128edo: Difference between revisions
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See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer) | See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer) | ||
== Regular temperament properties == | |||
{| class="wikitable center-1 center-2 center-3" | |||
|+Rank-2 temperaments | |||
!Periods | |||
per octave | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
Ratio | |||
!Temperaments | |||
|- | |||
|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 | |||
|[[Gamelismic clan#Lagaca|Lagaca]] | |||
|- | |||
|2 | |||
|15\128 | |||
|140.625 | |||
|27/25 | |||
|[[Fifive]] | |||
|- | |||
|4 | |||
|15\128 | |||
|140.625 | |||
|27/25 | |||
|[[Fifive family#Fourfives|Fourfives]] | |||
|- | |||
|4 | |||
|53\128 | |||
(11\128) | |||
|496.875 | |||
(103.125) | |||
|4/3 | |||
|[[Undim]] (7-limit) | |||
|} | |||
== Scales == | == Scales == | ||
Revision as of 02:42, 30 October 2022
| ← 127edo | 128edo | 129edo → |
Template:EDO introIt is notable because it is the equal division corresponding to a standard MIDI piano roll of 128 notes.
Theory
| 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) | |
It is the optimal patent val for 7-limit Rodan temperament. It tempers out 2109375/2097152 in the 5-limit; 245/243, 1029/1024 and 5120/5103 in the 7-limit; 385/384 and 441/440 in the limit. Being the power of two closest to division of the octave by the Germanic long hundred, it has a unit step which is the binary (fine) relative cent (or relative heptamu in MIDI terms) of 1edo.
See also 128 notes per octave on Alto Saxophone (Demo by Philipp Gerschlauer)
Regular temperament properties
| Periods
per octave |
Generator
(reduced) |
Cents
(reduced) |
Associated
Ratio |
Temperaments |
|---|---|---|---|---|
| 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) |