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5L 1s: Difference between revisions

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{{User:IlL/Template:RTT restriction}}
{{Infobox MOS}}
{{Infobox MOS
{{MOS intro}}
| Name = machinoid
This scale can be seen as the equal-tempered whole-tone scale ([[6edo]]), but with one "whole tone" that is smaller than the others.
| Periods = 1
 
| nLargeSteps = 5
== Name ==
| nSmallSteps = 1
[[TAMNAMS]] suggests the temperament-agnostic name '''machinoid''', from the [[temperament]] [[machine]].
| Equalized = 1
 
| Paucitonic = 1
== Scale properties ==
| Pattern = LLLLLs
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Proposed names ===
Names for the modes have been proposed by [https://twitter.com/Lilly__Flores/status/1702242780700098576 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.
{{MOS modes
| Mode Names=
Erev $
Oplen $Layla $
Shemesh $
Boqer $
Tsohorayim $
}}
}}
'''5L 1s''' refers to [[MOS scales|MOS scales]] with 5 large steps and 1 small step. When L=s we have [[6edo|6edo]], the equal-tempered "whole tone scale" of impressionistic fame. At the other end of the spectrum, we approach [[5edo|5edo]], with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a "whole tone" which is smaller than all the others — perhaps not a "whole tone" at all.


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


Scales with this pattern are always [[Rothenberg_propriety|proper]], because there is only one small step.
== Scale tree ==
 
{{MOS tuning spectrum
{| class="wikitable"
| 6/5 = [[Quadrimage]] ↑
|-
| 13/8 = Golden [[machine]] (213.5979{{¢}})
! colspan="7" | generator
| 13/5 = Golden [[kumonga]] (222.9668{{¢}})
! | scale
| 3/1 = [[Clyndro]]
! | large step (L)
| 7/2 = [[Laconic]]
! | small step (s)
| 4/1 = [[Gorgo]]
! | comments
| 5/1 = [[Gidorah]]
|-
| 6/1 = [[Slendric]] ↓
| style="text-align:center;" | 1\[[5edo|5]]
}}
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 1 1 1 1 1 0
| style="text-align:center;" | 240
| style="text-align:center;" | 0
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 7\36
| style="text-align:center;" | 7 7 7 7 7 1
| style="text-align:center;" | 233.3
| style="text-align:center;" | 33.3
| style="text-align:center;" | Slendric is around here
|-
| |
| |
| |
| |
| |
| | 6\31
| |
| style="text-align:center;" | 6 6 6 6 6 1
| style="text-align:center;" | 232.3
| style="text-align:center;" | 38.7
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\[[26edo|26]]
| |
| |
| style="text-align:center;" | 5 5 5 5 5 1
| style="text-align:center;" | 230.8
| style="text-align:center;" | 46.2
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 4\[[21edo|21]]
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 4 4 4 4 4 1
| style="text-align:center;" | 228.6
| style="text-align:center;" | 57.1
| style="text-align:center;" | L/s = 4
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\[[37edo|37]]
| |
| |
| style="text-align:center;" | 7 7 7 7 7 2
| style="text-align:center;" | 227.0
| style="text-align:center;" | 64.9
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | pi pi pi pi pi 1
| style="text-align:center;" | 225.6
| style="text-align:center;" | 71.8
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 3\[[16edo|16]]
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 3 3 3 3 3 1
| style="text-align:center;" | 225
| style="text-align:center;" | 75
| style="text-align:center;" | Gorgo is around here


L/s = 3
[[Category:6-tone scales]]
|-
[[Category:machinoid]]
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | e e e e e 1
| style="text-align:center;" | 223.55
| style="text-align:center;" | 82.2
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 8\[[43edo|43]]
| |
| |
| style="text-align:center;" | 8 8 8 8 8 3
| style="text-align:center;" | 223.3
| style="text-align:center;" | 83.7
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">phi+1 phi+1 phi+1 phi+1 phi+1 1</span>
| style="text-align:center;" | 223
| style="text-align:center;" | 85.2
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\[[27edo|27]]
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 5 5 5 5 5 2
| style="text-align:center;" | 222.2
| style="text-align:center;" | 88.9
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\[[38edo|38]]
| |
| |
| style="text-align:center;" | 7 7 7 7 7 3
| style="text-align:center;" | 221.1
| style="text-align:center;" | 94.7
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | 2\[[11edo|11]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 2 2 2 2 2 1
| style="text-align:center;" | 218.2
| style="text-align:center;" | 109.1
| style="text-align:center;" | Optimum rank range (L/s=2/1) machine
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\[[39edo|39]]
| |
| |
| style="text-align:center;" | 7 7 7 7 7 4
| style="text-align:center;" | 215.4
| style="text-align:center;" | 123.1
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="background-color: #ffffff;">√3 √3 √3 √3 √3 1</span>
| style="text-align:center;" | 215.2
| style="text-align:center;" | 124.2
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\[[28edo|28]]
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 5 5 5 5 5 3
| style="text-align:center;" | 214.3
| style="text-align:center;" | 128.6
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 13\73
| |
| style="text-align:center;" | 13 13 13 13 8
| style="text-align:center;" | 213.7
| style="text-align:center;" | 131.5
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | phi phi phi phi phi 1
| style="text-align:center;" | 213.6
| style="text-align:center;" | 1200/(1+5phi)
| style="text-align:center;" | Golden machine
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 8\[[45edo|45]]
| |
| |
| style="text-align:center;" | 8 8 8 8 8 5
| style="text-align:center;" | 213.3
| style="text-align:center;" | 133.3
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">pi pi pi pi pi 2</span>
| style="text-align:center;" | 212.9
| style="text-align:center;" | 135.5
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 3\[[17edo|17]]
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 3 3 3 3 3 2
| style="text-align:center;" | 211.8
| style="text-align:center;" | 141.2
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\[[40edo|40]]
| |
| |
| style="text-align:center;" | 7 7 7 7 7 5
| style="text-align:center;" | 210
| style="text-align:center;" | 150
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 4\[[23edo|23]]
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 4 4 4 4 4 3
| style="text-align:center;" | 208.7
| style="text-align:center;" | 156.5
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\[[29edo|29]]
| |
| |
| style="text-align:center;" | 5 5 5 5 5 4
| style="text-align:center;" | 206.9
| style="text-align:center;" | 165.5
| style="text-align:center;" |
|-
|
|
|
|
|
|6\35
|
|6 6 6 6 6 5
|205.7
|171.4
|Whole tone scales proper begin here
|-
|
|
|
|
|
|
|7\41
|7 7 7 7 7 6
|204.9
|175.6
|
|-
| style="text-align:center;" | 1\[[6edo|6]]
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 1 1 1 1 1 1
| colspan="2" style="text-align:center;" | 200
| style="text-align:center;" |
|}
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