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

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→Tunings: Sandboxing proposed table output for template
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Reduced number of columns in test table
Line 29: Line 29:
! rowspan="2" |Degree
! rowspan="2" |Degree
! rowspan="2" |Note name
! rowspan="2" |Note name
! colspan="2" |2/1 step ratio
!2/1 step ratio
(11edo)
!3/1 step ratio
! colspan="2" |3/1 step ratio
!3/2 step ratio
(15edo)
! colspan="2" |3/2 step ratio
(18edo)
|-
|-
!Steps
!Steps of 11edo
!Cents
(cents)
!Steps
!Steps of 15edo
!Cents
(cents)
!Steps
!Steps of 18edo
!Cents
(cents)
|-
|-
|Perf. 0-mosstep (unison)
|Perf. 0-mosstep (unison)
|J
|J
|0
|0\11
|0¢
(0¢)
|0
|0\15
|0¢
(0¢)
|0
|0\18
|0¢
(0¢)
|-
|-
|Perf. 5-mosstep
|Perf. 5-mosstep
|O
|O
|8
|8\11
|872.7¢
(872.7¢)
|11
|11\15
|880¢
(880¢)
|13
|13\18
|866.7¢
(866.7¢)
|-
|-
|Maj. 3-mosstep
|Maj. 3-mosstep
|M
|M
|5
|5\11
|545.5¢
(545.5¢)
|7
|7\15
|560¢
(560¢)
|8
|8\18
|533.3¢
(533.3¢)
|-
|-
|Maj. 1-mosstep
|Maj. 1-mosstep
|K
|K
|2
|2\11
|218.2¢
(218.2¢)
|3
|3\15
|240¢
(240¢)
|3
|3\18
|200¢
(200¢)
|-
|-
|Maj. 6-mosstep
|Maj. 6-mosstep
|P&
|P&
|10
|10\11
|1090.9¢
(1090.9¢)
|14
|14\15
|1120¢
(1120¢)
|16
|16\18
|1066.7¢
(1066.7¢)
|-
|-
|Maj. 4-mosstep
|Maj. 4-mosstep
|N&
|N&
|7
|7\11
|763.6¢
(763.6¢)
|10
|10\15
|800¢
(800¢)
|11
|11\18
|733.3¢
(733.3¢)
|-
|-
|Aug. 2-mosstep
|Aug. 2-mosstep
|L&
|L&
|4
|4\11
|436.4¢
(436.4¢)
|6
|6\15
|480¢
(480¢)
|6
|6\18
|400¢
(400¢)
|-
|-
|Aug. 0-mosstep (unison)
|Aug. 0-mosstep (unison)
|J&
|J&
|1
|1\11
|109.1¢
(109.1¢)
|2
|2\15
|160¢
(160¢)
|1
|1\18
|66.7¢
(66.7¢)
|-
|-
|Aug. 5-mosstep
|Aug. 5-mosstep
|O&
|O&
|9
|9\11
|981.8¢
(981.8¢)
|13
|13\15
|1040¢
(1040¢)
|14
|14\18
|933.3¢
(933.3¢)
|-
|-
|Aug. 3-mosstep
|Aug. 3-mosstep
|M&
|M&
|6
|6\11
|654.5¢
(654.5¢)
|9
|9\15
|720¢
(720¢)
|9
|9\18
|600¢
(600¢)
|-
|-
|Aug. 1-mosstep
|Aug. 1-mosstep
|K&
|K&
|3
|3\11
|327.3¢
(327.3¢)
|5
|5\15
|400¢
(400¢)
|4
|4\18
|266.7¢
(266.7¢)
|-
|-
|Dim. 6-mosstep
|Dim. 6-mosstep
|P@
|P@
|8
|8\11
|872.7¢
(872.7¢)
|10
|10\15
|800¢
(800¢)
|14
|14\18
|933.3¢
(933.3¢)
|-
|-
|Dim. 4-mosstep
|Dim. 4-mosstep
|N@
|N@
|5
|5\11
|545.5¢
(545.5¢)
|6
|6\15
|480¢
(480¢)
|9
|9\18
|600¢
(600¢)
|-
|-
|Dim. 2-mosstep
|Dim. 2-mosstep
|L@
|L@
|2
|2\11
|218.2¢
(218.2¢)
|2
|2\15
|160¢
(160¢)
|4
|4\18
|266.7¢
(266.7¢)
|-
|-
|Dim. 7-mosstep (equave)
|Dim. 7-mosstep (equave)
|J@
|J@
|10
|10\11
|1090.9¢
(1090.9¢)
|13
|13\15
|1040¢
(1040¢)
|17
|17\18
|1133.3¢
(1133.3¢)
|-
|-
|Dim. 5-mosstep
|Dim. 5-mosstep
|O@
|O@
|7
|7\11
|763.6¢
(763.6¢)
|9
|9\15
|720¢
(720¢)
|12
|12\18
|800¢
(800¢)
|-
|-
|Min. 3-mosstep
|Min. 3-mosstep
|M@
|M@
|4
|4\11
|436.4¢
(436.4¢)
|5
|5\15
|400¢
(400¢)
|7
|7\18
|466.7¢
(466.7¢)
|-
|-
|Min. 1-mosstep
|Min. 1-mosstep
|K@
|K@
|1
|1\11
|109.1¢
(109.1¢)
|1
|1\15
|80¢
(80¢)
|2
|2\18
|133.3¢
(133.3¢)
|-
|-
|Min. 6-mosstep
|Min. 6-mosstep
|P
|P
|9
|9\11
|981.8¢
(981.8¢)
|12
|12\15
|960¢
(960¢)
|15
|15\18
|1000¢
(1000¢)
|-
|-
|Min. 4-mosstep
|Min. 4-mosstep
|N
|N
|6
|6\11
|654.5¢
(654.5¢)
|8
|8\15
|640¢
(640¢)
|10
|10\18
|666.7¢
(666.7¢)
|-
|-
|Perf. 2-mosstep
|Perf. 2-mosstep
|L
|L
|3
|3\11
|327.3¢
(327.3¢)
|4
|4\15
|320¢
(320¢)
|5
|5\18
|333.3¢
(333.3¢)
|-
|-
|Perf. 7-mosstep (equave)
|Perf. 7-mosstep (equave)
|(J)
|(J)
|11
|11\11
|1200¢
(1200¢)
|15
|15\15
|1200¢
(1200¢)
|18
|18\18
|1200¢
(1200¢)
|}
|}


