2101edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 2101 factors into primes as {{nowrap| 11 × 191 }}, 2101edo contains [[11edo]] and [[191edo]] as subset edos. As every eighth step of [[16808edo]], one step of 2101edo is exactly 8 jinns. | Since 2101 factors into primes as {{nowrap| 11 × 191 }}, 2101edo contains [[11edo]] and [[191edo]] as subset edos. As every eighth step of [[16808edo]], the smallest edo which is [[Consistency#Consistency to distance d|(distinctly) consistent to distance 2]] in the [[23-odd-limit]] and also up to the [[35-odd-limit]], one step of 2101edo is exactly 8 jinns. | ||
Latest revision as of 11:50, 27 July 2025
| ← 2100edo | 2101edo | 2102edo → |
2101 equal divisions of the octave (abbreviated 2101edo or 2101ed2), also called 2101-tone equal temperament (2101tet) or 2101 equal temperament (2101et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2101 equal parts of about 0.571 ¢ each. Each step represents a frequency ratio of 21/2101, or the 2101st root of 2.
2101edo has an excellent perfect fifth, and is consistent to the 11-odd-limit tending flat. As an equal temperament, it tempers out the monzisma in the 5-limit, the wizma in the 7-limit, and 3025/3024, 117649/117612, and 234375/234256 in the 11-limit. It also has an accurately tuned 23rd harmonic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.004 | -0.212 | -0.144 | -0.152 | +0.215 | +0.137 | +0.060 | -0.002 | +0.218 | +0.133 |
| Relative (%) | +0.0 | -0.6 | -37.1 | -25.3 | -26.6 | +37.6 | +24.1 | +10.4 | -0.4 | +38.2 | +23.4 | |
| Steps (reduced) |
2101 (0) |
3330 (1229) |
4878 (676) |
5898 (1696) |
7268 (965) |
7775 (1472) |
8588 (184) |
8925 (521) |
9504 (1100) |
10207 (1803) |
10409 (2005) | |
Subsets and supersets
Since 2101 factors into primes as 11 × 191, 2101edo contains 11edo and 191edo as subset edos. As every eighth step of 16808edo, the smallest edo which is (distinctly) consistent to distance 2 in the 23-odd-limit and also up to the 35-odd-limit, one step of 2101edo is exactly 8 jinns.