6edo: Difference between revisions

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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.

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 limits 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.

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 {{Harmonics 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.
+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 limits 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.