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-~~9_Hexany~~.scl

! 1-5-7-9_by_4/3_Bihexany.scl

!

1 5 7 9 2-combination ~~Hexany~~

1 5 7 9 by 4/3 2-combination Bihexany

12

!

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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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-! 1-5-7-9_Hexany.scl
+! 1-5-7-9_by_4/3_Bihexany.scl
 !
-5 7 9 2-combination Hexany
+5 7 9 by 4/3 2-combination Bihexany
 !