5L 1s

From Xenharmonic Wiki
Jump to navigation Jump to search
← 4L 1s5L 1s 6L 1s →
↙ 4L 2s ↓5L 2s 6L 2s ↘
┌╥╥╥╥╥┬┐
│║║║║║││
││││││││
└┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLs
sLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 1\6 to 1\5 (200.0¢ to 240.0¢)
Dark 4\5 to 5\6 (960.0¢ to 1000.0¢)
TAMNAMS information
Name machinoid
Prefix mech-
Abbrev. mech
Related MOS scales
Parent 1L 4s
Sister 1L 5s
Daughters 6L 5s, 5L 6s
Neutralized 4L 2s
2-Flought 11L 1s, 5L 7s
Equal tunings
Equalized (L:s = 1:1) 1\6 (200.0¢)
Supersoft (L:s = 4:3) 4\23 (208.7¢)
Soft (L:s = 3:2) 3\17 (211.8¢)
Semisoft (L:s = 5:3) 5\28 (214.3¢)
Basic (L:s = 2:1) 2\11 (218.2¢)
Semihard (L:s = 5:2) 5\27 (222.2¢)
Hard (L:s = 3:1) 3\16 (225.0¢)
Superhard (L:s = 4:1) 4\21 (228.6¢)
Collapsed (L:s = 1:0) 1\5 (240.0¢)

5L 1s, named machinoid in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 200¢ to 240¢, or from 960¢ to 1000¢. Scales of this form are always proper because there is only one small step. This scale can be seen as the equal-tempered whole-tone scale (6edo), but with one "whole tone" that is smaller than the others.

Name

TAMNAMS suggests the temperament-agnostic name machinoid, from the temperament machine.

Intervals

Intervals of 5L 1s
Intervals Steps subtended Range in cents Average of HE
(from HE Calc)
Min of HE
Generic[1] Specific[2] Abbrev.[3]
0-mechstep Perfect 0-mechstep P0ms 0 0.0¢ ~2.4654 nats ~2.4654 nats
1-mechstep Diminished 1-mechstep d1ms s 0.0¢ to 200.0¢ ~4.6838 nats ~4.6172 nats
Perfect 1-mechstep P1ms L 200.0¢ to 240.0¢ ~4.5842 nats ~4.5840 nats
2-mechstep Minor 2-mechstep m2ms L + s 240.0¢ to 400.0¢ ~4.5803 nats ~4.5404 nats
Major 2-mechstep M2ms 2L 400.0¢ to 480.0¢ ~4.6063 nats ~4.6002 nats
3-mechstep Minor 3-mechstep m3ms 2L + s 480.0¢ to 600.0¢ ~4.5846 nats ~4.4763 nats
Major 3-mechstep M3ms 3L 600.0¢ to 720.0¢ ~4.5831 nats ~4.3779 nats
4-mechstep Minor 4-mechstep m4ms 3L + s 720.0¢ to 800.0¢ ~4.6261 nats ~4.6047 nats
Major 4-mechstep M4ms 4L 800.0¢ to 960.0¢ ~4.5446 nats ~4.4255 nats
5-mechstep Perfect 5-mechstep P5ms 4L + s 960.0¢ to 1000.0¢ ~4.5518 nats ~4.5305 nats
Augmented 5-mechstep A5ms 5L 1000.0¢ to 1200.0¢ ~4.6321 nats ~4.6048 nats
6-mechstep Perfect 6-mechstep P6ms 5L + s 1200.0¢ ~3.3273 nats ~3.3273 nats

  1. Generic intervals are denoted solely by the number of steps they subtend.
  2. Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
  3. Abbreviations can be further shortened to 'ms' if context allows.

Theory

Low harmonic entropy scales

The only notable low-harmonic-entropy scale with this MOS pattern is slendric, in which the large step is 8/7 and three of them make a 3/2.

Modes

These mode names are advocated by Lilly Flores.

He noted the frequent use of this scale in 31EDO, and further pointed out that the monstrosity Mothra derives from a moth. It was also named using Hebrew, the language that would be geographically closest to Egyptian language, where the machine was first invented. Hence, these names are Hebrew for the time beginning with 'night' when moths fly around.

Modes of 5L 1s
UDP Rotational order Step pattern Mode names
5|0 1 LLLLLs Erev
4|1 2 LLLLsL Oplen
3|2 3 LLLsLL Layla
2|3 4 LLsLLL Shemesh
1|4 5 LsLLLL Boqer
0|5 6 sLLLLL Tsohorayim

Scale tree

Scale Tree and Tuning Spectrum of 5L 1s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\6 200.000 1000.000 1:1 1.000 Equalized 5L 1s
6\35 205.714 994.286 6:5 1.200 Quadrimage
5\29 206.897 993.103 5:4 1.250
9\52 207.692 992.308 9:7 1.286
4\23 208.696 991.304 4:3 1.333 Supersoft 5L 1s
11\63 209.524 990.476 11:8 1.375
7\40 210.000 990.000 7:5 1.400
10\57 210.526 989.474 10:7 1.429
3\17 211.765 988.235 3:2 1.500 Soft 5L 1s
11\62 212.903 987.097 11:7 1.571
8\45 213.333 986.667 8:5 1.600
13\73 213.699 986.301 13:8 1.625 Golden machine (213.5979¢)
5\28 214.286 985.714 5:3 1.667 Semisoft 5L 1s
12\67 214.925 985.075 12:7 1.714
7\39 215.385 984.615 7:4 1.750
9\50 216.000 984.000 9:5 1.800
2\11 218.182 981.818 2:1 2.000 Basic 5L 1s
9\49 220.408 979.592 9:4 2.250
7\38 221.053 978.947 7:3 2.333
12\65 221.538 978.462 12:5 2.400
5\27 222.222 977.778 5:2 2.500 Semihard 5L 1s
13\70 222.857 977.143 13:5 2.600 Golden kumonga (222.9668¢)
8\43 223.256 976.744 8:3 2.667
11\59 223.729 976.271 11:4 2.750
3\16 225.000 975.000 3:1 3.000 Hard 5L 1s
Clyndro
10\53 226.415 973.585 10:3 3.333
7\37 227.027 972.973 7:2 3.500 Laconic
11\58 227.586 972.414 11:3 3.667
4\21 228.571 971.429 4:1 4.000 Superhard 5L 1s
Gorgo
9\47 229.787 970.213 9:2 4.500
5\26 230.769 969.231 5:1 5.000 Gidorah
6\31 232.258 967.742 6:1 6.000 Slendric
1\5 240.000 960.000 1:0 → ∞ Collapsed 5L 1s