7L 7s/13:7: Difference between revisions
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The ''' | {{breadcrumb}} | ||
The '''13:7 7L 7s scale''' is the 14-tone [[MOS scale]] from [[140edo]] with the step pattern [[7L 7s]] and [[step ratio]] 13:7. It can be thought of as a [[whitewood]][14] scale. | |||
It was first explored by [[jonorangejuicy]] on the [[Xenharmonic Alliance]] Discord server in early October 2025. | It was first explored by [[jonorangejuicy]] on the [[Xenharmonic Alliance]] Discord server in early October 2025. | ||
== Properties == | == Properties == | ||
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* 4L+3s functions as 10/7 (+8.2¢) | * 4L+3s functions as 10/7 (+8.2¢) | ||
In [[bright]] mode, degrees 0-2-5-8 approximate [[10:11:13:15]], with the [[13-limit|13th harmonic]] being very clear (great for achieving [[xenharmonic|xenharmony]]), the 11th being ~6.4¢ sharp of just, and | In [[bright]] mode, degrees 0-2-5-8 approximate [[10:11:13:15]], with the [[13-limit|13th harmonic]] being very clear (great for achieving [[xenharmonic|xenharmony]]), the 11th being ~6.4¢ sharp of just, and the 15th being 16.3¢ flat... This can be extended with 6L+6s to give a somewhat unstable [[10:11:13:15:18]] pentad, or with 6L+5s to stabilise with an outside 7/4. Or spacing it out can yield [[5:9:11:13]] or [[5:9:11:13:15]]. | ||
Its "5th-inversion" (in quotes because we're remaining in bright mode instead of flipping to dark mode) 0-3-6-8 gives a [[mu chord|mu-chord]]-like [[6:7:8:9]] tetrad. Though it sounds better as just 6:7:9 or 6:7:8, since the 8:9 interval is some 32¢ off. | Its "5th-inversion" (in quotes because we're remaining in bright mode instead of flipping to dark mode) 0-3-6-8 gives a [[mu chord|mu-chord]]-like [[6:7:8:9]] tetrad. Though it sounds better as just 6:7:9 or 6:7:8, since the 8:9 interval is some 32¢ off. | ||
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The [[utonal]] versions of the bright-mode chords should be available here. | The [[utonal]] versions of the bright-mode chords should be available here. | ||
[[Category:14-tone scales]][[Category:Tempered scales]][[Category:MOS scales]][[Category:140edo]] | == Intervals == | ||
From 140edo: | |||
* 13 7 13 7 13 7 13 7 13 7 13 7 13 7 | |||
In cents (with nearby [[JI]]): | |||
* 111.429 ([[16/15]], [[15/14]]) | |||
* 171.429 ([[11/10]], [[10/9]]) | |||
* 282.857 ([[7/6]], [[13/11]]) | |||
* 342.857 ([[11/9]]) | |||
* 454.286 ([[9/7]], [[13/10]]) | |||
* 514.286 ([[4/3]], [[27/20]]) | |||
* 625.714 ([[10/7]]) | |||
* 685.714 ([[40/27]], [[3/2]]) | |||
* 797.143 ([[11/7]], [[8/5]]) | |||
* 857.143 ([[13/8]], [[18/11]]) | |||
* 968.571 ([[7/4]]) | |||
* 1028.571 ([[9/5]], [[20/11]]) | |||
* 1140.000 ([[25/13]], [[27/14]]) | |||
* 1200.000 ([[2/1]]) | |||
== Scala file == | |||
<pre> | |||
! 7L_7s_140edo.scl | |||
! | |||
7L 7s scale in 140edo, with L = 13\140 and s = 7\140 | |||
! | |||
111.42857 | |||
171.42857 | |||
282.85714 | |||
342.85714 | |||
454.28571 | |||
514.28571 | |||
625.71429 | |||
685.71429 | |||
797.14286 | |||
857.14286 | |||
968.57143 | |||
1028.57143 | |||
1140.00000 | |||
2/1 | |||
</pre> | |||
== [[Scale Workshop]] url == | |||
* [https://scaleworkshop.plainsound.org/scale/kEtI5geIj Scale Workshop/kEtI5geIj] | |||
[[Category:14-tone scales]] | |||
[[Category:Tempered scales]] | |||
[[Category:MOS scales]] | |||
[[Category:140edo]] | |||