128edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|128}}It is notable | {{EDO intro|128}} It is notable for being the equal division corresponding to a standard MIDI piano roll of 128 notes. | ||
== Theory == | == Theory == | ||
128edo | 128edo [[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 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 [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) | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|128|columns=11}} | {{Harmonics in equal|128|columns=11}} | ||
=== Subsets and supersets === | |||
Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs| 2, 4, 8, 16, 32, and 64 }}. | |||
=== Miscellaneous properties === | === Miscellaneous properties === | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center- | {| class="wikitable center-all left-5" | ||
|+Rank-2 temperaments | |+Rank-2 temperaments by generators | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator<br>(Reduced) | ! Generator<br>(Reduced) | ||
| Line 72: | Line 75: | ||
== Scales == | == Scales == | ||
* [[ | * [[Radon5]] | ||
* [[ | * [[Radon11]] | ||
* [[ | * [[Radon16]] | ||
[[Category:Rodan]] | [[Category:Rodan]] | ||
[[Category:Fourfives]] | |||
Revision as of 07:37, 29 June 2023
| ← 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
128edo 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 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.
Miscellaneous properties
Being the power of two closest to division of the octave by the Germanic long hundred, 128edo has a unit step which is the binary (fine) relative cent (or relative heptamu in MIDI terms) of 1edo.
Regular temperament properties
| Periods per 8ve |
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) |