User:Moremajorthanmajor/9L 4s (7/2-equivalent): Difference between revisions

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|1\35
|1\35
''62; 1, 6''
''62; 1, 6''
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|2\57
''77; 5, 5, 2''
| rowspan="2" |1\22
| rowspan="2" |1\22
''100''
''100''
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|2\35
|2\35
''125; 1, 2, 2''
''125; 1, 2, 2''
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|3\57
''115; 1, 3, 1, 3''
|2\53
|2\53
''83; 53''
''83; 53''
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|3\35
|3\35
''188; 1, 1, 3''
''188; 1, 1, 3''
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|5\57
''192; 1, 56''
|2\22
|2\22
''200''
''200''
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|4\35
|4\35
''251; 2, 3''
''251; 2, 3''
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|7\57
''270; 5, 1, 2, 3''
| rowspan="2" |3\22
| rowspan="2" |3\22
''300''
''300''
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|5\35
|5\35
''314; 3, 2''
''314; 3, 2''
|
|8\57
''308; 1, 3, 2, 1, 1, 2''
|7\53
|7\53
''290; 1, 1, 3, 3, 2''
''290; 1, 1, 3, 3, 2''
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|6\35
|6\35
''377; 7''
''377; 7''
|
|10\57
''385; 1, 27, 2''
|4\22
|4\22
''400''
''400''
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| rowspan="2" |7\35
| rowspan="2" |7\35
''440''
''440''
|
|12\57
''463; 6, 3''
|5\22
|5\22
''500''
''500''
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|10\48
|10\48
''458.{{Overline|3}}''
''458.{{Overline|3}}''
|
|11\57
''424; 1, 1, 3, 1, 1, 3''
|4\22
|4\22
''400''
''400''
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|'''8\35'''
|'''8\35'''
'''''502; 1, 6'''''
'''''502; 1, 6'''''
|
|'''13\57'''
'''''501; 1, 3, 14'''''
|'''5\22'''
|'''5\22'''
'''''500'''''
'''''500'''''
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|9\35
|9\35
''565; 1, 2, 2''
''565; 1, 2, 2''
|
|15\57
''578; 1, 18''
| rowspan="2" |6\22
| rowspan="2" |6\22
''600''
''600''
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|10\35
|10\35
''628; 1, 1, 3''
''628; 1, 1, 3''
|
|16\57
''617; 1, 1, 5, 5''
|14\53
|14\53
''581; 7, 1, 1, 3''
''581; 7, 1, 1, 3''
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|11\35
|11\35
''691; 2, 3''
''691; 2, 3''
|
|18\57
''694; 1, 2, 1, 4''
|7\22
|7\22
''700''
''700''
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|12\35
|12\35
''754; 3, 2''
''754; 3, 2''
|
|20\57
''771; 1, 13, 4''
| rowspan="2" |8\22
| rowspan="2" |8\22
''800''
''800''
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|13\35
|13\35
''817; 7''
''817; 7''
|
|21\57
''810; 1, 1, 9''
|19\53
|19\53
''788; 1, 2, 8, 2''
''788; 1, 2, 8, 2''
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|14\35
|14\35
''880''
''880''
|
|23\57
''887; 1, 2, 1, 1, 3, 2''
|9\22
|9\22
''900''
''900''
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|15\35
|15\35
''942; 1, 6''
''942; 1, 6''
|
|25\57
''964; 1, 10, 3, 2''
| rowspan="2" |10\22
| rowspan="2" |10\22
''1000''
''1000''
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|16\35
|16\35
''1005; 1, 2, 2''
''1005; 1, 2, 2''
|
|26\57
''1003; 1, 1, 28''
|24\53
|24\53
''996: 4, 2, 2, 2''
''996: 4, 2, 2, 2''
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|17\35
|17\35
''1068; 1, 1, 3''
''1068; 1, 1, 3''
|
|28\57
''1080; 1, 2, 2, 1, 5''
|11\22
|11\22
''1100''
''1100''
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| rowspan="2" |18\35
| rowspan="2" |18\35
''1131; 2, 3''
''1131; 2, 3''
|
|30\57
''1157; 1, 8, 2''
|12\22
|12\22
''1200''
''1200''
|30\29
|30\29
''1245; 3, 1, 1, 7''
''1245; 3, 1, 1, 7''
|15\31
|18\31
''1064; 1, 1, 15''
''1277; 2, 2, 1, 1, 2''
|24\40
|24\40
''1320''
''1320''
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|25\48
