4L 1s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Aura (talk | contribs)
autopatrolled
5,920 edits
No edit summary
→Scale tree: + more temps
 
(19 intermediate revisions by 12 users not shown)
Line 1: Line 1:
The scale with the lowest harmonic entropy for this [[MOSScales|MOS]] pattern is [[Semaphore|semaphore]], in which two generators make a 4/3. The other interesting scale is [[Semicomma_family|orwell]], in which the generator is approximately 7/6 and three of them make an 8/5.
{{Infobox MOS}}
{{MOS intro}}
The scale with the lowest harmonic entropy for this [[mos]] pattern is [[semaphore]], in which two generators make a [[4/3]]. The other interesting scale is [[orwell]], in which the generator is approximately [[7/6]] and three of them make an [[8/5]].


All scales of this form are necessarily proper (because there is only one small step).
== Names ==
The [[TAMNAMS]] system uses the name '''manual''', a name that is thematically inspired by the Latin word "manus".


== Names ==
== Intervals ==
The [[TAMNAMS]] system suggests the name '''roach''', a name that is thematically inspired by [[bug]] temperament, and is a reference to the popular Mexican folk song "[[Wikipedia:La Cucaracha|La Cucaracha]]"- specifically versions of the song in which the titular cockroach is missing a leg.
{{MOS intervals}}
 
== Modes ==
Modes of 4L 1s can be named systematically either with [[modal UDP notation]], rotational order (with 1 being the [[bright]]est mode) or the [[step pattern]].
{{MOS mode degrees}}


== Scale Tree ==
=== Proposed names ===
{| class="wikitable"
Additionally, [[User: CellularAutomaton|CellularAutomaton]] has proposed names based on Latin names for fingers of the hand for increased distinctiveness and memorability.
|-
{| class="wikitable mw-collapsible mw-collapsed"
! colspan="6" | Generator
|+ style=white-space:nowrap | Modes names of 4L 1s
! | Cents
! UDP
! | s
! Step pattern
! | L-s
! CellularAutomaton's names
! | Comments
|-
|-
| | 1\5
| 4|0
| |
| LLLLs
| |
| Minimal
| |
| |
| |
| | 240
| | 240
| | 0
| style="text-align:center;" |
|-
|-
|
| 3|1
|
| LLLsL
|
| Medicinal
|
|
|6\29
|248.28
|206.9
|41.38
|
|-
|-
| |  
| 2|2
| |
| LLsLL
| |
| Medial
| |
| | 5\24
| |
| | 250
| | 200
| | 50
| style="text-align:center;" | Semaphore is around here
|-
|-
| |  
| 1|3
| |
| LsLLL
| |
| Indical
| | 4\19
| |
| |
| | 252.63
| | 189.47
| | 63.16
| style="text-align:center;" |
|-
|-
| |  
| 0|4
| |
| sLLLL
| | 3\14
| Pollical
| |
| |
| |
| | 257.14
| | 171.43
| | 85.71
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 258.81
| | 164.76
| | 92.05
| |
|-
| |
| |
| |
| |
| | 8\37
| |
| | 259.46
| | 162.16
| | 97.3
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 1200/(3+phi)
| | 160.6
| | 99.25
| style="text-align:center;" | Golden [[Bug|bug]] / golden [[superpelog|superpelog]]
|-
| |
| |
| |
| | 5\23
| |
| |
| | 260.87
| | 156.52
| | 104.35
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 262.16
| | 151.36
| | 110.8
| |
|-
| |
| | 2\9
| |
| |
| |
| |
| | 266.67
| | 133.33
| | 133.33
| style="text-align:center;" | Optimum rank range (L/s=2/1) bug
|-
| |
| |
| |
| |
| | 7\31
| |
| | 270.97
| | 116.13
| | 154.84
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 12\53
| | 271.70
| | 113.21
| | 158.49
| style="text-align:center;" | Orwell is around here
|-
| |
| |
| |
| | 5\22
| |
| |
| | 272.73
| | 109.09
| | 163.64
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| | 274.73
| | 101.07
| | 173.66
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| | 3\13
| |
| |
| |
| | 276.92
| | 92.31
| | 184.62
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| | 277.89
| | 88.45
| | 189.43
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| |
| | 4\17
| |
| |
| | 282.35
| | 70.59
| | 211.76
| style="text-align:center;" | L/s = 4
|-
|
|
|
|
|5\21
|
|285.71
|57.14
|228.57
|
|-
|
|
|
|
|
|6\25
|288
|48
|240
|
|-
| | 1\4
| |
| |
| |
| |
| |
| | 300
| | 0
| | 300
| style="text-align:center;" |
|}
|}


[[Category:Abstract MOS patterns]]
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = [[Immunity]]↑
| 5/4 = [[Semaphore]]
| 4/3 = [[Godzilla]]
| 13/8 = Golden [[bug]]
| 5/3 = [[Superpelog]]
| 9/5 = [[Septimin]]
| 9/4 = [[Infraorwell]]
| 12/5 = [[Orwell]]
| 9/2 = [[Subklei]]
| 6/1 = [[Quasitemp]]↓
}}
 
[[Category:Manual]]
[[Category:5-tone scales]]

