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

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=== Simple tunings ===
=== Simple tunings ===
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 2/1; 3/2}}
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 2/1; 3/2}}
{| class="wikitable sortable"
|+Proposed table output for MOS degrees template (not a template)
! rowspan="2" |Degree
! rowspan="2" |Note name
! colspan="2" |2/1 step ratio
(11edo)
! colspan="2" |3/1 step ratio
(15edo)
! colspan="2" |3/2 step ratio
(18edo)
|-
!Steps
!Cents
!Steps
!Cents
!Steps
!Cents
|-
|Perf. 0-mosstep (unison)
|J
|0
|0¢
|0
|0¢
|0
|0¢
|-
|Perf. 5-mosstep
|O
|8
|872.7¢
|11
|880¢
|13
|866.7¢
|-
|Maj. 3-mosstep
|M
|5
|545.5¢
|7
|560¢
|8
|533.3¢
|-
|Maj. 1-mosstep
|K
|2
|218.2¢
|3
|240¢
|3
|200¢
|- bgcolor="#eaeaff"
|Maj. 6-mosstep
|P&
|10
|1090.9¢
|14
|1120¢
|16
|1066.7¢
|- bgcolor="#eaeaff"
|Maj. 4-mosstep
|N&
|7
|763.6¢
|10
|800¢
|11
|733.3¢
|- bgcolor="#eaeaff"
|Aug. 2-mosstep
|L&
|4
|436.4¢
|6
|480¢
|6
|400¢
|- bgcolor="#eaeaff"
|Aug. 0-mosstep (unison)
|J&
|1
|109.1¢
|2
|160¢
|1
|66.7¢
|- bgcolor="#eaeaff"
|Aug. 5-mosstep
|O&
|9
|981.8¢
|13
|1040¢
|14
|933.3¢
|- bgcolor="#eaeaff"
|Aug. 3-mosstep
|M&
|6
|654.5¢
|9
|720¢
|9
|600¢
|- bgcolor="#eaeaff"
|Aug. 1-mosstep
|K&
|3
|327.3¢
|5
|400¢
|4
|266.7¢
|- bgcolor="#eaeaff"
|Dim. 6-mosstep
|P@
|8
|872.7¢
|10
|800¢
|14
|933.3¢
|- bgcolor="#eaeaff"
|Dim. 4-mosstep
|N@
|5
|545.5¢
|6
|480¢
|9
|600¢
|- bgcolor="#eaeaff"
|Dim. 2-mosstep
|L@
|2
|218.2¢
|2
|160¢
|4
|266.7¢
|- bgcolor="#eaeaff"
|Dim. 7-mosstep (equave)
|J@
|10
|1090.9¢
|13
|1040¢
|17
|1133.3¢
|- bgcolor="#eaeaff"
|Dim. 5-mosstep
|O@
|7
|763.6¢
|9
|720¢
|12
|800¢
|- bgcolor="#eaeaff"
|Min. 3-mosstep
|M@
|4
|436.4¢
|5
|400¢
|7
|466.7¢
|- bgcolor="#eaeaff"
|Min. 1-mosstep
|K@
|1
|109.1¢
|1
|80¢
|2
|133.3¢
|-
|Min. 6-mosstep
|P
|9
|981.8¢
|12
|960¢
|15
|1000¢
|-
|Min. 4-mosstep
|N
|6
|654.5¢
|8
|640¢
|10
|666.7¢
|-
|Perf. 2-mosstep
|L
|3
|327.3¢
|4
|320¢
|5
|333.3¢
|-
|Perf. 7-mosstep (equave)
|(J)
|11
|1200¢
|15
|1200¢
|18
|1200¢
|}
=== Soft tunings ===
=== Soft tunings ===
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=4/3; 3/2; 5/3}}
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=4/3; 3/2; 5/3}}

Revision as of 09:36, 24 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 ¢.

Notation

Step ratio Gamut
2:1 (11edo) J, J&/K@, K, L, L&/M@, M, N, N&/O@, O, P, P&/J@, J
3:1 (15edo) J, K@, J&, K, L, M@, L&, M, N, O@, N&, O, P, J@, P&, J
3:2 (18edo) J, J&, K@, K, K&/L@, L, L&, M@, M, M&/N@, N, N&, O@, O, O&/P@, P, P&, J@, J

Tunings

Simple 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) 11edo (Basic, L:s = 2:1) 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 80 1 109.1 2 133.3
Major 1-smidegree 3 240 2 218.2 3 200
Perfect 2-smidegree 4 320 3 327.3 5 333.3
Augmented 2-smidegree 6 480 4 436.4 6 400
Minor 3-smidegree 5 400 4 436.4 7 466.7
Major 3-smidegree 7 560 5 545.5 8 533.3
Minor 4-smidegree 8 640 6 654.5 10 666.7
Major 4-smidegree 10 800 7 763.6 11 733.3
Diminished 5-smidegree 9 720 7 763.6 12 800
Perfect 5-smidegree 11 880 8 872.7 13 866.7
Minor 6-smidegree 12 960 9 981.8 15 1000
Major 6-smidegree 14 1120 10 1090.9 16 1066.7
Perfect 7-smidegree (octave) 15 1200 11 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 25edo (Supersoft, L:s = 4:3) 18edo (Soft, L:s = 3:2) 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 3 144 2 133.3 3 124.1
Major 1-smidegree 4 192 3 200 5 206.9
Perfect 2-smidegree 7 336 5 333.3 8 331
Augmented 2-smidegree 8 384 6 400 10 413.8
Minor 3-smidegree 10 480 7 466.7 11 455.2
Major 3-smidegree 11 528 8 533.3 13 537.9
Minor 4-smidegree 14 672 10 666.7 16 662.1
Major 4-smidegree 15 720 11 733.3 18 744.8
Diminished 5-smidegree 17 816 12 800 19 786.2
Perfect 5-smidegree 18 864 13 866.7 21 869
Minor 6-smidegree 21 1008 15 1000 24 993.1
Major 6-smidegree 22 1056 16 1066.7 26 1075.9
Perfect 7-smidegree (octave) 25 1200 18 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 26edo (Semihard, L:s = 5:2) 15edo (Hard, L:s = 3:1) 19edo (Superhard, L:s = 4:1) 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 92.3 1 80 1 63.2
Major 1-smidegree 5 230.8 3 240 4 252.6
Perfect 2-smidegree 7 323.1 4 320 5 315.8
Augmented 2-smidegree 10 461.5 6 480 8 505.3
Minor 3-smidegree 9 415.4 5 400 6 378.9
Major 3-smidegree 12 553.8 7 560 9 568.4
Minor 4-smidegree 14 646.2 8 640 10 631.6
Major 4-smidegree 17 784.6 10 800 13 821.1
Diminished 5-smidegree 16 738.5 9 720 11 694.7
Perfect 5-smidegree 19 876.9 11 880 14 884.2
Minor 6-smidegree 21 969.2 12 960 15 947.4
Major 6-smidegree 24 1107.7 14 1120 18 1136.8
Perfect 7-smidegree (octave) 26 1200 15 1200 19 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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