviated 1001edo or 1001ed2), also called 1001-tone equal temperament (1001tet) or 1001 equal temperament (1001et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1001 equal parts of about 1.2 ¢ each. Each step represents a frequency ratio of 21/1001, or the 1001st root of 2.
1001edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise, it has good approximations to harmonics 7, 9, 11, 13, 19, and 23, making it suitable for a 2.9.7.11.13.19.23 subgroup interpretation, with an optional addition of either 5, or 15. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832.
Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the parakleisma.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.543 | -0.300 | -0.195 | -0.114 | +0.131 | -0.168 | +0.243 | +0.539 | -0.210 | +0.348 | -0.103 |
| Relative (%) | +45.3 | -25.0 | -16.2 | -9.5 | +10.9 | -14.0 | +20.3 | +45.0 | -17.5 | +29.0 | -8.6 | |
| Steps (reduced) |
1587 (586) |
2324 (322) |
2810 (808) |
3173 (170) |
3463 (460) |
3704 (701) |
3911 (908) |
4092 (88) |
4252 (248) |
4397 (393) |
4528 (524) | |
Subsets and supersets
Since 1001 factorizes as 7 × 11 × 13, 1001edo has subset edos 7, 11, 13, 77, 91, and 143.