275edo
Theory
If harmonic 5 is used, 275et tends very sharp. It tempers out [24 -21 4⟩ (vulture comma) and [19 10 -15⟩ (trisedodge comma) in the 5-limit; 6144/6125 and 10976/10935 in the 7-limit.
The 275e val ⟨275 436 639 772 952] being the best, tempers out 441/440, 4000/3993, 14700/14641, and 19712/19683. This can be extended to the 13-limit through 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079.
The 275 val ⟨275 436 639 772 951] tempers out 3025/3024, 3773/3750, 8019/8000. This can be extended to the 13-limit through 352/351, 676/675, 1716/1715, 2200/2197, and 3584/3575.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.59 | +2.05 | -0.10 | -1.50 | +1.65 | -0.23 | -0.79 | +0.09 | +0.24 | -1.76 |
| Relative (%) | +0.0 | +13.5 | +47.0 | -2.3 | -34.4 | +37.9 | -5.2 | -18.0 | +2.0 | +5.5 | -40.4 | |
| Steps (reduced) |
275 (0) |
436 (161) |
639 (89) |
772 (222) |
951 (126) |
1018 (193) |
1124 (24) |
1168 (68) |
1244 (144) |
1336 (236) |
1362 (262) | |
Subsets and supersets
Since 275 factors into 52 × 11, 275edo has subset edos 5, 11, 25 and 55.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [436 -275⟩ | [⟨275 436]] | −0.1863 | 0.1862 | 4.27 |- | 2.3.5 | [24 -21 4⟩, [19 10 -15⟩ | [⟨275 436 639]] | −0.4184 | 0.3618 | 8.29 |- | 2.3.5.7 | 6144/6125, 10976/10935, 9882516/9765625 | [⟨275 436 639 772]] | −0.3051 | 0.3698 | 8.48 |- | 2.3.5.7.11 | 441/440, 4000/3993, 6144/6125, 10976/10935 | [⟨275 436 639 772 952]] (275e) | −0.4096 | 0.3912 | 8.97 |- | 2.3.5.7.11.13 | 364/363, 441/440, 676/675, 6144/6125, 10976/10935 | [⟨275 436 639 772 952 1018]] (275e) | −0.4158 | 0.3574 | 8.19 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 6\275
| 26.18
| 1594323/1562500
| Sfourth (5-limit)
|-
| 1
| 109\275
| 485.64
| 320/243
| Vulture (5-limit)
|-
| 1
| 128\275
| 558.55
| 112/81
| Condor (275e)
|-
| 5
| 17\275
| 74.18
| 25/24
| Countdown (275e)
|-
| 11
| 114\275
(11\275)
| 497.45
(48.00)
| 4/3
(36/35)
| Hendecatonic
Template:Rank-2 end
Template:Orf