|25\48
''1145.8{{Overline|3}}''
''1145.8{{Overline|3}}''
|
|29\57
''1119; 3, 2, 1, 5''
|11\22
|11\22
''1100''
''1100''
|26\53
|26\53
''1079; 4, 13''
''1079; 4, 13''
|18\31
|15\31
''1277; 2, 3, 1, 2''
''1064; 1, 1, 15''
|19\40
|19\40
''1045''
''1045''
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|19\35
|19\35
''1194: 3, 2''
''1194: 3, 2''
|
|31\57
''1196; 2, 28''
|12\22
|12\22
''1200''
''1200''
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|20\35
|20\35
''1257: 7''
''1257: 7''
|
|33\57
''1273; 1, 2, 6''
| rowspan="2" |13\22
| rowspan="2" |13\22
''1300''
''1300''
|32\53
|32\53
''1328; 3, 3, 5''
''1328; 3, 3, 5''
|18\31
|19\31
''1277; 2, 3, 1, 2''
''1348; 2, 1, 1, 2, 2''
|25\40
|25\40
''1375''
''1375''
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|せ (しb)
|せ (しb)
|29\48
|29\48
''1329.1''{{Overline|6}}
''1329.1{{Overline|6}}''
|21\35
|21\35
''1320''
''1320''
|
|34\57
''1312; 3, 1, 1, 3, 2''
|31\53
|31\53
''1286; 1, 3, 1, 1, 2''
''1286; 1, 3, 1, 1, 2''
|19\31
|18\31
''1348; 2, 1, 1, 2, 2''
''1277; 2, 2, 1, 1, 2''
|23\40
|23\40
''1265''
''1265''
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|22\35
|22\35
''1382; 1, 6''
''1382; 1, 6''
|
|36\57
''1389; 2, 9''
|14\22
|14\22
''1400''
''1400''
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|23\35
|23\35
''1445; 1, 2, 2''
''1445; 1, 2, 2''
|
|38\57
''1466.{{Overline|6}}''
| rowspan="2" |15\22
| rowspan="2" |15\22
''1500''
''1500''
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|24\35
|24\35
''1508; 1, 1, 3''
''1508; 1, 1, 3''
|
|39\57
''1505; 3, 1, 4''
|36\53
|36\53
''1394; 2, 1, 17''
''1394; 2, 1, 17''
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|25\35
|25\35
''1571; 2, 3''
''1571; 2, 3''
|
|41\57
''1582; 2, 5, 5''
|16\22
|16\22
''1600''
''1600''
Line 1,032: Line 1,059:
| rowspan="2" |26\35
| rowspan="2" |26\35
''1633; 3, 2''
''1633; 3, 2''
|
|43\57
''1659; 1, 1, 1, 5, 1, 3''
|17\22
|17\22
''1700''
''1700''
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|36\48
|36\48
''1650''
''1650''
|
|42\57
''1621; 19''
|16\22
|16\22
''1600''
''1600''
Line 1,060: Line 1,089:
|'''27\35'''
|'''27\35'''
'''''1696; 7'''''
'''''1696; 7'''''
|
|'''44\57'''
'''''1699; 4, 14'''''
|'''17\22'''
|'''17\22'''
'''''1700'''''
'''''1700'''''
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|28\35
|28\35
''1760''
''1760''
|
|46\57
''1775; 2, 3, 1, 1, 3''
| rowspan="2" |18\22
| rowspan="2" |18\22
''1800''
''1800''
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|29\35
|29\35
''1822; 1, 6''
''1822; 1, 6''
|
|47\57
''1814; 28, 2''
|43\53
|43\53
''1784; 1, 9, 1, 1, 2''
''1784; 1, 9, 1, 1, 2''
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|30\35
|30\35
''1885; 1, 2, 2''
''1885; 1, 2, 2''
|
|49\57
''1891; 4, 2, 1, 1, 2''
|19\22
|19\22
''1900''
''1900''
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|31\35
|31\35
''1948; 1, 1, 3''
''1948; 1, 1, 3''
|
|51\57
''1968; 2, 2, 1, 2''
| rowspan="2" |20\22
| rowspan="2" |20\22
''2000''
''2000''
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|32\35
|32\35
''2011; 2, 3''
''2011; 2, 3''
|
|52\57
''2007; 57''
|48\53
|48\53
''1992; 2, 4, 1, 4''
''1992; 2, 4, 1, 4''
Line 1,146: Line 1,181:
|33\35
|33\35
''2075; 3, 2''
''2075; 3, 2''
|
|54\57
2084; 4, 1, 3
|21\22
|21\22
''2100''
''2100''
Line 1,160: Line 1,196:
''2108.{{Overline|3}}''
''2108.{{Overline|3}}''
| rowspan="2" |34\35
| rowspan="2" |34\35
2138; 7
''2138; 7''
|
|56\57
''2161; 2, 2, 11''
|22\22
|22\22
''2200''
''2200''
Line 1,174: Line 1,211:
|47\48
|47\48
''2154.1{{Overline|6}}''
''2154.1{{Overline|6}}''
|
|55\57
''2122; 1, 4, 5, 2''
|21\22
|21\22
''2100''
''2100''
Line 1,185: Line 1,223:
|-
|-
!く
!く
! colspan="7" |''2200''
! colspan="6" |''2200''
!
|}
 
