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User:Moremajorthanmajor/9L 4s (minor fourteenth-equivalent): Difference between revisions

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'''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
'''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
{| class="wikitable"
{| class="wikitable"
|+Cents<ref name=":0">Fractions repeating more than 4 digits written as continued fractions </ref>
|+Cents
!Notation
!Notation
!Supersoft
!Supersoft
Line 32: Line 32:
|-
|-
|か (く#)
|か (く#)
|1\48
|1\48, 46.154
46; 6, 2
|1\35, 63.158
|1\35
|2\57, 77.419
63: 6, 3
| rowspan="2" |1\22, 100
|2\57
|3\53, 124.138
77; 2, 2, 1, 1
|2\31, 141.176
| rowspan="2" |1\22
|3\40, 163.636
100
|3\53
124; 7, 4
|2\31
141; 5, 1, 2
|3\40
163.{{Overline|63}}
|-
|-
|そ (すb)
|そ (すb)
|3\48
|3\48, 138.462
138; 2, 6
|2\35, 126.316
|2\35
|3\57, 116.129
126; 3, 6
|2\53, 82.759
|3\57
|1\31, 70.588
116; 7, 1, 3
|1\40, 54.545
|2\53
82; 1, 3, 7
|1\31
70; 1, 1, 2, 3
|1\40
54.{{Overline|54}}
|-
|-
|す
| す
|4\48
|4\48, 184.615
184; 1, 1, 1, 1, 2
|3\35, 189.454
|3\35
|5\57, 193.548
189; 2, 9
|2\22, 200
|5\57
|5\53, 206.897
193; 1, 1, 4, 1, 2
|3\31, 211.765
|2\22
|4\40, 218.182
200
|5\53
206; 1, 8, 1, 2
|3\31
211; 1, 3, 4
|4\40
218.{{Overline|18}}
|-
|-
|さ (す#)
|さ (す#)
|5\48
|5\48, 230.769
230; 1, 3, 3
|4\35, 252.632
|4\35
|7\57, 270.968
252; 1, 1, 1, 2, 2
| rowspan="2" |3\22, 300
|7\57
|8\53, 331.034
270; 1, 30
|5\31, 352.941
| rowspan="2" |3\22
| 7\40, 381.818
300
|8\53
331; 29
|5\31
352; 1, 16
|7\40
381.{{Overline|81}}
|-
|-
|と (つb)
|と (つb)
|7\48
|7\48, 323.077
323; 13
|5\35, 315.789
|5\35
|8\57, 309.677
315; 1, 3, 1, 3
|7\53, 289.655
|8\57
|4\31, 282.353
309; 1, 2, 10
|5\40, 272.727
|7\53
289; 1, 1, 1, 9
|4\31
282; 2, 1, 5
|5\40
272.{{Overline|72}}
|-
|-
|つ
|つ
|8\48
|8\48, 369.231
369; 4, 3
|6\35, 378.947
|6\35
|10\57, 387.097
378; 1, 18
|4\22, 400
|10\57
|10\53, 413.739
387; 10, 3
|6\31, 423.529
|4\22
|8\40, 436.364
400
|10\53
413; 1, 3, 1, 5
|6\31
423; 1, 1, 8
|8\40
436.{{Overline|36}}
|-
|-
|た (つ#)
|た (つ#)
|9\48
| 9\48, 415.385
415; 2, 1, 1, 2
| rowspan="2" |7\35, 442.105
| rowspan="2" |7\35
|12\57, 464.516
442; 9, 2
|5\22, 500
|12\57
|13\53, 537.069
464; 1, 1, 15
| 8\31, 564.706
|5\22
|11\40, 600
500
|13\53
537; 13, 2
|8\31
564; 1, 2, 2, 2
|11\40
600
|-
|-
|の (ぬb)
|の (ぬb)
|10\48
|10\48. 461.538
461; 1, 1, 6
|11\57, 425.806
|11\57
|4\22, 400
425; 1, 4, 6
|9\53, 372.414
|4\22
|5\31, 352.941
400
|6\40, 327.273
|9\53
372; 2, 2, 2, 2
|5\31
352; 1, 16
|6\40
327.{{Overline|27}}
|-
|-
|'''ぬ'''
|'''ぬ'''
|'''11\48'''
|'''11\48,''' '''507.692'''
'''507; 1, 2, 4'''
|'''8\35,''' '''505.263'''
|'''8\35'''
|'''13\57,''' '''503.226'''
'''505; 3, 1, 4'''
|'''5\22,''' '''500'''
|'''13\57'''
|'''12\53,''' '''496.552'''
'''503; 4, 2, 3'''
|'''7\31,''' '''494.118'''
|'''5\22'''
|'''9\40,''' '''490.909'''
'''500'''
|'''12\53'''
'''496; 1, 1, 4, 3'''
