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

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 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/こ

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 こ

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/こb み#/こ

Cents

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
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, 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
ぬ	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
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; 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
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, 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; 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
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, 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; 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
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
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
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

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
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
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
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

ぬ

く

に

き

ふ

す

ひ

し

む

つ

み

ち

ゆ

→

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 = 506.8820

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 = 486.8323

Mapping: [⟨1 1 2], ⟨0 -2 -5]]

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

Scale tree

The spectrum looks like this:

Generator			Normalized	ed22\12 (→ed11\6)	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