== Intervals ==
{| class="wikitable"
|+
!Generators
!Fourteenth notation
!Interval category name
!Generators
!Notation of 7/2ish inverse
!Interval category name
|-
| colspan="6" |The 13-note MOS has the following intervals (from some root):
|-
|0
|く
|perfect unison
|0
|く
|“perfect” minor fourteenth
|-
|1
|に
|natural eleventh
| -1
|ぬ
|natural fourth
|-
|2
|き
|perfect octave
| -2
|け (ゆb)
|minor seventh
|-
|3
|ふ
|natural fifth
| -3
|て (ちb)
|minor tenth
|-
|4
|す
|major second
| -4
|め (みb)
|minor thirteenth
|-
|5
|ひ
|natural twelfth (tritave)
| -5
|と (つb)
|minor third
|-
|6
|し
|major ninth
| -6
|も (むb)
|minor sixth
|-
|7
|む
|major sixth
| -7
|せ (しb)
|minor ninth
|-
|8
|つ
|major third
| -8
|へ (ひb)
|diminished twelfth
|-
|9
|み
|major thirteenth
| -9
|そ (すb)
|minor second
|-
|10
|ち
|major tenth
| -10
|ほ (ふb)
|diminished fifth
|-
|11
|ゆ
|major seventh
| -11
|ま (きb)
|diminished octave
|-
|12
|な (ぬ#)
|augmented fourth
| -12
|ね (にb)
|diminished eleventh
|-
|13
|か (く#)
|augmented unison
| -13
|け (くb)
|diminished fourteenth
|-
| colspan="6" |The chromatic 22-note MOS (either [[13L 9s (minor fourteenth equivalent)|13L 9s]], [[9L 13s (minor fourteenth equivalent)|9L 13s]] or [[22edXIV]]) also has these intervals
|-
|14
|に#
|augmented eleventh
| -14
|の (ぬb)
|diminished fourth
|-
|15
|き#
|augmented octave
| -15
|けb (ゆbb)
|diminished seventh
|-
|16
|は (ふ#)
|augmented fifth
| -16
|てb (ちbb)
|diminished tenth
|-
|17
|さ (す#)
|augmented second
| -17
|めb (みbb)
|diminished thirteenth
|-
|18
|に#
|augmented twelfth
| -18
|とb (つbb)
|diminished third
|-
|19
|し#
|augmented ninth
| -19
|もb (むbb)
|diminished sixth
|-
|20
|よ (む#)
|augmented sixth
| -20
|せb (しbb)
|diminished ninth
|-
|21
|た (つ#)
|augmented third
| -21
|へb (ひbb)
|doubly diminished twelfth
|}
|}

Revision as of 22:31, 28 July 2022

Shōsūshī - so named because of the four small steps in its diatonic MOS - is an excellent 8*-limit temperament tempering out 64/63 or an excellent 9 (18)-limit temperament tempering out 81/80.

