720edo: Difference between revisions
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{{EDO intro|720}} | {{EDO intro|720}} | ||
720edo is the 14th [[superabundant EDO]], and also the 6th factorial EDO (720 = 1*2*3*4*5*6 = 6!), which means it contains a massive amount of sub-EDOs, limited modes of transposition, and fraction-octave MOSses. | == Theory == | ||
{{Harmonics in equal|720}} | |||
720edo is the 14th [[superabundant EDO]], and also the 6th factorial EDO (720 = 1*2*3*4*5*6 = 6!), which means it contains a massive amount of sub-EDOs, limited modes of transposition, and fraction-octave MOSses. With 720edo, it's better to use various vals mimicking smaller EDOs instead of the patent val, because it sounds as if the patent val is ''creating'' commas, not tempering them out. | |||
== | === Simple interpretations === | ||
Nonetheless, in low-complexity tones, it is consistent in the 2.3.5.11 subgroup and provides satisfactory representation of the 17-limit. | |||
In the 11-limit, it provides the optimal patent val for the [[Schismatic family#Octant|octant]] temperament, period 8. This also means that 720edo tempers out the schisma. | |||
=== Highly melodic theory === | |||
Since 720 = 72 x 10, its possible to conceptualize it as a superset of [[72edo]] and [[10edo]], which are interesting in their own right. | |||
However, the patent val's 5/4 of 720edo comes from [[90edo]], and not 72edo. | |||
=== Other === | |||
720edo patent val can be thought of as a 2.3.17.23.31.43 subgroup-suited val, because these harmonics have error of less than 1 standard deviaiton away from step. In it. it supports the 195 & 720 temperament, period 15. | |||
[[Category:Highly melodic]] | [[Category:Highly melodic]] | ||
Revision as of 21:05, 21 August 2022
Theory
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.288 | +0.353 | -0.493 | +0.349 | -0.528 | +0.045 | +0.820 | +0.059 | +0.423 | -0.036 |
| Relative (%) | +0.0 | -17.3 | +21.2 | -29.6 | +20.9 | -31.7 | +2.7 | +49.2 | +3.5 | +25.4 | -2.1 | |
| Steps (reduced) |
720 (0) |
1141 (421) |
1672 (232) |
2021 (581) |
2491 (331) |
2664 (504) |
2943 (63) |
3059 (179) |
3257 (377) |
3498 (618) |
3567 (687) | |
720edo is the 14th superabundant EDO, and also the 6th factorial EDO (720 = 1*2*3*4*5*6 = 6!), which means it contains a massive amount of sub-EDOs, limited modes of transposition, and fraction-octave MOSses. With 720edo, it's better to use various vals mimicking smaller EDOs instead of the patent val, because it sounds as if the patent val is creating commas, not tempering them out.
Simple interpretations
Nonetheless, in low-complexity tones, it is consistent in the 2.3.5.11 subgroup and provides satisfactory representation of the 17-limit.
In the 11-limit, it provides the optimal patent val for the octant temperament, period 8. This also means that 720edo tempers out the schisma.
Highly melodic theory
Since 720 = 72 x 10, its possible to conceptualize it as a superset of 72edo and 10edo, which are interesting in their own right.
However, the patent val's 5/4 of 720edo comes from 90edo, and not 72edo.
Other
720edo patent val can be thought of as a 2.3.17.23.31.43 subgroup-suited val, because these harmonics have error of less than 1 standard deviaiton away from step. In it. it supports the 195 & 720 temperament, period 15.