User:BudjarnLambeth/Ed255/128: Difference between revisions
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An '''equal division of reduced harmonic 255''' ('''ed255/128''') is an [[equal-step tuning]] in which the octave-reduced 255th harmonic ([[255/128]]) is [[Just intonation|justly tuned]] and is divided in a given number of equal steps. 255/128 is very close to the [[octave]], 2/1, but it is slightly flatter. This makes it suitable as an alternative to edos whose consonances are too sharp, such as [[6edo]]. | |||
Ed255/128s really only make sense for that purpose with 65 or fewer tones per [[pseudo-octave]]. With more tones than that, the relative error on 2/1 becomes unacceptably high and it makes more sense to switch to a different tuning like a [[zpi]] or ed511/256. | |||
Ed255/128s are the complementary opposite of [[ed257/128]]s. | |||
== 6ed255/128 == | == 6ed255/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|6|255|128|intervals= | {{Harmonics in equal|6|255|128|intervals=odd}} | ||
6edo for comparison: | 6edo for comparison: | ||
{{Harmonics in equal|6|intervals= | {{Harmonics in equal|6|intervals=odd|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 33: | Line 22: | ||
* 795.483 | * 795.483 | ||
* 994.353 | * 994.353 | ||
* 1193.224 | * 1193.224 | ||
| Line 57: | Line 27: | ||
== 11ed255/128 == | == 11ed255/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|11|255|128|intervals= | {{Harmonics in equal|11|255|128|intervals=odd}} | ||
[[11edo]] for comparison: | [[11edo]] for comparison: | ||
{{Harmonics in equal|11|intervals= | {{Harmonics in equal|11|intervals=odd|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 78: | Line 48: | ||
== 15ed255/128 == | == 15ed255/128 == | ||
15ed255/128 is very close to [[zpi|47zpi]]. The [[5- to 10-tone scales in 47zpi]] are also useable in 15ed255/128. | |||
=== Harmonics === | === Harmonics === | ||
| Line 104: | Line 73: | ||
* 1113.676 | * 1113.676 | ||
* 1193.224 | * 1193.224 | ||
| Line 136: | Line 106: | ||
== 18ed255/128 == | == 18ed255/128 == | ||
=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|18|255|128|intervals= | {{Harmonics in equal|18|255|128|intervals=odd}} | ||
[[18edo]] for comparison: | [[18edo]] for comparison: | ||
{{Harmonics in equal|18|intervals= | {{Harmonics in equal|18|intervals=odd|collapsed=1}} | ||
=== Intervals === | === Intervals === | ||
| Line 225: | Line 195: | ||
===Scales=== | ===Scales=== | ||
<br> | |||
;[[MOS scale]]s | ;[[MOS scale]]s | ||
* Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3''' | * Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3''' | ||
| Line 247: | Line 217: | ||
** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6''' | ** Undecimal lydian-aeolian pentatonic: '''8 14 3 11 6''' | ||
** Yokai pentatonic: '''3 14 8 3 14''' | ** Yokai pentatonic: '''3 14 8 3 14''' | ||
== 49ed255/128 == | == 49ed255/128 == | ||
| Line 255: | Line 227: | ||
[[49edo]] for comparison: | [[49edo]] for comparison: | ||
{{Harmonics in equal|49|intervals=prime|collapsed=1}} | {{Harmonics in equal|49|intervals=prime|collapsed=1}} | ||
== 54ed255/128 == | |||
=== Harmonics === | |||
{{Harmonics in equal|54|255|128|intervals=prime}} | |||
[[54edo]] for comparison: | |||
{{Harmonics in equal|54|intervals=prime|collapsed=1}} | |||
== Related concepts == | == Related concepts == | ||
* [[Substitute harmonic]] | * [[Substitute harmonic]] | ||
* [[Equal-step tuning]] | * [[Equal-step tuning]] | ||
[[Category:Edonoi]][[Category:5edo]][[Category:5-tone scales]] | [[Category:Edonoi]][[Category:5edo]][[Category:5-tone scales]] | ||