7L 7s/13:7: Difference between revisions
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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 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. | ||
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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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* 1140.000 ([[25/13]], [[27/14]]) | * 1140.000 ([[25/13]], [[27/14]]) | ||
* 1200.000 ([[2/1]]) | * 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 == | == [[Scale Workshop]] url == | ||
* [https://scaleworkshop.plainsound.org/scale/kEtI5geIj Scale Workshop/kEtI5geIj] | * [https://scaleworkshop.plainsound.org/scale/kEtI5geIj Scale Workshop/kEtI5geIj] | ||
[[Category:14-tone scales]][[Category:Tempered scales]][[Category:MOS scales]][[Category:140edo]] | [[Category:14-tone scales]] | ||
[[Category:Tempered scales]] | |||
[[Category:MOS scales]] | |||
[[Category:140edo]] | |||
Latest revision as of 06:01, 16 July 2026
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.
Properties
jonorangejuicy's observations
It resembles 7L 7s from 21edo but with the odd scale degrees flattened by about 3¢ to give an essentially just 13/10 and 7/4 (<0.2¢ error each). The small step is exactly 60¢ (1\20) and the large step is a very accurate 16/15 (<0.4¢).
Other intervals are recognizable but are notably detuned, with 10-20¢ error, such as:
- 3/2 and 4/3 (4\7 and 3\7 respective) are 16.3¢ off
- 2L+1s is closer to 13/11 (-6.3¢) than 7/6 (+16¢)
- 6L+6s (being 6\7) functions as 9/5 (+11¢) but encroaches on 11/6 (-21¢)
- 4L+3s functions as 10/7 (+8.2¢)
In bright mode, degrees 0-2-5-8 approximate 10:11:13:15, with the 13th harmonic being very clear (great for achieving 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-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.
The dark mode has has: - The very accurate 8/7 supermajor second (1L+2s), 20/13 fifth/sixth (4L+5s), and 15/8 major seventh (6L+7s) - 2L+3s is a familiar-sounding 12edo-ish major third (+2.9¢) - 5L+6s is a mildly sharp major sixth that is accurate to 17/10 (-1.5¢) and 13\17 (-0.5¢) The utonal versions of the bright-mode chords should be available here.
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
! 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