5L 1s: Difference between revisions

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Modes: added mode names advocaded by Lilly
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This scale can be seen as the equal-tempered whole-tone scale ([[6edo]]), but with one "whole tone" that is smaller than the others.
This scale can be seen as the equal-tempered whole-tone scale ([[6edo]]), but with one "whole tone" that is smaller than the others.


Scales with this pattern are always [[Rothenberg propriety|proper]], because there is only one small step.
== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''machinoid''', from [[machine]] temperament.
== Theory ==
=== Low harmonic entropy scales ===
The only notable low-harmonic-entropy scale with this MOS pattern is [[Gamelismic clan #Slendric|slendric]], in which the large step is 8/7 and three of them make a 3/2.
The only notable low-harmonic-entropy scale with this MOS pattern is [[Gamelismic clan #Slendric|slendric]], in which the large step is 8/7 and three of them make a 3/2.
Scales with this pattern are always [[Rothenberg propriety|proper]], because there is only one small step.


== Modes ==
== Modes ==
Line 15: Line 21:


== Scale tree ==
== Scale tree ==
Generator ranges:
{{Scale tree|Comments=6/5: [[Quadrimage]]↑;
* Chroma-positive generator: 200 cents (1\6) to 240 cents (1\5)
13/8: Golden [[machine]] (213.5979¢);
* Chroma-negative generator: 960 cents (4\5) to 1000 cents (5\6)
13/5: Golden [[kumonga]] (222.9668¢);
 
3/1: [[Clyndro]];
{| class="wikitable center-all"
7/2: [[Laconic]];
! colspan="6" | Generator
4/1: [[Gorgo]];
! Cents
5/1: [[Gidorah]];
!Remainder
6/1: [[Slendric]]↓}}
! L
! s
! L/s
! Comments
|-
| 1\6 || || || || || || 200.000
|200.000|| 1 || 1 || 1.000 ||
|-
| || || || || || 6\35 || 205.714
|171.429|| 6 || 5 || 1.200 || [[Quadrimage]]↑
|-
| || || || || 5\29 || || 206.897
|165.517|| 5 || 4 || 1.250 ||
|-
| || || || || || 9\52 || 207.692
|161.538|| 9 || 7 || 1.286 ||
|-
| || || || 4\23 || || || 208.696
|156.521|| 4 || 3 || 1.333 ||
|-
| || || || || || 11\63 || 209.524
|152.381|| 11 || 8 || 1.375 ||
|-
| || || || || 7\40 || || 210.000
|150.000|| 7 || 5 || 1.400 ||
|-
| || || || || || 10\57 || 210.528
|147.368|| 10 || 7 || 1.429 ||
|-
| || || 3\17 || || || || 211.765
|141.118|| 3 || 2 || 1.500 ||
|-
| || || || || || 11\62 || 212.903
|135.484|| 11 || 7 || 1.571 ||
|-
| || || || || 8\45 || || 213.333
|133.333|| 8 || 5 || 1.600 ||
|-
| || || || || || 13\73 || 213.699
|131.507|| 13 || 8 || 1.625 || Golden [[machine]] (213.5979¢)
|-
| || || || 5\28 || || || 214.286
|128.571|| 5 || 3 || 1.667 || Machine
|-
| || || || || || 12\67 || 214.925
|125.373|| 12 || 7 || 1.714 ||
|-
| || || || || 7\39 || || 215.385
|123.077|| 7 || 4 || 1.750 ||
|-
| || || || || || 9\50 || 216.000
|120.000|| 9 || 5 || 1.800 ||
|-
| || 2\11 || || || || || 218.182
|109.091|| 2 || 1 || 2.000 || Basic machinoid
|-
| || || || || || 9\49 || 220.408
|97.959|| 9 || 4 || 2.250 ||
|-
| || || || || 7\38 || || 221.053
|94.737|| 7 || 3 || 2.333 ||
|-
| || || || || || 12\65 || 221.538
|92.308|| 12 || 5 || 2.400 ||
|-
| || || || 5\27 || || || 222.222
|88.889|| 5 || 2 || 2.500 ||
|-
| || || || || || 13\70 || 222.857
|85.714|| 13 || 5 || 2.600 || Golden [[kumonga]] (222.9668¢)
|-
| || || || || 8\43 || || 223.256
|83.721|| 8 || 3 || 2.667 ||
|-
| || || || || || 11\59 || 223.729
|81.356|| 11 || 4 || 2.750 ||
|-
| || || 3\16 || || || || 224.000
|75.000|| 3 || 1 || 3.000 || [[Clyndro]]
|-
| || || || || || 10\53 || 226.415
|67.925|| 10 || 3 || 3.333 ||
|-
| || || || || 7\37 || || 227.027
|64.865|| 7 || 2 || 3.500 || [[Laconic]]
|-
| || || || || || 11\58 || 227.586
|62.069|| 11 || 3 || 3.667 ||
|-
| || || || 4\21 || || || 228.571
|57.143|| 4 || 1 || 4.000 || [[Gorgo]]
|-
| || || || || || 9\47 || 229.787
|51.064|| 9 || 2 || 4.500 ||
|-
| || || || || 5\26 || || 230.769
|46.154|| 5 || 1 || 5.000 || [[Gidorah]]
|-
| || || || || || 6\31 || 232.258
|38.710|| 6 || 1 || 6.000 || [[Slendric]]↓
|-
| 1\5 || || || || || || 240.000
|0.000|| 1 || 0 || → inf ||
|}
 
[[Category:6-tone scales]]
[[Category:6-tone scales]]
[[Category:machinoid]]
[[Category:machinoid]]

Revision as of 11:01, 7 October 2023

← 4L 1s 5L 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. mk
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.

Scales with this pattern are always proper, because there is only one small step.

Name

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

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 Cyclic
order
Step
pattern
5|0 1 LLLLLs
4|1 2 LLLLsL
3|2 3 LLLsLL
2|3 4 LLsLLL
1|4 5 LsLLLL
0|5 6 sLLLLL

Scale tree

Template:Scale tree