282edo
| ← 281edo | 282edo | 283edo → |
Theory
282edo is the smallest edo distinctly 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.
The equal temperament tempers out 6144/6125 (porwell), 118098/117649 (stearnsma), and 250047/250000 (landscape comma) 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, 2080/2079, and 10648/10647.
It allows essentially tempered chords including swetismic chords, squbemic chords, and petrmic chords in the 13-odd-limit, in addition to nicolic chords in the 15-odd-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.17 | +0.92 | +1.39 | +1.87 | +2.03 | +1.43 | +0.36 | +1.51 | +0.21 | -0.35 |
| Relative (%) | +0.0 | +4.1 | +21.6 | +32.6 | +44.0 | +47.6 | +33.5 | +8.4 | +35.6 | +4.9 | -8.3 | |
| Steps (reduced) |
282 (0) |
447 (165) |
655 (91) |
792 (228) |
976 (130) |
1044 (198) |
1153 (25) |
1198 (70) |
1276 (148) |
1370 (242) |
1397 (269) | |
Subsets and supersets
Since 282 factors into 2 × 3 × 47, 282edo has subset edos 2, 3, 47, 94, and 141.
Regular temperament properties
Template:Comma basis begin |- | 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 Template:Comma basis end
- 282et has a lower relative error than any previous equal temperaments in the 23-limit, past 270 and before 311.
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 13\282
| 55.32
| 33/32
| Escapade
|-
| 1
| 133\282
| 565.96
| 4096/2835
| Trident (282ef)
|-
| 2
| 13\282
| 55.32
| 33/32
| Septisuperfourth
|-
| 2
| 43\282
| 182.98
| 10/9
| Unidecmic
|-
| 3
| 33\282
| 140.43
| 243/224
| Septichrome
|-
| 3
| 37\282
| 157.45
| 35/32
| Nessafof (7-limit)
|-
| 6
| 51\282
(4\282)
| 217.02
(17.02)
| 17/15
(105/104)
| Stearnscape
|-
| 6
| 80\282
(14\282)
| 340.43
(59.57)
| 162/133
(88/85)
| Semiseptichrome
|-
| 6
| 117\282
(23\282)
| 497.87
(97.87)
| 4/3
(128/121)
| Sextile
Template:Rank-2 end
Template:Orf