Properties

In shōsūshī, the just major 21st (15/2) is divided into 7 equal steps. These steps form quartal harmonies (1-4/3-7/4-7/3…). Alternately, the ‘perfect eleventh’ 8/3 also makes a good shōsūshī generator. Compatible equal temperaments include 22edXIV; 31edXIV, 40edXIV and 49edXIV (7-ward) and 35edXIV, 48edXIV and 61edXIV (9-ward).

Notation

Because shōsūshī is a Mahjong hand, its MOS has 13 tones, as in the 13 tiles in a Mahjong hand and its “13 han” Japanese value. Thus the nominals are given as Japanese kana, and to avoid confusion with traditional Japanese notations, hiragana are used.

The notation used in this article is く す つ ぬ ふ む ゆ き し ち に ひ み = LLsLLLsLLsLLs (Ionian b14), #/b mostly two chromas up/down.

Thus the 22edXIV gamut is as follows:

く/み# か/そ す さ/と つ/の ぬ/た な/ほ ふ は/も む ま/よ ゆ/け き/や き#/せ し し#/て ち/ね ち#/に に#/へ ひ ひ#/め み/け

The 31edXIV gamut is notated as follows:

く み#/そ か す と さ/の つ ぬ た/ほ な ふ も は む よ ま/け ゆ き や/せ き# し て し#/ね ち に ち#/へ に# ひ め ひ#/け み

The 35edXIV gamut:

く か/そb そ/か# す さ/とb と/さ# つ/のb た/の ぬ/た# な/ほb ほ/な# ふ は/もb も/は# む よ/けb け/よ# ゆ/やb や/ま き/ま# き#/せb せ し し#/てb て ち/ねb ち#/ね に に#/へb へ ひ ひ#/めb め み/けb み#/け

Cents[1]
Notation Supersoft Soft Semisoft Basic Semihard Hard Superhard
か (く#) 1\48

