320edo
| ← 319edo | 320edo | 321edo → |
Theory
320edo is consistent in the 19-odd-limit and a fairly good tuning for the 19-limit. It has a flat tendency for most prime harmonics from 3 to 19, with the sole exception of 17.
The equal temperament tempers out 65625/65536 (horwell comma) and 420175/419904 (wizma) in the 7-limit and 441/440, 8019/8000 and 9801/9800 in the 11-limit, and so supports the varuna temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the optimal patent val. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out 729/728, 1001/1000, 1575/1573, 4225/4224 and 6656/6655 in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to an extension of varuna.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.71 | -0.06 | -1.33 | -0.07 | -0.53 | +0.04 | -1.26 | +1.73 | +1.67 | -1.29 |
| Relative (%) | +0.0 | -18.8 | -1.7 | -35.4 | -1.8 | -14.1 | +1.2 | -33.7 | +46.0 | +44.6 | -34.3 | |
| Steps (reduced) |
320 (0) |
507 (187) |
743 (103) |
898 (258) |
1107 (147) |
1184 (224) |
1308 (28) |
1359 (79) |
1448 (168) |
1555 (275) |
1585 (305) | |
Subsets and supersets
Since 320 factors into 26 × 5, 320edo has subset edos 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-507 320⟩ | [⟨320 507]] | +0.2224 | 0.2224 | 5.93 |- | 2.3.5 | [23 6 -14⟩, [-28 25 -5⟩ | [⟨320 507 743]] | +0.1574 | 0.2036 | 5.43 |- | 2.3.5.7 | 65625/65536, 235298/234375, 321489/320000 | [⟨320 507 743 898]] | +0.2361 | 0.2229 | 5.94 |- | 2.3.5.7.11 | 441/440, 8019/8000, 41503/41472, 65625/65536 | [⟨320 507 743 898 1107]] | +0.1928 | 0.2173 | 5.80 |- | 2.3.5.7.11.13 | 441/440, 729/728, 1001/1000, 4225/4224, 6656/6655 | [⟨320 507 743 898 1107 1184]] | +0.1845 | 0.1993 | 5.31 |- | 2.3.5.7.11.13.17 | 441/440, 729/728, 833/832, 1001/1000, 1089/1088, 4225/4224 | [⟨320 507 743 898 1107 1184 1308]] | +0.1565 | 0.1968 | 5.25 |- | 2.3.5.7.11.13.17.19 | 441/440, 513/512, 729/728, 833/832, 969/968, 1001/1000, 1521/1520 | [⟨320 507 743 898 1107 1184 1308 1359]] | +0.1741 | 0.1899 | 5.06 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 7\320
| 26.25
| [-2 13 -8⟩
| Sfourth (5-limit)
|-
| 1
| 131\320
| 491.25
| 3645/2744
| Fifthplus
|-
| 1
| 157\320
| 588.75
| 45/32
| Untriton (5-limit)
|-
| 1
| 93\320
| 348.75
| 6144/3757
| Hectosaros leap week
|-
| 2
| 19\320
| 71.25
| 25/24
| Narayana
|-
| 5
| 133\320
(5\320)
| 498.75
(18.75)
| 4/3
(81/80)
| Pental
|-
| 8
| 133\320
(9\320)
| 566.25
(33.75)
| 104/75
(55/54)
| Octowerck
|-
| 10
| 19\320
(13\320)
| 71.25
(48.75)
| 25/24
(36/35)
| Decavish
|-
| 10
| 133\320
(5\320)
| 498.75
(18.75)
| 4/3
(81/80)
| Decal
|-
| 20
| 151\320
(7\320)
| 566.25
(26.25)
| 165/119
(?)
| Soviet ferris wheel
|-
| 32
| 133\320
(3\320)
| 498.75
(11.25)
| 4/3
(?)
| Bezique
|-
| 80
| 99\320
(3\320)
| 371.25
(11.25)
| 2275/1836
(?)
| Mercury
|-
| 80
| 133\320
(1\320)
| 498.75
(3.75)
| 4/3
(245/243)
| Octogintic
Template:Rank-2 end
Template:Orf