Yourmusic Productions: add missing note

2025-11-14T19:57:50Z

add missing note

← Older revision		Revision as of 19:57, 14 November 2025
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	[[File:3-7-13-15_by_4-3_Hexany.png\|thumb\|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png\|thumb\|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany\|base hexany]] out to a detemper of the [[Modes_of_Negri-9\|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.		[[File:3-7-13-15_by_4-3_Hexany.png\|thumb\|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png\|thumb\|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany\|base hexany]] out to a detemper of the [[Modes_of_Negri-9\|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes, 6 perfect fifths and 1 17 cent flat one which is usable if you can tolerate 7edo fifths. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.

	<pre>		<pre>
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	498.044		498.044
	617.487		617.487
			636.617
	756.060		756.060
	884.358		884.358

Yourmusic Productions: Create Page.

2025-11-13T10:58:17Z

Create Page.

New page

[[File:3-7-13-15_by_4-3_Hexany.png|thumb|Circle diagram.]] [[File:3-7-13-15_by_3-2_Hexany.png|thumb|Circle diagram.(rotated)]] A [[13-limit]] [[bihexany]]. This creates a scale of 1 15/14 13/12 65/56 26/21 5/4 4/3 10/7 13/9 65/42 5/3 13/7 2/1, with steps of 15/14 91/90 15/14 16/15 105/104 16/15 15/14 91/90 15/14 14/13 39/35 14/13. Since 4 steps in [[negri]] reach 4/3, this is the natural choice to extend the [[3-7-13-15_hexany|base hexany]] out to a detemper of the [[Modes_of_Negri-9|augmented major mode]] of the [[1L 8s]] negri scale, with three of the notes split into two notes a microtone apart, which gives you a rich selection of simple chords as long as you select the correct versions of the microtonal intervals to avoid the wolf notes. Using a 3/2 as the offset interval gives the same scale, but the Carolingan mode of it, which puts a 5/4 and 3/2 above the root but has slightly more complex intervals overall as they do not cancel as many factors.

<pre>
! 3-7-13-15_by_4/3_Bihexany.scl
!
3 7 13 15 by 4/3 2-combination Hexany
12
!
119.442
138.572
258.015
369.746
386.313
498.044
617.487
756.060
884.358
1071.701
1200
</pre>

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

3-7-13-15 by 4/3 bihexany - Revision history

Yourmusic Productions: add missing note

Yourmusic Productions: Create Page.