128edo: Difference between revisions
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== Theory == | == Theory == | ||
128edo 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. | |||
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) | ||
=== Prime harmonics === | |||
{{Harmonics in equal|128|columns=11}} | |||
=== Miscellaneous properties === | |||
Being the power of two closest to division of the octave by the Germanic [[Wikipedia: long hundred|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 == | == Regular temperament properties == | ||
{| class="wikitable center-1 center-2 center-3" | {| class="wikitable center-1 center-2 center-3" | ||
|+Rank-2 temperaments | |+Rank-2 temperaments | ||
!Periods | ! Periods<br>per 8ve | ||
per | ! Generator<br>(Reduced) | ||
!Generator | ! Cents<br>(Reduced) | ||
( | ! Associated<br>Ratio | ||
!Cents | ! Temperaments | ||
( | |||
!Associated | |||
Ratio | |||
!Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
|25\128 | | 25\128 | ||
|234.375 | | 234.375 | ||
|8/7 | | 8/7 | ||
|[[Rodan]] | | [[Rodan]] | ||
|- | |- | ||
|1 | | 1 | ||
|29\128 | | 29\128 | ||
|271.875 | | 271.875 | ||
|75/64 | | 75/64 | ||
|[[Orson]] | | [[Orson]] | ||
|- | |- | ||
|1 | | 1 | ||
|33\128 | | 33\128 | ||
|309.375 | | 309.375 | ||
|448/375 | | 448/375 | ||
|[[Triwell]] | | [[Triwell]] | ||
|- | |- | ||
|1 | | 1 | ||
|53\128 | | 53\128 | ||
|496.875 | | 496.875 | ||
|4/3 | | 4/3 | ||
|[[Undecental]] | | [[Undecental]] | ||
|- | |- | ||
|2 | | 2 | ||
|13\128 | | 13\128 | ||
|121.875 | | 121.875 | ||
|15/14 | | 15/14 | ||
|[[ | | [[Lagaca]] | ||
|- | |- | ||
|2 | | 2 | ||
|15\128 | | 15\128 | ||
|140.625 | | 140.625 | ||
|27/25 | | 27/25 | ||
|[[Fifive]] | | [[Fifive]] | ||
|- | |- | ||
|4 | | 4 | ||
|15\128 | | 15\128 | ||
|140.625 | | 140.625 | ||
|27/25 | | 27/25 | ||
|[[ | | [[Fourfives]] | ||
|- | |- | ||
|4 | | 4 | ||
|53\128 | | 53\128<br>(11\128) | ||
(11\128) | | 496.875<br>(103.125) | ||
|496.875 | | 4/3 | ||
| [[Undim]] (7-limit) | |||
(103.125) | |||
|4/3 | |||
|[[Undim]] (7-limit) | |||
|} | |} | ||
== Scales == | == Scales == | ||
* [[radon5]] | * [[radon5]] | ||
* [[radon11]] | * [[radon11]] | ||