User:Ganaram inukshuk/4L 3s

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Scale structure
Step pattern LLsLsLs
sLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\7 to 3\4 (857.1 ¢ to 900.0 ¢)
Dark 1\4 to 2\7 (300.0 ¢ to 342.9 ¢)
TAMNAMS information
Name smitonic
Prefix smi-
Abbrev. smi
Related MOS scales
Parent 3L 1s
Sister 3L 4s
Daughters 7L 4s, 4L 7s
Neutralized 1L 6s
2-Flought 11L 3s, 4L 10s
Equal tunings
Equalized (L:s = 1:1) 5\7 (857.1 ¢)
Supersoft (L:s = 4:3) 18\25 (864.0 ¢)
Soft (L:s = 3:2) 13\18 (866.7 ¢)
Semisoft (L:s = 5:3) 21\29 (869.0 ¢)
Basic (L:s = 2:1) 8\11 (872.7 ¢)
Semihard (L:s = 5:2) 19\26 (876.9 ¢)
Hard (L:s = 3:1) 11\15 (880.0 ¢)
Superhard (L:s = 4:1) 14\19 (884.2 ¢)
Collapsed (L:s = 1:0) 3\4 (900.0 ¢)
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This is a test page. For the main page, see 4L 3s.

4L 3s, named smitonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 3 small steps, repeating every octave. Generators that produce this scale range from 857.1 ¢ to 900 ¢, or from 300 ¢ to 342.9 ¢. 4L 3s can be though of as a warped diatonic scale, where one large step of diatonic (5L 2s) is replaced with a small step.

Name

TAMNAMS suggests the name smitonic smy-TON-ik /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of 6/5 (just minor 3rd, 315.6¢).

Notation

Interval names

Names for intervals and scale degrees are based on TAMNAMS, where names for mossteps (intervals) and mosdegrees (scale degrees) are numbered starting at 0 for the unison. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.

Being a moment-of-symmetry scale, every interval class of 4L 3s, except for the unison and octave, has two varieties (or sizes), whose relative qualities are denoted as major or minor, or augmented, perfect, and diminished for the generators.

TODO: make this into a template
Interval class Large variety Small variety
Size Quality Size Quality
0-mosstep (unison) 0 Perfect 0 Perfect
1-mosstep L Major s Minor
2-mosstep L+s Augmented 2L Perfect
3-mosstep L + 2s Major 2L + s Minor
4-mosstep 2L + 2s Perfect 3L + 1s Minor
5-mosstep 2L + 3s Perfect 3L + 2s Diminished
6-mosstep 2L + 3s Major 3L + 3s Minor
7-mosstep (octave) 4L + 3s Perfect 4L + 3s Perfect

Note names

For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following:

J, J&/K@, K, L, L&/M@, M, N, N&/O@, O, P, P&/J@, J

Theory

RTT-related stuff here?

Tunings

The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Raising or lowering certain nominals by a chroma produces the following scale degrees.

MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 11edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-smidegree (unison) 0 0 1/1 (exact)
Minor 1-smidegree 1 109.1
Major 1-smidegree 2 218.2
Perfect 2-smidegree 3 327.3
Augmented 2-smidegree 4 436.4
Minor 3-smidegree 4 436.4
Major 3-smidegree 5 545.5
Minor 4-smidegree 6 654.5
Major 4-smidegree 7 763.6
Diminished 5-smidegree 7 763.6
Perfect 5-smidegree 8 872.7
Minor 6-smidegree 9 981.8
Major 6-smidegree 10 1090.9
Perfect 7-smidegree (octave) 11 1200 2/1 (exact)

Simple tunings

MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 11edo (Basic, L:s = 2:1) 15edo (Hard, L:s = 3:1) 18edo (Soft, L:s = 3:2) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-smidegree 1 109.1 1 80 2 133.3
Major 1-smidegree 2 218.2 3 240 3 200
Perfect 2-smidegree 3 327.3 4 320 5 333.3
Augmented 2-smidegree 4 436.4 6 480 6 400
Minor 3-smidegree 4 436.4 5 400 7 466.7
Major 3-smidegree 5 545.5 7 560 8 533.3
Minor 4-smidegree 6 654.5 8 640 10 666.7
Major 4-smidegree 7 763.6 10 800 11 733.3
Diminished 5-smidegree 7 763.6 9 720 12 800
Perfect 5-smidegree 8 872.7 11 880 13 866.7
Minor 6-smidegree 9 981.8 12 960 15 1000
Major 6-smidegree 10 1090.9 14 1120 16 1066.7
Perfect 7-smidegree (octave) 11 1200 15 1200 18 1200 2/1 (exact)

