125edo
| ← 124edo | 125edo | 126edo → |
Theory
The equal temperament tempers out 15625/15552 in the 5-limit; 225/224 and 4375/4374 in the 7-limit; 385/384 and 540/539 in the 11-limit. It defines the optimal patent val for 7- and 11-limit slender temperament. In the 13-limit the 125f val ⟨125 198 290 351 432 462] does a better job, where it tempers out 169/168, 325/324, 351/350, 625/624 and 676/675, providing a good tuning for catakleismic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -1.16 | -2.31 | +0.77 | -4.12 | +4.27 | +0.64 | +0.09 | -4.27 | -2.38 | -2.64 |
| Relative (%) | +0.0 | -12.0 | -24.1 | +8.1 | -42.9 | +44.5 | +6.7 | +0.9 | -44.5 | -24.8 | -27.5 | |
| Steps (reduced) |
125 (0) |
198 (73) |
290 (40) |
351 (101) |
432 (57) |
463 (88) |
511 (11) |
531 (31) |
565 (65) |
607 (107) |
619 (119) | |
Subsets and supersets
Since 125 factors into 53, 125edo contains 5edo and 25edo as its subsets. Being the cube closest to division of the octave by the Germanic long hundred, 125edo has a unit step which is the cubic (fine) relative cent of 1edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-198 125⟩ | [⟨125 198]] | +0.364 | 0.364 | 3.80 |- | 2.3.5 | 15625/15552, 17433922005/17179869184 | [⟨125 198 290]] | +0.575 | 0.421 | 4.39 |- | 2.3.5.7 | 225/224, 4375/4374, 589824/588245 | [⟨125 198 290 351]] | +0.362 | 0.519 | 5.40 |- | 2.3.5.7.11 | 225/224, 385/384, 1331/1323, 4375/4374 | [⟨125 198 290 351 432]] | +0.528 | 0.570 | 5.94 |- | 2.3.5.7.11.13 | 169/168, 225/224, 325/324, 385/384, 1331/1323 | [⟨125 198 290 351 432 462]] (125f) | +0.680 | 0.622 | 6.47 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 4\125
| 38.4
| 49/48
| Slender
|-
| 1
| 12\125
| 115.2
| 77/72
| Semigamera
|-
| 1
| 19\125
| 182.4
| 10/9
| Mitonic
|-
| 1
| 24\125
| 230.4
| 8/7
| Gamera
|-
| 1
| 33\125
| 316.8
| 6/5
| Catakleismic
|-
| 1
| 52\125
| 499.2
| 4/3
| Gracecordial
|-
| 1
| 61\125
| 585.6
| 7/5
| Merman
|-
| 5
| 26\125
(1\125)
| 249.6
(9.6)
| 81/70
(176/175)
| Hemipental
|-
| 5
| 52\125
(2\125)
| 499.2
(19.2)
| 4/3
(81/80)
| Pental
Template:Rank-2 end
Template:Orf