46; 6, 2

1\35

63: 6, 3

2\57

77; 2, 2, 1, 1

1\22

100

3\53

124; 7, 4

2\31

141; 5, 1, 2

3\40

163.63

そ (すb) 3\48

138; 3, 4

2\35

126; 3, 6

3\57

116; 7, 1, 3

2\53

82; 1, 3, 7

1\31

70; 1, 1, 2, 3

1\40

54.54

す 4\48

184; 1, 1, 1, 1, 2

3\35

189; 2, 9

5\57

193; 1, 1, 4, 1, 2

2\22

200

5\53

206; 1, 8, 1, 2

3\31

211; 1, 3, 4

4\40

218.18

さ (す#) 5\48

230; 1, 3, 3

4\35

252; 1, 1, 1, 2, 2

7\57

270; 1, 30

3\22

300

8\53

331; 29

5\31

352; 1, 16

7\40

381.81

と (つb) 7\48

323; 13

5\35

315; 1, 3, 1, 3

8\57

309; 1, 2, 10

7\53

289; 1, 1, 1, 9

4\31

282; 2, 1, 5

5\40

272.72

つ 8\48

369; 4, 3

6\35

378; 1, 18

10\57

387; 10, 3

4\22

400

10\53

413; 1, 3, 1, 5

6\31

423; 1, 1, 8

8\40

436.36

た (つ#) 9\48

415; 2, 2, 2

7\35

442; 9, 2

12\57

464; 1, 1, 15

5\22

500

13\53

537; 13, 2

8\31

564; 1, 2, 2, 2

11\40

600

の (ぬb) 10\48

461; 1, 1, 6

11\57

425; 1, 4, 6

4\22

400

9\53

372; 2, 2, 2, 2

5\31

352; 1, 16

6\40

327.27

ぬ 11\48

507; 1, 1, 2, 4

8\35

505; 3, 1, 4

13\57

503; 4, 2, 3

5\22

500

12\53

496; 1, 1, 4, 3

7\31

494; 8, 2

9\40

490.90

な (ぬ#) 12\48

553; 1, 5, 2

9\35

568; 2, 2, 1, 2

15\57

580; 1, 1, 4, 2

6\22

600

15\53

620; 1, 2, 4, 2

9\31

635; 3, 2, 2

12\40

654.54

ほ (ふb) 14\48

646; 6, 2

10\35

631; 1, 1, 2, 1, 2

16\57

619; 2, 4, 2

14\53

579; 9, 1, 2

8\31

564; 1, 2, 2, 2

10\40

545.45

ふ 15\48

692; 3, 4

11\35

694; 1, 2, 1, 4

18\57

696; 1, 3, 2, 3

7\22

700

17\53

703; 2, 4, 3

10\31

705; 1, 7, 2

13\40

709.09

は (ふ#) 16\48

738; 3, 4

12\35

757; 1, 8, 2

20\57

774; 5, 6

8\22

800

20\53

827; 1, 1, 2, 2, 2

12\31

847; 17

16\40

872.72

も (むb) 18\48

830; 1, 3, 3

13\35

821; 19

21\57

812; 1, 9, 3

19\53

786; 4, 1, 5

11\31

776; 2, 8

14\40

763.63

む 19\48

876; 1, 12

14\35

884; 4, 1, 3

23\57

890; 3, 10

9\22

900

22\53

910; 2, 1, 9

13\31

917; 1, 1, 1, 5

17\40

927.27

よ (む#) 20\48

923; 13

15\35

947; 2, 1, 2, 2

25\57

967; 1, 2, 1, 7

10\22

1000

25\53

1034; 2, 14

15\31

1058; 1, 4, 1, 2

20\40

1090.90

け (ゆb) 22\48

1015; 2, 2, 2

16\35

1010; 1, 1, 9

26\57

1006; 2, 4, 1, 2

24\53

993: 9, 1, 2

14\31

988; 4, 4

18\40

981.81

ゆ 23\48

1061; 1, 1, 6

17\35

1073; 1, 2, 6

28\57

1083; 1, 6, 1, 3

11\22

1100

27\53

1127; 4, 7

16\31

1129; 2, 2, 3

21\40

1145.45

や (ゆ#) 24\48

1107; 1, 1, 2, 4

18\35

1136; 1, 5, 3

30\57

1161; 3, 2, 4

12\22

1200

30\29

1241; 2, 1, 1, 1, 3

15\31

1058; 1, 4, 1, 2

24\40

1309.09

ま (きb) 25\48

1153; 1, 5, 2

29\57

1122; 1, 1, 2, 1, 1

11\22

1100

26\53

1075; 1, 6, 4

18\31

1270; 1, 1, 2, 3

19\40

1036.36

き 26\48

1200

