User:Overthink/22edo decatonic theory: Difference between revisions
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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 that appear in the 2L 8s scale. | ||
{| class="wikitable" | {| class="wikitable right-all left-4" | ||
|+ style="font-size: 105%" | Decatonic intervals | |+ style="font-size: 105%" | Decatonic intervals | ||
|- | |- | ||
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| Augmented 1sn || 54.5 || rowspan=2 | 1 || [[25/24]], [[28/27]], [[49/48]] | | Augmented 1sn || 54.5 || rowspan=2 | 1 || [[25/24]], [[28/27]], [[49/48]] | ||
|- | |- | ||
| Diminished 2nd || 54.5 || style="left" | [[36/35]], [[81/80]] | | Diminished 2nd || 54.5 || style="text-align: left;" | [[36/35]], [[81/80]] | ||
|- | |- | ||
| Perfect 2nd || 109.1 || 2 || [[16/15]], [[15/14]], [[21/20]] | | Perfect 2nd || 109.1 || 2 || [[16/15]], [[15/14]], [[21/20]] | ||
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| Augmented 10th || 1145.5 || rowspan=2 | 21 || [[27/14]], [[48/25]], [[96/49]] | | Augmented 10th || 1145.5 || rowspan=2 | 21 || [[27/14]], [[48/25]], [[96/49]] | ||
|- | |- | ||
| Diminished 11ve || 1145.5 || [[35/18]], [[160/81]] | | Diminished 11ve || 1145.5 || style="text-align: left;" | [[35/18]], [[160/81]] | ||
|- | |- | ||
| Perfect 11ve || 1200.0 || 22 || [[2/1]] | | Perfect 11ve || 1200.0 || 22 || [[2/1]] | ||