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

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→Tunings: Sandboxing proposed table output for template
Line 28: Line 28:
|+Proposed table output for MOS degrees template
|+Proposed table output for MOS degrees template
! rowspan="2" |Degree
! rowspan="2" |Degree
! rowspan="2" |Note name on J
! rowspan="2" |Note name
! colspan="2" |2/1 step ratio (11edo)
! colspan="2" |2/1 step ratio
! colspan="2" |3/1 step ratio (15edo)
(11edo)
! colspan="2" |3/2 step ratio (18edo)
! colspan="2" |3/1 step ratio
(15edo)
! colspan="2" |3/2 step ratio
(18edo)
|-
|-
!Steps
!Steps
Line 40: Line 43:
!Cents
!Cents
|-
|-
|Perf. unison
|Perf. 0-mosstep (unison)
|J
|J
|0
|0
Line 49: Line 52:
|0¢
|0¢
|-
|-
|Aug. unison
|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¢
|-
|Maj. 6-mosstep
|P&
|10
|1090.9¢
|14
|1120¢
|16
|1066.7¢
|-
|Maj. 4-mosstep
|N&
|7
|763.6¢
|10
|800¢
|11
|733.3¢
|-
|Aug. 2-mosstep
|L&
|4
|436.4¢
|6
|480¢
|6
|400¢
|-
|Aug. 0-mosstep (unison)
|J&
|J&
|1
|1
Line 58: Line 115:
|66.7¢
|66.7¢
|-
|-
|Min. 1-smidegree
|Aug. 5-mosstep
|O&
|9
|981.8¢
|13
|1040¢
|14
|933.3¢
|-
|Aug. 3-mosstep
|M&
|6
|654.5¢
|9
|720¢
|9
|600¢
|-
|Aug. 1-mosstep
|K&
|3
|327.3¢
|5
|400¢
|4
|266.7¢
|-
|Dim. 6-mosstep
|P@
|8
|872.7¢
|10
|800¢
|14
|933.3¢
|-
|Dim. 4-mosstep
|N@
|5
|545.5¢
|6
|480¢
|9
|600¢
|-
|Dim. 2-mosstep
|L@
|2
|218.2¢
|2
|160¢
|4
|266.7¢
|-
|Dim. 7-mosstep (equave)
|J@
|10
|1090.9¢
|13
|1040¢
|17
|1133.3¢
|-
|Dim. 5-mosstep
|O@
|7
|763.6¢
|9
|720¢
|12
|800¢
|-
|Min. 3-mosstep
|M@
|4
|436.4¢
|5
|400¢
|7
|466.7¢
|-
|Min. 1-mosstep
|K@
|K@
|1
|1
Line 67: Line 205:
|133.3¢
|133.3¢
|-
|-
|. . .
|Min. 6-mosstep
|
|P
|
|9
|
|981.8¢
|
|12
|
|960¢
|
|15
|
|1000¢
|-
|-
|Dim. octave
|Min. 4-mosstep
|J@
|N
|6
|654.5¢
|8
|640¢
|10
|10
|1090.9¢
|666.7¢
|13
|-
|1040¢
|Perf. 2-mosstep
|17
|L
|1133.3¢
|3
|327.3¢
|4
|320¢
|5
|333.3¢
|-
|-
|Perf. octave
|Perf. 7-mosstep (equave)
|J
|(J)
|11
|11
|1200¢
|1200¢

Revision as of 22:29, 22 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 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)
User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 15edo (Hard, L:s = 3:1) Approx. JI Ratios
Steps Cents
Perfect 0-smidegree (unison) 0 0 1/1 (exact)
Minor 1-smidegree 1 80
Major 1-smidegree 3 240
Perfect 2-smidegree 4 320
Augmented 2-smidegree 6 480
Minor 3-smidegree 5 400
Major 3-smidegree 7 560
Minor 4-smidegree 8 640
Major 4-smidegree 10 800
Diminished 5-smidegree 9 720
Perfect 5-smidegree 11 880
Minor 6-smidegree 12 960
Major 6-smidegree 14 1120
Perfect 7-smidegree (octave) 15 1200 2/1 (exact)
User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 18edo (Soft, L:s = 3:2) Approx. JI Ratios
Steps Cents
Perfect 0-smidegree (unison) 0 0 1/1 (exact)
Minor 1-smidegree 2 133.3
Major 1-smidegree 3 200
Perfect 2-smidegree 5 333.3
Augmented 2-smidegree 6 400
Minor 3-smidegree 7 466.7
Major 3-smidegree 8 533.3
Minor 4-smidegree 10 666.7
Major 4-smidegree 11 733.3
Diminished 5-smidegree 12 800
Perfect 5-smidegree 13 866.7
Minor 6-smidegree 15 1000
Major 6-smidegree 16 1066.7
Perfect 7-smidegree (octave) 18 1200 2/1 (exact)
Proposed table output for MOS degrees template
Degree Note name 2/1 step ratio

(11edo)

3/1 step ratio

(15edo)

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¢
Maj. 6-mosstep P& 10 1090.9¢ 14 1120¢ 16 1066.7¢
Maj. 4-mosstep N& 7 763.6¢ 10 800¢ 11 733.3¢
Aug. 2-mosstep L& 4 436.4¢ 6 480¢ 6 400¢
Aug. 0-mosstep (unison) J& 1 109.1¢ 2 160¢ 1 66.7¢
Aug. 5-mosstep O& 9 981.8¢ 13 1040¢ 14 933.3¢
Aug. 3-mosstep M& 6 654.5¢ 9 720¢ 9 600¢
Aug. 1-mosstep K& 3 327.3¢ 5 400¢ 4 266.7¢
Dim. 6-mosstep P@ 8 872.7¢ 10 800¢ 14 933.3¢
Dim. 4-mosstep N@ 5 545.5¢ 6 480¢ 9 600¢
Dim. 2-mosstep L@ 2 218.2¢ 2 160¢ 4 266.7¢
Dim. 7-mosstep (equave) J@ 10 1090.9¢ 13 1040¢ 17 1133.3¢
Dim. 5-mosstep O@ 7 763.6¢ 9 720¢ 12 800¢
Min. 3-mosstep M@ 4 436.4¢ 5 400¢ 7 466.7¢
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¢

Supersoft

Semisoft

Semihard

Superhard

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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