19\35

1200

31\57

1200

12\22

1200

29\53

1200

17\31

1200

22\40

1200

き# 27\48

1246; 6, 2

20\35

1263: 6, 3

33\57

1277; 2, 2, 1, 1

13\22

1300

32\53

1324; 7, 4

18\31

1270; 1, 1, 2, 3

25\40

1363.63

せ (しb) 29\48

1338; 3, 4

21\35

1326; 3, 6

34\57

1316; 7, 1, 3

31\53

1282; 1, 3, 7

19\31

1341; 5, 1, 2

23\40

1254.54

し 30\48

1384; 1, 1, 1, 1, 2

22\35

1389; 2, 9

36\57

1393; 1, 1, 4, 1, 2

14\22

1400

34\53

1406; 1, 8, 1, 2

20\31

1411; 1, 3, 4

26\40

1418.18

し# 31\48

1430; 1, 3, 3

23\35

1452; 1, 1, 1, 2, 2

38\57

1470; 1, 30

15\22

1500

37\53

1531; 29

22\31

1552; 1, 16

29\40

1581.81

て (ちb) 33\48

1523; 13

24\35

1515; 1, 3, 1, 3

39\57

1509; 1, 2, 10

36\53

1389; 1, 1, 1, 9

21\31

1482; 2, 1, 5

27\40

1472.72

ち 34\48

1569; 4, 3

25\35

1578; 1, 18

41\57

1587; 10, 3

16\22

1600

39\53

1613; 1, 3, 1, 5

23\31

1623; 1, 1, 8

30\40

1636.36

ち# 35\48

1615; 2, 2, 2

26\35

1642; 9, 2

43\57

1664; 1, 1, 15

17\22

1700

42\53

1737; 13, 2

25\31

1764; 1, 2, 2, 2

33\40

1800

ね (にb) 36\48

1661; 1, 1, 6

42\57

1625; 1, 4, 6

16\22

1600

38\53

1572; 2, 2, 2, 2

22\31

1552; 1, 16

28\40

1527.27

に 37\48

1707; 1, 1, 2, 4

27\35

1705; 3, 1, 4

44\57

1703; 4, 2, 3

17\22

1700

41\53

1696; 1, 1, 4, 3

24\31

1694; 8, 2

31\40

1690.90

に# 38\48

1753; 1, 5, 2

28\35

1768; 2, 2, 1, 2

46\57

1780; 1, 1, 4, 2

18\22

1800

44\53

1820; 1, 2, 4, 2

26\31

1835; 3, 2, 2

34\40

1854.54

へ (ひb) 40\48

1846; 6, 2

29\35

1831; 1, 1, 2, 1, 2

47\57

1819; 2, 4, 2

43\53

1779; 9, 1, 2

25\31

1764; 1, 2, 2, 2

32\40

1745.45

ひ 41\48

1892; 3, 4

30\35

1894; 1, 2, 1, 4

49\57

1896; 1, 3, 2, 3

19\22

1900

46\53

1903; 2, 4, 3

27\31

1905; 1, 7, 2

35\40

1909.09

ひ# 42\48

1938; 3, 4

31\35

1957; 1, 8, 2

51\57

1974; 5, 6

20\22

2000

49\53

2027; 1, 1, 2, 2, 2

29\31

2047; 17

38\40

2072.72

め (みb) 44\48

2030; 1, 3, 3

32\35

2021; 19

52\57

2012; 1, 9, 3

48\53

1986; 4, 1, 5

28\31

1976; 2, 8

36\40

1963.63

み 45\48

2076; 1, 12

33\35

2084; 4, 1, 3

54\57

2090; 3, 10

21\22

2100

51\53

2110; 2, 1, 9

30\31

2117; 1, 1, 1, 5

39\40

2127.27

み# 46\48

2123; 13

34\35

2147; 2, 1, 2, 2

56\57

2167; 1, 2, 1, 7

22\22

2200

54\53

2234; 2, 14

32\31

2258; 1, 4, 1, 2

42\40

2290.90

け (くb) 47\48

2169; 4, 3

55\57

2129; 31

21\22

2100

50\53

2068; 1, 28

29\31

2047; 17

37\40

2018.18

く 48\48

2215; 2, 2, 2

35\35

2210; 1, 1, 9

57\57

2206; 2, 4, 1, 2

22\22

2200

53\53

2193; 9, 1, 2

31\31

2188; 4, 4

40\40

2181.81

Relative Cents[1]
Notation Supersoft Soft Semisoft Basic Semihard Hard Superhard
か (く#) 1\48

