User:Overthink/22edo decatonic theory: Difference between revisions

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== Interval classification ==

We will classify intervals based on the 2L 8s mos, with names "unison", "second", etc. However, since we have 10 note classes, the interval of equivalence is not an "octave" as in diatonic, but a "hendecave". In this system, 1sns, 2nds, 5ths, 6ths, 7ths, 10ths, and 11ves are perfect, while 3rds, 4ths, 8ths, and 9ths are imperfect. Pajara has a half-octave (600{{c}}) [[period]] representing both [[7/5]] and [[10/7]], and a [[~]][[3/2]] [[generator]] (~709{{c}} in [[22edo]]). The half-octave is a perfect 6th, and the [[3/2]] is a perfect 7th. (From now on, interval names are decatonic unless specified.) Here is a table of intervals ~~that appear in~~ the 2L 8s scale.

We will classify intervals based on the 2L 8s mos, with names "unison", "second", etc. However, since we have 10 note classes, the interval of equivalence is not an "octave" as in diatonic, but a "hendecave". In this system, 1sns, 2nds, 5ths, 6ths, 7ths, 10ths, and 11ves are perfect, while 3rds, 4ths, 8ths, and 9ths are imperfect. Pajara has a half-octave (600{{c}}) [[period]] representing both [[7/5]] and [[10/7]], and a [[~]][[3/2]] [[generator]] (~709{{c}} in [[22edo]]). The half-octave is a perfect 6th, and the [[3/2]] is a perfect 7th. (From now on, interval names are decatonic unless specified.) Here is a table of intervals classified by the 2L 8s scale.

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 == Interval classification ==
-We will classify intervals based on the 2L 8s mos, with names "unison", "second", etc. However, since we have 10 note classes, the interval of equivalence is not an "octave" as in diatonic, but a "hendecave". In this system, 1sns, 2nds, 5ths, 6ths, 7ths, 10ths, and 11ves are perfect, while 3rds, 4ths, 8ths, and 9ths are imperfect. Pajara has a half-octave (600{{c}}) [[period]] representing both [[7/5]] and [[10/7]], and a [[~]][[3/2]] [[generator]] (~709{{c}} in [[22edo]]). The half-octave is a perfect 6th, and the [[3/2]] is a perfect 7th. (From now on, interval names are decatonic unless specified.) Here is a table of intervals that appear in the 2L 8s scale.
+We will classify intervals based on the 2L 8s mos, with names "unison", "second", etc. However, since we have 10 note classes, the interval of equivalence is not an "octave" as in diatonic, but a "hendecave". In this system, 1sns, 2nds, 5ths, 6ths, 7ths, 10ths, and 11ves are perfect, while 3rds, 4ths, 8ths, and 9ths are imperfect. Pajara has a half-octave (600{{c}}) [[period]] representing both [[7/5]] and [[10/7]], and a [[~]][[3/2]] [[generator]] (~709{{c}} in [[22edo]]). The half-octave is a perfect 6th, and the [[3/2]] is a perfect 7th. (From now on, interval names are decatonic unless specified.) Here is a table of intervals classified by the 2L 8s scale.
 {| class="wikitable right-all left-4"