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

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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 (ku-su-tsu-nu-fu-mu-yu-ki-shi-chi-ni-hi-mi) = LLsLLLsLLsLLs (Ionian b14), #/b mostly two chromas up/down.

Thus the 22edXIV gamut is as follows:

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

The 31edXIV gamut is notated as follows:

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

The 35edXIV gamut:

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

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; 2, 6

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

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

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, 1, 1, 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

11\48

507; 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

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; 2, 6

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

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

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, 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

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; 2, 6

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

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

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

37\48

1707; 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

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; 2, 6

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

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

こ (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

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

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

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

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

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

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

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

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

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

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

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

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

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

こ (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

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 perfect unison 0 “perfect” minor fourteenth
1 natural eleventh -1 natural fourth
2 perfect octave -2 け (ゆb) minor seventh
3 natural fifth -3 て (ちb) minor tenth
4 major second -4 め (みb) minor thirteenth
5 natural twelfth (tritave) -5 と (つb) minor third
6 major ninth -6 も (むb) minor sixth
7 major sixth -7 せ (しb) minor ninth
8 major third -8 へ (ひb) diminished twelfth
9 major thirteenth -9 そ (すb) minor second
10 major tenth -10 ほ (ふb) diminished fifth
11 major seventh -11 ま (きb) diminished octave
12 な (ぬ#) augmented fourth -12 ね (にb) diminished eleventh
The chromatic 22-note MOS (either 13L 9s, 9L 13s or 22edXIV) also has these intervals
13 か (く#) augmented unison -13 こ (くb) diminished fourteenth
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

Genchain

The generator chain for this scale is as follows:

へb (ひbb) せb (しbb) もb (むbb) とb (つbb) めb (みbb) てb (ちbb) けb (ゆbb)
dd12 d9 d6 d3 d13 d10 d7
の (ぬb) こ (くb) ね (にb) ま (きb) ほ (ふb) そ (すb) へ (ひb) せ (しb) も (むb) と (つb) め (みb) て (ちb) け (ゆb)
d4 d14 d11 d8 d5 m2 d12 m9 m6 m3 m13 m10 m7
N4 P1 N11 P8 N5 M2 N12 M9 M6 M3 M13 M10 M7
な (ぬ#) か (く#) に# き# は (ふ#) さ (す#) に# し# よ (む#) た (つ#)
A4 A1 A11 A8 A5 A2 A12 A9 A6 A3

Modes

The mode names are based on the diatonic scale:

Mode Scale UDP Interval type
name pattern notation 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th
Lydian Dominant ♮ 11 LLLsLLsLLsLLs 12|0 M M A P M M P M M P P M
Major b14 LLsLLLsLLsLLs 11|1 M M P P M M P M M P P M
Mixolydian LLsLLsLLLsLLs 10|2 M M P P M m P M M P P M
Mixolydian b10 (Persian) LLsLLsLLsLLLs 9|3 M M P P M m P M m P P M
Aeolian Dominant ♮6 LLsLLsLLsLLsL 8|4 M M P P M m P M m P P m
Dorian b13 LsLLLsLLsLLsL 7|5 M m P P M m P M m P P m
Minor LsLLsLLLsLLsL 6|6 M m P P m m P M m P P m
Phrygian ♮2 LsLLsLLsLLLsL 5|7 M m P P m m P m m P P m
Locrian ♮2 ♮5 LsLLsLLsLLsLL 4|8 M m P P m m P m m P P m
Locrian ♮5 sLLLsLLsLLsLL 3|9 m m P P m m P m m P P m
Locrian sLLsLLLsLLsLL 2|10 m m P d m m P m m P P m
Locrian b8 sLLsLLsLLLsLL 1|11 m m P d m m d m m P d m
Locrian b8 b11 sLLsLLsLLsLLL 0|12 m m P d m m d m m d d m

Temperaments

The Shōsūshī temperament spells its major hexad 24:30:36:45:54:64 or 84:108:126:162:189:224 root-2(4g-3p)-(3g-2p)-(11g-8p)-2(3g-2p)-(1g) (p = 18/5 or 7/2, g = 8/3) and its minor hexad 12:14:18:21:27:32 or 60:72:90:108:135:160 root-(-5g-p)-(3g-2p)-(-2g)-2(3g-2p)-(1g) (p = 18/5 or 7/2, g = 8/3).

Shōsūshī-Meantone

Subgroup: 18/5.2.3

Comma list: 81/80

POL2 generator: ~4/3 = [[1]]

Mapping: [1 1 2], 0 -2 -5]]

Vals: 22edXIV, 35edXIV, 48edXIV, 61edXIV

Shōsūshī-Superpyth

Subgroup: 7/2.2.3

Comma list: 64/63

POL2 generator: ~4/3 = [[2]]

Mapping: [1 1 2], 0 -2 -5]]

Vals: 22edXIV, 31edXIV, 40edXIV, 49edXIV

Scale tree

The spectrum looks like this:

Generator Normalized[1] ed22\12[1] L s L/s Comments
3\13 514; 3, 2 507; 1, 3, 3 1 1 1.000 Equalised
17\74 510 505; 2, 2, 7 6 5 1.200
14\61 509.09 504; 1, 11, 5 5 4 1.250
25\109 508; 2, 9, 3 504; 1, 1, 2, 2, 1, 2, 2 9 7 1.286
11\48 507; 1, 3, 3 504.16 4 3 1.333
19\83 506.6 503; 1, 1, 1, 1, 2, 6 7 5 1.400
8\35 505; 3, 1, 4 502; 1, 6 3 2 1.500 Shōsūshī-Meantone starts here
21\92 504 502; 5, 1, 3 8 5 1.600
13\57 503; 4, 2, 3 501; 1, 3, 14 5 3 1.667
18\79 502; 3, 14 501; 3, 1, 3, 5 7 4 1.750
23\101 501.81 500.0099 9 5 1.800
5\22 500 500 2 1 2.000 Shōsūshī-Meantone ends, Shōsūshī-Pythagorean begins
27\119 498; 2, 6 499; 6, 3, 1, 4 11 5 2.200
22\97 498; 8, 1, 5 498; 1, 31, 3 9 4 2.250
17\75 497; 1, 1, 3, 1, 1, 2 498.6 7 3 2.333
12\53 496; 1, 1, 4, 3 498; 8, 1, 5 5 2 2.500 Shōsūshī-Neogothic heartland is from here…
19\84 495; 1, 1, 1, 7 497; 1, 1, 1, 1, 1, 2 8 3 2.667 …to here
7\31 494; 8, 2 496; 1, 3, 2, 3 3 1 3.000 Shōsūshī-Pythagorean ends, Shōsūshī-Superpyth begins
30\133 493; 6, 1, 1, 1, 3 496; 4, 6, 2, 2 13 4 3.250
23\102 492.83 496; 12, 1, 3 10 3 3.333
16\71 492; 3, 4 495; 1, 3, 2, 3, 2 7 2 3.500
25\111 491; 1, 4, 12 495; 2, 55 11 3 3.667
9\40 490.90 495 4 1 4.000
20\89 489; 1, 3, 1, 9 494; 2, 1, 1, 1, 1, 1, 1, 2 9 2 4.500
11\49 488.8 493; 1, 7, 6 5 1 5.000 Shōsūshī-Superpyth ends
13\58 487.5 493; 9, 1, 2 6 1 6.000
2\9 480 488.8 1 0 → inf Paucitonic
  1. 1.0 1.1 1.2 1.3 Fractions repeating more than 4 digits written as continued fractions