282edo
| ← 281edo | 282edo | 283edo → |
The 282 equal divisions of the octave (282edo), or the 282(-tone) equal temperament (282tet, 282et) when viewed from a regular temperament perspective, is the equal division of the octave into 282 parts of 4.2553 cents each.
Theory
282edo is the smallest equal temperament uniquely consistent through to the 23-odd-limit, and also the smallest consistent to the 29-odd-limit. It shares the same 3rd, 7th, and 13th harmonics with 94edo (282 = 3 × 94), as well as 11/10 and 20/17 (supporting the garistearn temperament). It has a distinct sharp tendency for odd harmonics up to 29. It tempers out 16875/16807, 19683/19600 and 65625/65536 in the 7-limit, and 540/539 and 5632/5625 in the 11-limit, so that it provides the optimal patent val for the jupiter temperament; it also tempers out 4000/3993 and 234375/234256, providing the optimal patent val for septisuperfourth temperament. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079.
Prime harmonics
Script error: No such module "primes_in_edo".
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3.5 | [32 -7 -9⟩, [-7 22 -12⟩ | [⟨282 447 655]] | -0.1684 | 0.1671 | 3.93 |
| 2.3.5.7 | 6144/6125, 118098/117649, 250047/250000 | [⟨282 447 655 792]] | -0.2498 | 0.2020 | 4.75 |
| 2.3.5.7.11 | 540/539, 4000/3993, 5632/5625, 137781/137500 | [⟨282 447 655 792 976]] | -0.3081 | 0.2151 | 5.06 |
| 2.3.5.7.11.13 | 540/539, 729/728, 1575/1573, 2200/2197, 3584/3575 | [⟨282 447 655 792 976 1044]] | -0.3480 | 0.2156 | 5.07 |
| 2.3.5.7.11.13.17 | 540/539, 729/728, 936/935, 1156/1155, 1575/1573, 2200/2197 | [⟨282 447 655 792 976 1044 1153]] | -0.3481 | 0.1996 | 4.69 |
| 2.3.5.7.11.13.17.19 | 456/455, 540/539, 729/728, 936/935, 969/968, 1156/1155, 1575/1573 | [⟨282 447 655 792 976 1044 1153 1198]] | -0.3152 | 0.2061 | 4.84 |
| 2.3.5.7.11.13.17.19.23 | 456/455, 540/539, 729/728, 760/759, 936/935, 969/968, 1156/1155, 1288/1287 | [⟨282 447 655 792 976 1044 1153 1198 1276]] | -0.3173 | 0.1944 | 4.57 |