45.83

1\35

62; 1, 6

2\57

77; 5, 5, 2

1\22

100

3\53

124; 1, 1, 8, 3

2\31

141; 1, 14, 2

3\40

165

そ (すb) 3\48

137.5

2\35

125; 1, 2, 2

3\57

115; 1, 3, 1, 3

2\53

83; 53

1\31

70; 1, 30

1\40

55

す 4\48

183.3

3\35

188; 1, 1, 3

5\57

192; 1, 56

2\22

200

5\53

207; 1, 1, 4, 1, 4

3\31

212; 1, 9, 3

4\40

220

さ (す#) 5\48

229.16

4\35

251; 2, 3

7\57

270; 5, 1, 2, 3

3\22

300

8\53

332; 13, 4

5\31

354; 1, 5, 5

7\40

385

と (つb) 7\48

320.83

5\35

314; 3, 2

8\57

308; 1, 3, 2, 1, 1, 2

7\53

290; 1, 1, 3, 3, 2

4\31

283; 1, 6, 1, 3

5\40

275

つ 8\48

366.6

6\35

377; 7

10\57

385; 1, 27, 2

4\22

400

10\53

415; 10, 1, 1, 2

6\31

425; 1, 4, 6

8\40

440

た (つ#) 9\48

412.5

7\35

440

12\57

463; 6, 3

5\22

500

13\53

539; 1, 1, 1, 1, 1, 6

8\31

567; 1, 2, 1, 7

11\40

605

の (ぬb) 10\48

458.3

11\57

424; 1, 1, 3, 1, 1, 3

4\22

400

9\53

373; 1, 1, 2, 2, 4

5\31

354; 1, 5, 5

6\40

330

ぬ 11\48

504.16

8\35

502; 1, 6

13\57

501; 1, 3, 14

5\22

500

12\53

498; 8, 1, 5

7\31

496; 1, 3, 2, 3

9\40

495

な (ぬ#) 12\48

550

9\35

565; 1, 2, 2

15\57

578; 1, 18

6\22

600

15\53

622; 1, 1, 1, 3, 1, 3

9\31

638; 1, 2, 2, 4

12\40

660

ほ (ふb) 14\48

641.6

10\35

628; 1, 1, 3

16\57

617; 1, 1, 5, 5

14\53

581; 7, 1, 1, 3

8\31

567; 1, 2, 1, 7

10\40

550

ふ 15\48

687.5

11\35

691; 2, 3

18\57

694; 1, 2, 1, 4

7\22

700

17\53

705; 1, 1, 1, 17

10\31

709; 1, 2, 10

13\40

715

は (ふ#) 16\48

733.3

12\35

754; 3, 2

20\57

771; 1, 13, 4

8\22

800

20\53

830; 5, 3, 3

12\31

851; 1, 1, 1, 1, 2, 2

16\40

880

も (むb) 18\48

825

13\35

817; 7

21\57

810; 1, 1, 9

19\53

788; 1, 2, 8, 2

11\31

780; 1, 1, 1, 4, 2

14\40

770

む 19\48

870.83

14\35

880

23\57

887; 1, 2, 1, 1, 3, 2

9\22

900

22\53

913; 4, 1, 4, 2

13\31

922; 1, 1, 2, 1, 1, 2

17\40

935

よ (む#) 20\48

916.6

15\35

942; 1, 6

25\57

964; 1, 10, 3, 2

10\22

1000

25\53

1037; 1, 2, 1, 3, 1, 2

15\31

1064; 1, 1, 15

20\40

1100

け (ゆb) 22\48

1013.3

16\35

1005; 1, 2, 2

26\57

1003; 1, 1, 28

24\53

996: 4, 2, 2, 2

14\31

993; 1, 1, 4, 1, 2

18\40

990

ゆ 23\48

1059.16

17\35

1068; 1, 1, 3

28\57

1080; 1, 2, 2, 1, 5

11\22

1100

27\53

1130; 1, 3, 13

16\31

1135; 2, 15

21\40

1155

や (ゆ#) 24\48

1100

18\35

1131; 2, 3

30\57

1157; 1, 8, 2

12\22

1200

30\29

1245; 3, 1, 1, 7

18\31

1277; 2, 2, 1, 1, 2

24\40

1320

ま (きb) 25\48

1145.83

29\57

1119; 3, 2, 1, 5

11\22

1100

26\53

1079; 4, 13

15\31

1064; 1, 1, 15

19\40

1045

き 26\48

1191.6

19\35

1194: 3, 2

31\57

1196; 2, 28

12\22

1200

29\53

1203; 1, 3, 2, 2, 2

17\31

1206; 2, 3, 1, 2

22\40

1210

き# 27\48

1237.5

20\35

1257: 7

33\57

1273; 1, 2, 6

13\22

1300

32\53

1328; 3, 3, 5

19\31

1348; 2, 1, 1, 2, 2

25\40

1375

せ (しb) 29\48

1329.16

21\35

1320

34\57

1312; 3, 1, 1, 3, 2

31\53

1286; 1, 3, 1, 1, 2

18\31

1277; 2, 2, 1, 1, 2

23\40

1265

し 30\48

1375

22\35

1382; 1, 6

36\57

1389; 2, 9

14\22

1400

34\53

1411; 3, 8, 2

20\31

1419; 2, 4, 2

26\40

1430

し# 31\48

1420.83

23\35

1445; 1, 2, 2

38\57

1466.6

15\22

1500

37\53

1535; 1, 5, 1, 1, 1, 2

22\31

1561; 3, 2, 4

29\40

