5L 1s
← 4L 1s | 5L 1s | 6L 1s → |
↙ 4L 2s | ↓5L 2s | 6L 2s ↘ |
┌╥╥╥╥╥┬┐ │║║║║║││ ││││││││ └┴┴┴┴┴┴┘
sLLLLL
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 exotemperament machine.
Intervals
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 |
- Generic intervals are denoted solely by the number of steps they subtend.
- Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
- 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.
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
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 |