Soft tunings

MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 18edo (Soft, L:s = 3:2) 25edo (Supersoft, L:s = 4:3) 29edo (Semisoft, L:s = 5:3) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-smidegree 2 133.3 3 144 3 124.1
Major 1-smidegree 3 200 4 192 5 206.9
Perfect 2-smidegree 5 333.3 7 336 8 331
Augmented 2-smidegree 6 400 8 384 10 413.8
Minor 3-smidegree 7 466.7 10 480 11 455.2
Major 3-smidegree 8 533.3 11 528 13 537.9
Minor 4-smidegree 10 666.7 14 672 16 662.1
Major 4-smidegree 11 733.3 15 720 18 744.8
Diminished 5-smidegree 12 800 17 816 19 786.2
Perfect 5-smidegree 13 866.7 18 864 21 869
Minor 6-smidegree 15 1000 21 1008 24 993.1
Major 6-smidegree 16 1066.7 22 1056 26 1075.9
Perfect 7-smidegree (octave) 18 1200 25 1200 29 1200 2/1 (exact)

Hard tunings

MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 15edo (Hard, L:s = 3:1) 19edo (Superhard, L:s = 4:1) 26edo (Semihard, L:s = 5:2) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-smidegree 1 80 1 63.2 2 92.3
Major 1-smidegree 3 240 4 252.6 5 230.8
Perfect 2-smidegree 4 320 5 315.8 7 323.1
Augmented 2-smidegree 6 480 8 505.3 10 461.5
Minor 3-smidegree 5 400 6 378.9 9 415.4
Major 3-smidegree 7 560 9 568.4 12 553.8
Minor 4-smidegree 8 640 10 631.6 14 646.2
Major 4-smidegree 10 800 13 821.1 17 784.6
Diminished 5-smidegree 9 720 11 694.7 16 738.5
Perfect 5-smidegree 11 880 14 884.2 19 876.9
Minor 6-smidegree 12 960 15 947.4 21 969.2
Major 6-smidegree 14 1120 18 1136.8 24 1107.7
Perfect 7-smidegree (octave) 15 1200 19 1200 26 1200 2/1 (exact)

Modes

Modes of 4L 3s
UDP Cyclic
order		 Step
pattern
6|0 1 LLsLsLs
5|1 6 LsLLsLs
4|2 4 LsLsLLs
3|3 2 LsLsLsL
2|4 7 sLLsLsL
1|5 5 sLsLLsL
0|6 3 sLsLsLL

Tuning spectrum

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 4L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\7 857.143 342.857 1:1 1.000 Equalized 4L 3s
28\39 861.538 338.462 6:5 1.200
23\32 862.500 337.500 5:4 1.250
41\57 863.158 336.842 9:7 1.286
18\25 864.000 336.000 4:3 1.333 Supersoft 4L 3s
49\68 864.706 335.294 11:8 1.375
31\43 865.116 334.884 7:5 1.400
44\61 865.574 334.426 10:7 1.429
13\18 866.667 333.333 3:2 1.500 Soft 4L 3s
47\65 867.692 332.308 11:7 1.571
34\47 868.085 331.915 8:5 1.600
55\76 868.421 331.579 13:8 1.625
21\29 868.966 331.034 5:3 1.667 Semisoft 4L 3s
50\69 869.565 330.435 12:7 1.714
29\40 870.000 330.000 7:4 1.750
37\51 870.588 329.412 9:5 1.800
8\11 872.727 327.273 2:1 2.000 Basic 4L 3s
Scales with tunings softer than this are proper
35\48 875.000 325.000 9:4 2.250
27\37 875.676 324.324 7:3 2.333
46\63 876.190 323.810 12:5 2.400
19\26 876.923 323.077 5:2 2.500 Semihard 4L 3s
49\67 877.612 322.388 13:5 2.600
30\41 878.049 321.951 8:3 2.667
41\56 878.571 321.429 11:4 2.750
11\15 880.000 320.000 3:1 3.000 Hard 4L 3s
36\49 881.633 318.367 10:3 3.333
25\34 882.353 317.647 7:2 3.500
39\53 883.019 316.981 11:3 3.667
14\19 884.211 315.789 4:1 4.000 Superhard 4L 3s
31\42 885.714 314.286 9:2 4.500
17\23 886.957 313.043 5:1 5.000
20\27 888.889 311.111 6:1 6.000
3\4 900.000 300.000 1:0 → ∞ Collapsed 4L 3s
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