1L 7s

Revision as of 16:03, 6 June 2022 by Eliora (talk | contribs) (I moved this to the top since bohlen-pierce proximity makes this just too notable to not be put on the bottom of the page)

1L 7s is the MOS pattern Lsssssss with small steps ranging from 0\1 (0¢) to 1\8 (one step of 8edo = 150¢).

↑ 1L 6s 2L 6s ↗
1L 7s 2L 7s →
↓ 1L 8s 2L 8s ↘
Scale structure
Step pattern Lsssssss
sssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\8 to 1\1 (1050.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\8 (0.0 ¢ to 150.0 ¢)
TAMNAMS information
Name antipine
Prefix apine-
Abbrev. ap
Related MOS scales
Parent 1L 6s
Sister 7L 1s
Daughters 8L 1s, 1L 8s
Neutralized 2L 6s
2-Flought 9L 7s, 1L 15s
Equal tunings
Equalized (L:s = 1:1) 7\8 (1050.0 ¢)
Supersoft (L:s = 4:3) 22\25 (1056.0 ¢)
Soft (L:s = 3:2) 15\17 (1058.8 ¢)
Semisoft (L:s = 5:3) 23\26 (1061.5 ¢)
Basic (L:s = 2:1) 8\9 (1066.7 ¢)
Semihard (L:s = 5:2) 17\19 (1073.7 ¢)
Hard (L:s = 3:1) 9\10 (1080.0 ¢)
Superhard (L:s = 4:1) 10\11 (1090.9 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
ViewTalkEdit

This MOS pattern is somewhat of a wasteland as far as low-harmonic-entropy scales are concerned. However, there is one interesting no-5's scale, bleu. In this scale, 5 steps make a 3/2, and the chord 11:12:13:14 is represented as three equal steps.

In 33edo and 41edo, one short step of this scale is close to the one step of Bohlen-Pierce, or bohpier, octave temperament which has a relationship with BP. The 33edo scale is notable outside of music in that this scale is a leap year pattern of the tabular Iranian calendar, where the leap year is inserted 7 times once in 4 years, with 1 gap of 5 years.

Modes

  • 7|0 Lsssssss
  • 6|1 sLssssss
  • 5|2 ssLsssss
  • 4|3 sssLssss
  • 3|4 ssssLsss
  • 2|5 sssssLss
  • 1|6 ssssssLs
  • 0|7 sssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1050 cents (7\8) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 150 cents (1\8)
Small step
(chroma-negative generator)
Cents L s L/s Comments
1\8 150.000 1 1 1.000
5\41 146.341 6 5 1.200 Bohpier
4\33 145.455 5 4 1.250
7\58 144.828 9 7 1.286
3\25 144.000 4 3 1.333
8\67 143.284 11 8 1.375
5\42 142.857 7 5 1.400
7\59 142.373 10 7 1.429
2\17 141.176 3 2 1.500
7\60 140.000 11 7 1.571 Bleu
5\43 139.535 8 5 1.600 Jerome/bleu
8\69 139.130 13 8 1.625 Golden jerome (139.2429¢)
3\26 138.462 5 3 1.667
7\61 137.705 12 7 1.714
4\35 137.143 7 4 1.750
5\44 136.364 9 5 1.800 Twothirdtonic
1\9 133.333 2 1 2.000 Basic 1L 7s
(small steps larger than this are proper)
4\37 129.730 9 4 2.250
3\28 128.571 7 3 2.333
5\47 127.660 12 5 2.400
2\19 126.316 5 2 2.500 Negri
5\48 125.000 13 5 2.600 Golden negri (124.7656¢)
3\29 124.138 8 3 2.667
4\39 123.077 11 4 2.750
1\10 120.000 3 1 3.000
3\31 116.129 10 3 3.333 Miracle
2\21 114.286 7 2 3.500
3\32 112.500 11 3 3.667
1\11 109.091 4 1 4.000
2\23 104.348 9 2 4.500
1\12 100.000 5 1 5.000 Passion, ripple
1\13 92.308 6 1 6.000
0\1 0.000 1 0 → inf