7L 7s in 140edo: Difference between revisions

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{{Todo|inline=1|discuss title|comment=This page is about the 7L 7s scale with hardness 13:7. "140edo" is ambiguous.}}

The '''140edo 7L 7s scale''' is the 14-tone [[MOS scale]] from [[140edo]] with the step pattern [[7L 7s]].

The ratio between its step sizes (its [[hardness]]) is 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.

~~== [[Scale Workshop]] url ==~~

* [https://scaleworkshop.plainsound.org/scale/kEtI5geIj Scale Workshop/kEtI5geIj]

== Properties ==

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* 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 ~~the15th~~ being 16.3¢ flat... ~~Thia~~ 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]].

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.

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- 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 ==

<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]]

@@ Line 1: / Line 1: @@
+{{Todo|inline=1|discuss title|comment=This page is about the 7L 7s scale with hardness 13:7. "140edo" is ambiguous.}}
 The '''140edo 7L 7s scale''' is the 14-tone [[MOS scale]] from [[140edo]] with the step pattern [[7L 7s]].
 The ratio between its step sizes (its [[hardness]]) is 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.
-== [[Scale Workshop]] url ==
-* [https://scaleworkshop.plainsound.org/scale/kEtI5geIj Scale Workshop/kEtI5geIj]
 == Properties ==
@@ Line 18: / Line 19: @@
 * 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 the15th being 16.3¢ flat... Thia 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]].
+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.
@@ Line 27: / Line 28: @@
 - 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 ==
+<pre>
+! 7L_7s_140edo.scl
+!
+L 7s scale in 140edo, with L = 13\140 and s = 7\140
+!
+.42857
+.42857
+.85714
+.85714
+.28571
+.28571
+.71429
+.71429
+.14286
+.14286
+.57143
+.57143
+.00000
+/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]]