6edo: Difference between revisions

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== Theory ==

6edo is identical to the 12edo whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic|7-form]] for 2.3.5 and the [[Pentatonic|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as 7edo for [[meantone]] or 5edo for [[superpyth]]. The root chord in this harmonic system can be seen as:

6edo is identical to the [[12edo]] whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic|7-form]] for 2.3.5 and the [[Pentatonic|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as [[7edo]] for [[meantone]] or [[5edo]] for [[superpyth]]. The root chord in this harmonic system can be seen as:

* [0 2 5] = 4:5:7, with the harmonic seventh as a bounding interval

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=== Odd harmonics ===

=== Subsets and supersets ===

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| Tridecimal neutral second

|}

== Octave stretch or compression ==

If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some compressed-octave 6edo tunings (least to most compressed) include [[equal tuning|19ed9]], [[equal tuning|20ed10]], [[14ed5]], [[zpi|12zpi]] or [[17ed7]].

== Instruments ==

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 == Theory ==
-edo is identical to the 12edo whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic|7-form]] for 2.3.5 and the [[Pentatonic|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as 7edo for [[meantone]] or 5edo for [[superpyth]]. The root chord in this harmonic system can be seen as:
+edo is identical to the [[12edo]] whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic|7-form]] for 2.3.5 and the [[Pentatonic|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as [[7edo]] for [[meantone]] or [[5edo]] for [[superpyth]]. The root chord in this harmonic system can be seen as:
 * [0 2 5] = 4:5:7, with the harmonic seventh as a bounding interval
@@ Line 26: / Line 26: @@
 === Odd harmonics ===
-{{Harmonics in equal|6|intervals=odd}}
+{{Harmonics in equal|6}}
 === Subsets and supersets ===
@@ Line 353: / Line 353: @@
 | Tridecimal neutral second
 |}
+== Octave stretch or compression ==
+If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some compressed-octave 6edo tunings (least to most compressed) include [[equal tuning|19ed9]], [[equal tuning|20ed10]], [[14ed5]], [[zpi|12zpi]] or [[17ed7]].
 == Instruments ==