1-5-15-17 by 6/5 bihexany: Difference between revisions

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[[File:1-5-15-17 by 6-5 Bihexany.png|thumb|Circle diagram.]] A [[17-odd-limit]] [[Hexany]]. This creates a scale of 1 51/50 17/16 9/8 6/5 51/40 3/2 51/32 17/10 9/5 15/8 153/80 2/1, with steps of 51/50 25/24 18/17 16/15 17/16 20/17 17/16 16/15 18/17 25/24 51/50 160/153. As the [[1-5-15-17_hexany|base hexany]] has 3/2's and 5/4's, but no 6/5's, this is a fairly obvious way to give it some familiar chords, with 6 perfect fifths and two more imperfect but still diatonic ones sharp by [[136/135]] and [[256/255]]. It does still have a large gap on one side and a cluster of microtones on the other, giving it some xenharmonic elements, but overall, it has more than enough familiar ones to compose tonal music with as well even if some keys will need to be mapped more than 100 cents away from 12edo on a standard keyboard.
[[File:1-5-15-17 by 6-5 Bihexany.png|thumb|Circle diagram.]] A [[17-odd-limit]] [[Bihexany]]. This creates a scale of 1 51/50 17/16 9/8 6/5 51/40 3/2 51/32 17/10 9/5 15/8 153/80 2/1, with steps of 51/50 25/24 18/17 16/15 17/16 20/17 17/16 16/15 18/17 25/24 51/50 160/153. As the [[1-5-15-17_hexany|base hexany]] has 3/2's and 5/4's, but no 6/5's, this is a fairly obvious way to give it some familiar chords, with 6 perfect fifths and two more imperfect but still diatonic ones sharp by [[136/135]] and [[256/255]]. It does still have a large gap on one side and a cluster of microtones on the other, giving it some xenharmonic elements, but overall, it has more than enough familiar ones to compose tonal music with as well even if some keys will need to be mapped more than 100 cents away from 12edo on a standard keyboard.


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Latest revision as of 02:49, 3 October 2026

Circle diagram.

A 17-odd-limit Bihexany. This creates a scale of 1 51/50 17/16 9/8 6/5 51/40 3/2 51/32 17/10 9/5 15/8 153/80 2/1, with steps of 51/50 25/24 18/17 16/15 17/16 20/17 17/16 16/15 18/17 25/24 51/50 160/153. As the base hexany has 3/2's and 5/4's, but no 6/5's, this is a fairly obvious way to give it some familiar chords, with 6 perfect fifths and two more imperfect but still diatonic ones sharp by 136/135 and 256/255. It does still have a large gap on one side and a cluster of microtones on the other, giving it some xenharmonic elements, but overall, it has more than enough familiar ones to compose tonal music with as well even if some keys will need to be mapped more than 100 cents away from 12edo on a standard keyboard. 

! 1-5-15-17_by_6/5_Bihexany.scl
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1 5 15 17 by 6/5 2-combination Bihexany
12
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34.282
104.955
203.910
315.641
420.596
701.955
806.910
918.641
1017.596
1088.268
1122.551
1200
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