1595

て (ちb) 33\48

1512.5

24\35

1508; 1, 1, 3

39\57

1505; 3, 1, 4

36\53

1394; 2, 1, 17

21\31

1490; 3, 10

27\40

1485

ち 34\48

1558.3

25\35

1571; 2, 3

41\57

1582; 2, 5, 5

16\22

1600

39\53

1618; 1, 6, 1, 1, 3

23\31

1632; 3, 1, 7

30\40

1650

ち# 35\48

1604.16

26\35

1633; 3, 2

43\57

1659; 1, 1, 1, 5, 1, 3

17\22

1700

42\53

1737; 13, 2

25\31

1774; 5, 6

33\40

1815

ね (にb) 36\48

1650

42\57

1621; 19

16\22

1600

38\53

1578; 2, 1, 3, 1, 3

22\31

1561; 3, 2, 4

28\40

1540

に 37\48

1695.83

27\35

1696; 7

44\57

1699; 4, 14

17\22

1700

41\53

1701; 1, 7, 1, 5

24\31

1703; 4, 2, 3

31\40

1705

に# 38\48

1741.6

28\35

1760

46\57

1775; 2, 3, 1, 1, 3

18\22

1800

44\53

1826; 2, 2,, 2, 4

26\31

1845; 5, 6

34\40

1870

へ (ひb) 40\48

1833.3

29\35

1822; 1, 6

47\57

1814; 28, 2

43\53

1784; 1, 9, 1, 1, 2

25\31

1774; 6, 5

32\40

1760

ひ 41\48

1879.16

30\35

1885; 1, 2, 2

49\57

1891; 4, 2, 1, 1, 2

19\22

1900

46\53

1909; 2, 3, 3, 2

27\31

1916; 7, 1, 3

35\40

1925

ひ# 42\48

1925

31\35

1948; 1, 1, 3

51\57

1968; 2, 2, 1, 2

20\22

2000

49\53

2033; 1, 25, 2

29\31

2058; 15, 2

38\40

2090

め (みb) 44\48

2016.6

32\35

2011; 2, 3

52\57

2007; 57

48\53

1992; 2, 4, 1, 4

28\31

1987; 10, 3

36\40

1980

み 45\48

2062.5

33\35

2075; 3, 2

54\57

2084; 4, 1, 3

21\22

2100

51\53

2116; 1, 52

30\31

2129; 31

39\40

2145

み# 46\48

2108.3

34\35

2138; 7

56\57

2161; 2, 2, 11

22\22

2200

54\53

2241; 1, 1, 26

32\31

2270; 1, 30

42\40

2310

け (くb) 47\48

2154.16

55\57

2122; 1, 4, 5, 2

21\22

2100

50\53

2075; 2, 8, 3

29\31

2058; 15, 2

37\40

2035

く 2200

Intervals

Generators Fourteenth notation Interval category name Generators Notation of 7/2ish inverse Interval category name
The 13-note MOS has the following intervals (from some root):
0 く perfect unison 0 く “perfect” minor fourteenth
1 に natural eleventh -1 ぬ natural fourth
2 き perfect octave -2 け (ゆb) minor seventh
3 ふ natural fifth -3 て (ちb) minor tenth
4 す major second -4 め (みb) minor thirteenth
5 ひ natural twelfth (tritave) -5 と (つb) minor third
6 し major ninth -6 も (むb) minor sixth
7 む major sixth -7 せ (しb) minor ninth
8 つ major third -8 へ (ひb) diminished twelfth
9 み major thirteenth -9 そ (すb) minor second
10 ち major tenth -10 ほ (ふb) diminished fifth
11 ゆ major seventh -11 ま (きb) diminished octave
12 な (ぬ#) augmented fourth -12 ね (にb) diminished eleventh
13 か (く#) augmented unison -13 け (くb) diminished fourteenth
The chromatic 22-note MOS (either 13L 9s, 9L 13s or 22edXIV) also has these intervals
14 に# augmented eleventh -14 の (ぬb) diminished fourth
15 き# augmented octave -15 けb (ゆbb) diminished seventh
16 は (ふ#) augmented fifth -16 てb (ちbb) diminished tenth
17 さ (す#) augmented second -17 めb (みbb) diminished thirteenth
18 に# augmented twelfth -18 とb (つbb) diminished third
19 し# augmented ninth -19 もb (むbb) diminished sixth
20 よ (む#) augmented sixth -20 せb (しbb) diminished ninth
21 た (つ#) augmented third -21 へb (ひbb) doubly diminished twelfth
  1. ↑ 1.0 1.1 Fractions repeating more than 4 digits written as continued fractions
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