Revision as of 22:51, 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 3/1 step ratio 3/2 step ratio
Steps of 11edo

(cents)

Steps of 15edo

(cents)

Steps of 18edo

(cents)

Perf. 0-mosstep (unison) J 0\11

(0¢)

0\15

(0¢)

0\18

(0¢)

Perf. 5-mosstep O 8\11

(872.7¢)

11\15

(880¢)

13\18

(866.7¢)

Maj. 3-mosstep M 5\11

(545.5¢)

7\15

(560¢)

8\18

(533.3¢)

Maj. 1-mosstep K 2\11

(218.2¢)

3\15

(240¢)

3\18

(200¢)

Maj. 6-mosstep P& 10\11

(1090.9¢)

14\15

(1120¢)

16\18

(1066.7¢)

Maj. 4-mosstep N& 7\11

(763.6¢)

10\15

(800¢)

11\18

(733.3¢)

Aug. 2-mosstep L& 4\11

(436.4¢)

6\15

(480¢)

6\18

(400¢)

Aug. 0-mosstep (unison) J& 1\11

(109.1¢)

2\15

(160¢)

1\18

(66.7¢)

Aug. 5-mosstep O& 9\11

(981.8¢)

13\15

(1040¢)

14\18

(933.3¢)

Aug. 3-mosstep M& 6\11

(654.5¢)

9\15

(720¢)

9\18

(600¢)

Aug. 1-mosstep K& 3\11

(327.3¢)

5\15

(400¢)

4\18

(266.7¢)

Dim. 6-mosstep P@ 8\11

(872.7¢)

10\15

(800¢)

14\18

(933.3¢)

Dim. 4-mosstep N@ 5\11

(545.5¢)

6\15

(480¢)

9\18

(600¢)

Dim. 2-mosstep L@ 2\11

(218.2¢)

2\15

(160¢)

4\18

(266.7¢)

Dim. 7-mosstep (equave) J@ 10\11

(1090.9¢)

13\15

(1040¢)

17\18

(1133.3¢)

Dim. 5-mosstep O@ 7\11

(763.6¢)

9\15

(720¢)

12\18

(800¢)

Min. 3-mosstep M@ 4\11

(436.4¢)

5\15

(400¢)

7\18

(466.7¢)

Min. 1-mosstep K@ 1\11

(109.1¢)

1\15

(80¢)

2\18

(133.3¢)

Min. 6-mosstep P 9\11

(981.8¢)

12\15

(960¢)

15\18

(1000¢)

Min. 4-mosstep N 6\11

(654.5¢)

8\15

(640¢)

10\18

(666.7¢)

Perf. 2-mosstep L 3\11

(327.3¢)

4\15

(320¢)

5\18

(333.3¢)

Perf. 7-mosstep (equave) (J) 11\11

(1200¢)

15\15

(1200¢)

18\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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