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 ==

Any instruments that can play the full gamut of 12edo (ie, not diatonic harmonicas, dulcimers or harps) can obviously also play 6edo as well, although it is significantly more ergonomic on some instruments than others.

If you want a more specialist design making 6edo music easy to play without having to worry about hitting out of key 12edo notes, a [[Lumatone mapping for 6edo]] is available, or you could remove all the unwanted bars on a xylophone or marimba.

== Music ==

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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 ==
+Any instruments that can play the full gamut of 12edo (ie, not diatonic harmonicas, dulcimers or harps) can obviously also play 6edo as well, although it is significantly more ergonomic on some instruments than others.
+If you want a more specialist design making 6edo music easy to play without having to worry about hitting out of key 12edo notes, a [[Lumatone mapping for 6edo]] is available, or you could remove all the unwanted bars on a xylophone or marimba.
 == Music ==