4L 1s: Difference between revisions

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{{Todo|Fix scale tree and standardize}}
{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
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.
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 ==
== Names ==
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{{MOS mode degrees}}
{{MOS mode degrees}}


===Proposed Names===
=== Proposed names ===
Additionally, cellularAutomaton has proposed names based on Latin names for fingers of the hand for increased distinctiveness and memorability.
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"
{| class="wikitable mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | Modes names of 4L 1s
|+ style=white-space:nowrap | Modes names of 4L 1s
! UDP
! UDP
! Step pattern
! Step pattern
! [[User:cellularAutomaton|cellularAutomaton]]'s names
! CellularAutomaton's names
|-
|-
| 4|0
| 4|0
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|}
|}


== Scale Tree ==
== Scale tree ==
Generator ranges:  
Generator ranges:  
* Chroma-positive generator: 240 cents (1\5) to 300 cents (1\4)
* Chroma-positive generator: 240 cents (1\5) to 300 cents (1\4)
* Chroma-negative generator: 900 cents (3\4) to 960 cents (4\5)
* Chroma-negative generator: 900 cents (3\4) to 960 cents (4\5)


{{todo|inline=1|complete table|Convert manually-generated scale tree table to MOS tuning spectrum}}
{{todo|inline=1|complete table|comment=Convert manually-generated scale tree table to mos tuning spectrum.}}
{| class="wikitable"
{| class="wikitable"
|-
|-
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| style="text-align:center;" |  
| style="text-align:center;" |  
|}
|}
== References ==
<references/>


[[Category:Manual]]
[[Category:Manual]]
[[Category:5-tone scales]]
[[Category:5-tone scales]]

Revision as of 11:08, 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

Generator ranges:

  • Chroma-positive generator: 240 cents (1\5) to 300 cents (1\4)
  • Chroma-negative generator: 900 cents (3\4) to 960 cents (4\5)
Todo: complete table

Convert manually-generated scale tree table to mos tuning spectrum.

Generator Cents s L-s Comments
1\5 240 240 0
6\29 248.28 206.9 41.38
5\24 250 200 50 Semaphore is around here
4\19 252.63 189.47 63.16
3\14 257.14 171.43 85.71
258.81 164.76 92.05
8\37 259.46 162.16 97.3
1200/(3+phi) 160.6 99.25 Golden bug / golden superpelog
5\23 260.87 156.52 104.35
262.16 151.36 110.8
2\9 266.67 133.33 133.33 Optimum rank range (L/s=2/1) bug
7\31 270.97 116.13 154.84
12\53 271.70 113.21 158.49 Orwell is around here
5\22 272.73 109.09 163.64
274.73 101.07 173.66 L/s = e
3\13 276.92 92.31 184.62 L/s = 3
277.89 88.45 189.43 L/s = pi
4\17 282.35 70.59 211.76 L/s = 4
5\21 285.71 57.14 228.57
6\25 288 48 240
1\4 300 0 300
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