Latest revision as of 12:06, 21 August 2025

← 3L 1s 4L 1s 5L 1s →
↙ 3L 2s ↓ 4L 2s 5L 2s ↘ 
┌╥╥╥╥┬┐
│║║║║││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern LLLLs
sLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\5 to 1\4 (240.0 ¢ to 300.0 ¢)
Dark 3\4 to 4\5 (900.0 ¢ to 960.0 ¢)
Related MOS scales
Parent 1L 3s
Sister 1L 4s
Daughters 5L 4s, 4L 5s
Neutralized 3L 2s
2-Flought 9L 1s, 4L 6s
Equal tunings
Equalized (L:s = 1:1) 1\5 (240.0 ¢)
Supersoft (L:s = 4:3) 4\19 (252.6 ¢)
Soft (L:s = 3:2) 3\14 (257.1 ¢)
Semisoft (L:s = 5:3) 5\23 (260.9 ¢)
Basic (L:s = 2:1) 2\9 (266.7 ¢)
Semihard (L:s = 5:2) 5\22 (272.7 ¢)
Hard (L:s = 3:1) 3\13 (276.9 ¢)
Superhard (L:s = 4:1) 4\17 (282.4 ¢)
Collapsed (L:s = 1:0) 1\4 (300.0 ¢)

4L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 240 ¢ to 300 ¢, or from 900 ¢ to 960 ¢. Scales of this form are always proper because there is only one small step. The scale with the lowest harmonic entropy for this mos pattern is semaphore, in which two generators make a 4/3. The other interesting scale is orwell, in which the generator is approximately 7/6 and three of them make an 8/5.

Names

The TAMNAMS system uses the name manual, a name that is thematically inspired by the Latin word "manus".

Intervals

Intervals of 4L 1s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 240.0 ¢
Perfect 1-mosstep P1ms L 240.0 ¢ to 300.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 300.0 ¢ to 480.0 ¢
Major 2-mosstep M2ms 2L 480.0 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 600.0 ¢ to 720.0 ¢
Major 3-mosstep M3ms 3L 720.0 ¢ to 900.0 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 900.0 ¢ to 960.0 ¢
Augmented 4-mosstep A4ms 4L 960.0 ¢ to 1200.0 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 1200.0 ¢

Modes

Modes of 4L 1s can be named systematically either with modal UDP notation, rotational order (with 1 being the brightest mode) or the step pattern.

Scale degrees of the modes of 4L 1s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5
4|0 1 LLLLs Perf. Perf. Maj. Maj. Aug. Perf.
3|1 2 LLLsL Perf. Perf. Maj. Maj. Perf. Perf.
2|2 3 LLsLL Perf. Perf. Maj. Min. Perf. Perf.
1|3 4 LsLLL Perf. Perf. Min. Min. Perf. Perf.
0|4 5 sLLLL Perf. Dim. Min. Min. Perf. Perf.

Proposed names

Additionally, CellularAutomaton has proposed names based on Latin names for fingers of the hand for increased distinctiveness and memorability.

Modes names of 4L 1s
UDP Step pattern CellularAutomaton's names
0 LLLLs Minimal
1 LLLsL Medicinal
2 LLsLL Medial
3 LsLLL Indical
4 sLLLL Pollical

Scale tree

Scale tree and tuning spectrum of 4L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\5 240.000 960.000 1:1 1.000 Equalized 4L 1s
6\29 248.276 951.724 6:5 1.200 Immunity↑
5\24 250.000 950.000 5:4 1.250 Semaphore
9\43 251.163 948.837 9:7 1.286
4\19 252.632 947.368 4:3 1.333 Supersoft 4L 1s
Godzilla
11\52 253.846 946.154 11:8 1.375
7\33 254.545 945.455 7:5 1.400
10\47 255.319 944.681 10:7 1.429
3\14 257.143 942.857 3:2 1.500 Soft 4L 1s
11\51 258.824 941.176 11:7 1.571
8\37 259.459 940.541 8:5 1.600
13\60 260.000 940.000 13:8 1.625 Golden bug
5\23 260.870 939.130 5:3 1.667 Semisoft 4L 1s
Superpelog
12\55 261.818 938.182 12:7 1.714
7\32 262.500 937.500 7:4 1.750
9\41 263.415 936.585 9:5 1.800 Septimin
2\9 266.667 933.333 2:1 2.000 Basic 4L 1s
9\40 270.000 930.000 9:4 2.250 Infraorwell
7\31 270.968 929.032 7:3 2.333
12\53 271.698 928.302 12:5 2.400 Orwell
5\22 272.727 927.273 5:2 2.500 Semihard 4L 1s
13\57 273.684 926.316 13:5 2.600
8\35 274.286 925.714 8:3 2.667
11\48 275.000 925.000 11:4 2.750
3\13 276.923 923.077 3:1 3.000 Hard 4L 1s
10\43 279.070 920.930 10:3 3.333
7\30 280.000 920.000 7:2 3.500
11\47 280.851 919.149 11:3 3.667
4\17 282.353 917.647 4:1 4.000 Superhard 4L 1s
9\38 284.211 915.789 9:2 4.500 Subklei
5\21 285.714 914.286 5:1 5.000
6\25 288.000 912.000 6:1 6.000 Quasitemp↓
1\4 300.000 900.000 1:0 → ∞ Collapsed 4L 1s
Retrieved from "https://en.xen.wiki/index.php?title=4L_1s&oldid=207877"