Yourmusic Productions: Linking.

2025-11-22T19:53:30Z

Linking.

← Older revision		Revision as of 19:53, 22 November 2025
Line 1:		Line 1:
	[[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.

	<pre>		<pre>
Line 7:		Line 7:
	</pre>		</pre>
	<pre>		<pre>
	! 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		12
	!		!

Yourmusic Productions: Create Page.

2025-11-22T19:50:20Z

Create Page.

New page

[[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.

<pre>
6/5 - 9/5
28/15 - 7/5 - 21/20 - 63/40< >4/3 - 1 - 3/2 - 9/8
7/6 - 7/4
</pre>
<pre>
! 1-5-7-9_Hexany.scl
!
1 5 7 9 2-combination Hexany
12
!
84.467
203.910
266.871
315.641
498.044
582.512
701.955
786.422
968.825
1017.596
1080.557
1200
</pre>

[[Category:Hexanies]]
[[Category:12-tone scales]]
[[Category:Pages with Scala files]]

1-5-7-9 by 4/3 bihexany - Revision history

Yourmusic Productions: Linking.

Yourmusic Productions: Create Page.