7L 7s in 140edo
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 was first explored by jonorangejuicy on the Xenharmonic Alliance Discord server in early October 2025.
Scale Workshop url
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 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.
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.