6edo: Difference between revisions

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'''6 equal divisions of the octave''' ('''6edo''') is the [[tuning system]] derived by dividing the [[octave]] into 6 equal steps of 200 [[cent]]s each, or the sixth root of 2. It is also known as the '''whole tone scale'''. As a subset of [[12edo|12edo]], it can be notated on a five-line staff with standard notation. It is the first [[edo]] that is not a [[The_Riemann_zeta_function_and_tuning #Zeta_edo_lists|zeta peak]], has lower [[Consistency_levels_of_small_EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for it's size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12 tone instrument.

'''6 equal divisions of the octave''' ('''6edo''') is the [[tuning system]] derived by dividing the [[octave]] into 6 equal steps of 200 [[cent]]s each, or the sixth root of 2. It is also known as the '''whole tone scale'''.

== Theory ==

As a subset of [[12edo]], 6edo can be notated on a five-line staff with standard notation. It is the first [[edo]] that is not a [[The Riemann zeta function and tuning #Zeta edo lists|zeta peak]], has lower [[Consistency levels of small EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for its size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12 tone instrument.

While 6edo does not well approximate the 3rd harmonic, it does contain a good approximation of the 9th harmonic. Therefore, 6edo can be treated as a 2.5.7.9 subgroup temperament.

Related edos:

* Subsets: [[~~2edo|~~2edo]], [[~~3edo|~~3edo]]

* Subsets: [[2edo]], [[3edo]]

* Supersets: [[~~12edo|~~12edo]], [[~~18edo|~~18edo]], [[~~24edo|~~24edo]]~~...~~

* Supersets: [[12edo]], [[18edo]], [[24edo]] …

* Neighbours: [[~~5edo|~~5edo]], [[~~7edo|~~7edo]]

* Neighbours: [[5edo]], [[7edo]]

== Intervals ==

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-'''6 equal divisions of the octave''' ('''6edo''') is the [[tuning system]] derived by dividing the [[octave]] into 6 equal steps of 200 [[cent]]s each, or the sixth root of 2. It is also known as the '''whole tone scale'''. As a subset of [[12edo|12edo]], it can be notated on a five-line staff with standard notation. It is the first [[edo]] that is not a [[The_Riemann_zeta_function_and_tuning #Zeta_edo_lists|zeta peak]], has lower [[Consistency_levels_of_small_EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for it's size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12 tone instrument.
+'''6 equal divisions of the octave''' ('''6edo''') is the [[tuning system]] derived by dividing the [[octave]] into 6 equal steps of 200 [[cent]]s each, or the sixth root of 2. It is also known as the '''whole tone scale'''.
 == Theory ==
-{{primes in equal|6}}
+{{Primes in equal|6|intervals=odd}}
+As a subset of [[12edo]], 6edo can be notated on a five-line staff with standard notation. It is the first [[edo]] that is not a [[The Riemann zeta function and tuning #Zeta edo lists|zeta peak]], has lower [[Consistency levels of small EDOs|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for its size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12 tone instrument.
 While 6edo does not well approximate the 3rd harmonic, it does contain a good approximation of the 9th harmonic. Therefore, 6edo can be treated as a 2.5.7.9 subgroup temperament.
 Related edos:
-* Subsets: [[2edo|2edo]], [[3edo|3edo]]
+* Subsets: [[2edo]], [[3edo]]
-* Supersets: [[12edo|12edo]], [[18edo|18edo]], [[24edo|24edo]]...
+* Supersets: [[12edo]], [[18edo]], [[24edo]] …
-* Neighbours: [[5edo|5edo]], [[7edo|7edo]]
+* Neighbours: [[5edo]], [[7edo]]
 == Intervals ==