128edo
| ← 127edo | 128edo | 129edo → |
Template:EDO intro It is notable for being the equal division corresponding to a standard MIDI piano roll of 128 notes.
Theory
The equal temperament tempers out 2109375/2097152 (semicomma) in the 5-limit; 245/243, 1029/1024 and 5120/5103 in the 7-limit; 385/384 and 441/440 in the 11-limit. It provides the optimal patent val for 7-limit rodan, the 41 & 87 temperament, as well as for 7-limit fourfives, the 60 & 68 temperament.
See also 128 notes per octave on Alto Saxophone (Demo by Philipp Gerschlauer)
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.17 | -1.94 | -3.20 | +1.81 | +3.22 | -1.83 | +2.49 | -0.15 | +1.67 | -1.29 |
| Relative (%) | +0.0 | +12.5 | -20.7 | -34.1 | +19.3 | +34.4 | -19.5 | +26.5 | -1.6 | +17.8 | -13.7 | |
| Steps (reduced) |
128 (0) |
203 (75) |
297 (41) |
359 (103) |
443 (59) |
474 (90) |
523 (11) |
544 (32) |
579 (67) |
622 (110) |
634 (122) | |
Subsets and supersets
Since 128 factors into 27, 128edo has subset edos 2, 4, 8, 16, 32, and 64.
Regular temperament properties
Template:Rank-2 begin
|-
| 1
| 25\128
| 234.375
| 8/7
| Rodan
|-
| 1
| 29\128
| 271.875
| 75/64
| Orson
|-
| 1
| 33\128
| 309.375
| 448/375
| Triwell
|-
| 1
| 53\128
| 496.875
| 4/3
| Undecental
|-
| 2
| 13\128
| 121.875
| 15/14
| Lagaca
|-
| 2
| 15\128
| 140.625
| 27/25
| Fifive
|-
| 4
| 15\128
| 140.625
| 27/25
| Fourfives
|-
| 4
| 53\128
(11\128)
| 496.875
(103.125)
| 4/3
| Undim (7-limit)
Template:Rank-2 end
Template:Orf