1-5-7-9 by 4/3 bihexany: Difference between revisions
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[[File:1-5-7-9_by_4-3_Bihexany.png|thumb|Circle diagram (rotated).]] A [[9-odd-limit]] [[Hexany]]. This creates a scale of 1 21/20 9/8 7/6 6/5 4/3 7/5 3/2 63/40 7/4 9/5 28/15 2/1, with steps of 21/20 15/14 28/27 36/35 10/9 21/20 15/14 21/20 10/9 36/35 28/27 15/14. Since the base hexany has two 9/8's but no 3/2's, offsetting two copies of it by this amount not only adds the inevitable 6 perfect fifths, but another 2 where one of the new 3/2's chains into the existing 9/8's, plus two that are flat by a [[syntonic comma]] and two that are sharp by a [[septimal comma]]. The relationship of these is particularly interesting, because instead of one simple chain of fifths with a few wolves in it that make for simpler intervals further along the line, it splits in the middle, giving you a choice of two different wolf fifths separated by 36/35 before reuniting again two fifths later, which adds some particularly novel twists to the otherwise mostly diatonic harmonic structure. | [[File:1-5-7-9_by_4-3_Bihexany.png|thumb|Circle diagram (rotated).]] A [[9-odd-limit]] [[Hexany]]. This creates a scale of 1 21/20 9/8 7/6 6/5 4/3 7/5 3/2 63/40 7/4 9/5 28/15 2/1, with steps of 21/20 15/14 28/27 36/35 10/9 21/20 15/14 21/20 10/9 36/35 28/27 15/14. Since the [[1-5-7-9_hexany|base hexany]] has two 9/8's but no 3/2's, offsetting two copies of it by this amount not only adds the inevitable 6 perfect fifths, but another 2 where one of the new 3/2's chains into the existing 9/8's, plus two that are flat by a [[syntonic comma]] and two that are sharp by a [[septimal comma]]. The relationship of these is particularly interesting, because instead of one simple chain of fifths with a few wolves in it that make for simpler intervals further along the line, it splits in the middle, giving you a choice of two different wolf fifths separated by 36/35 before reuniting again two fifths later, which adds some particularly novel twists to the otherwise mostly diatonic harmonic structure. | ||
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! 1-5-7- | ! 1-5-7-9_by_4/3_Bihexany.scl | ||
! | ! | ||
1 5 7 9 2-combination | 1 5 7 9 by 4/3 2-combination Bihexany | ||
12 | 12 | ||
! | ! | ||
Latest revision as of 19:53, 22 November 2025
A 9-odd-limit Hexany. This creates a scale of 1 21/20 9/8 7/6 6/5 4/3 7/5 3/2 63/40 7/4 9/5 28/15 2/1, with steps of 21/20 15/14 28/27 36/35 10/9 21/20 15/14 21/20 10/9 36/35 28/27 15/14. Since the base hexany has two 9/8's but no 3/2's, offsetting two copies of it by this amount not only adds the inevitable 6 perfect fifths, but another 2 where one of the new 3/2's chains into the existing 9/8's, plus two that are flat by a syntonic comma and two that are sharp by a septimal comma. The relationship of these is particularly interesting, because instead of one simple chain of fifths with a few wolves in it that make for simpler intervals further along the line, it splits in the middle, giving you a choice of two different wolf fifths separated by 36/35 before reuniting again two fifths later, which adds some particularly novel twists to the otherwise mostly diatonic harmonic structure.
6/5 - 9/5
28/15 - 7/5 - 21/20 - 63/40< >4/3 - 1 - 3/2 - 9/8
7/6 - 7/4
! 1-5-7-9_by_4/3_Bihexany.scl ! 1 5 7 9 by 4/3 2-combination Bihexany 12 ! 84.467 203.910 266.871 315.641 498.044 582.512 701.955 786.422 968.825 1017.596 1080.557 1200