User:Ganaram inukshuk/4L 3s: Difference between revisions

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Sandboxing a would-be rewrite for 4L 3s using the templates and mos page guide
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== Name ==
== 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 of the spectrum, 4\15 = 320¢ to 7\18 = 333.33¢, has minor third generators that are significantly sharp of 6/5.
[[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]] (315.6¢).


== Notation and intervals ==
== Notation ==
{| class="wikitable"
Note names are based on [[Diamond-mos notation|diamond-MOS notation]], where the nominals JKLMNOP are applied to the step pattern LsLsLsL and the symbols & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats.
|+
 
!Step ratio
Thus, the gamut for 11edo is the following:
!Gamut
 
|-
{{MOS gamut|Scale Signature=4L 3s}}
|2:1 (11edo)
 
|{{MOS gamut|Scale Signature=4L 3s}}
The notation for intervals and scale degrees are based on [[TAMNAMS]], where names for mossteps and mosdegrees start at 0 for the unison. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.
|-
|3:1 (15edo)
|{{MOS gamut|Scale Signature=4L 3s|Step Ratio=3/1}}
|-
|3:2 (18edo)
|{{MOS gamut|Scale Signature=4L 3s|Step Ratio=3/2}}
|}


== Tunings ==
== 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 any of the nominals by a [[chroma]] produces the following scale degrees.
=== '''Basic tuning''' ===
The basic tuning for 4L 3s has large steps that are 2 edosteps and small steps that are 1 edostep, which is supported by 11edo. Raising or lowering any of the nominals by a [[chroma]] produces the following scale degrees.
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1}}
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1}}
=== Simple tunings ===
=== Simple tunings ===

Revision as of 05:18, 26 June 2023

↖ 3L 2s ↑ 4L 2s 5L 2s ↗
← 3L 3s 4L 3s 5L 3s →
↙ 3L 4s ↓ 4L 4s 5L 4s ↘ 
┌╥╥┬╥┬╥┬┐
│║║│║│║││
│││││││││
└┴┴┴┴┴┴┴┘
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 ¢)
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 (315.6¢).

Notation

Note names are based on diamond-MOS notation, where the nominals JKLMNOP are applied to the step pattern LsLsLsL and the symbols & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats.

Thus, the gamut for 11edo is the following:

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

The notation for intervals and scale degrees are based on TAMNAMS, where names for mossteps and mosdegrees start at 0 for the unison. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.

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 any of the nominals by a chroma produces the following scale degrees.

User: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

User: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

User: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

User: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

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