|'''7\31'''
'''494; 8, 2'''
|'''9\40'''
'''490.{{Overline|90}}'''
|-
|-
|な (ぬ#)
|な (ぬ#)
|12\48
|12\48, 553.846
553; 1, 5, 2
|9\35, 568.421
|9\35
|15\57, 580.645
568; 2, 2, 1, 2
| rowspan="2" |6\22, 600
|15\57
|15\53, 620.690
580; 1, 1, 4, 2
|9\31, 635.294
| rowspan="2" |6\22
|12\40, 654.545
600
|15\53
620; 1, 2, 4, 2
|9\31
635; 3, 2, 2
|12\40
654.{{Overline|54}}
|-
|-
|ほ (ふb)
|ほ (ふb)
|14\48
|14\48, 646.154
646; 6, 2
|10\35, 631.579
|10\35
|16\57, 619.355
631; 1, 1, 2, 1, 2
| 14\53, 579.310
|16\57
| 8\31, 564.706
619; 2, 4, 2
|10\40, 545.455
|14\53
579; 9, 1, 2
|8\31
564; 1, 2, 2, 2
|10\40
545.{{Overline|45}}
|-
|-
|ふ
|ふ
|15\48
|15\48, 692.308
692; 3, 4
|11\35, 694.737
|11\35
|18\57, 696.774
694; 1, 2, 1, 4
|7\22, 700
|18\57
|17\53, 703.448
696; 1, 3, 2, 3
|10\31, 705.882
|7\22
|13\40, 709.091
700
|17\53
703; 2, 4, 3
|10\31
705; 1, 7, 2
|13\40
709.{{Overline|09}}
|-
|-
|は (ふ#)
|は (ふ#)
|16\48
|16\48, 738.462
738; 2, 6
|12\35, 757.895
|12\35
|20\57, 774.194
757; 1, 8, 2
| rowspan="2" |8\22, 800
|20\57
|20\53, 827.586
774; 5, 6
|12\31, 847.059
| rowspan="2" |8\22
|16\40, 872.727
800
|20\53
827; 1, 1, 2, 2, 2
|12\31
847; 17
|16\40
872.{{Overline|72}}
|-
|-
|も (むb)
|も (むb)
|18\48
|18\48, 830.769
830; 1, 3, 3
|13\35, 821.053
|13\35
|21\57, 812.903
821; 19
|19\53, 786.261
|21\57
|11\31, 776.471
812; 1, 9, 3
|14\40, 763.636
|19\53
786; 4, 1, 5
|11\31
776; 2, 8
|14\40
763.{{Overline|63}}
|-
|-
|む
|む
|19\48
|19\48, 876.923
876; 1, 12
|14\35, 884.211
|14\35
|23\57, 890.323
884; 4, 1, 3
|9\22, 900
|23\57
|22\53, 910.345
890; 3, 10
|13\31, 917.647
|9\22
|17\40, 927.273
900
|22\53
910; 2, 1, 9
|13\31
917; 1, 1, 1, 5
|17\40
927.{{Overline|27}}
|-
|-
|よ (む#)
|よ (む#)
|20\48
|20\48, 923.077
923; 13
|15\35, 947.638
|15\35
|25\57, 967.742
947; 2, 1, 2, 2
| rowspan="2" |10\22, 1000
|25\57
|25\53, 1034.483
967; 1, 2, 1, 7
|15\31, 1058.824
| rowspan="2" |10\22
|20\40, 1090.909
1000
|25\53
1034; 2, 14
|15\31
1058; 1, 4, 1, 2
|20\40
1090.{{Overline|90}}
|-
|-
|け (ゆb)
|け (ゆb)
|22\48
|22\48, 1015.385
1015; 2, 2, 2
|16\35, 1010.526
|16\35
|26\57, 1006.452
1010; 1, 1, 9
|24\53, 993.103
|26\57
|14\31, 988.235
1006; 2, 4, 1, 2
|18\40, 981.818
|24\53
993: 9, 1, 2
|14\31
988; 4, 4
|18\40
981.{{Overline|81}}
|-
|-
|ゆ
| ゆ
|23\48
|23\48, 1061.538
1061; 1, 1, 6
|17\35, 1073.684
|17\35
|28\57, 1083.871
1073; 1, 2, 6
|11\22, 1100
|28\57
|27\53, 1117.241
1083; 1, 6, 1, 3
|16\31, 1129.412
|11\22
|21\40, 1145.45
1100
|27\53
1127; 4, 7
|16\31
1129; 2, 2, 3
|21\40
1145.{{Overline|45}}
|-
|-
|や (ゆ#)
|や (ゆ#)
|24\48
|24\48, 1107.692
1107; 1, 2, 4
| rowspan="2" |18\35, 1136.842
| rowspan="2" |18\35
|30\57, 1161.290
1136; 1, 5, 3
|12\22, 1200
|30\57
|30\29, 1241.176
1161; 3, 2, 4
|15\31, 1058.824
|12\22
|24\40, 1309.091
1200
|30\29
1241; 2, 1, 1, 1, 3
|15\31
1058; 1, 4, 1, 2
|24\40
1309.{{Overline|09}}
|-
|-
|ま (きb)
|ま (きb)
|25\48
|25\48, 1153.846
1153; 1, 5, 2
|29\57, 1122.581
|29\57
|11\22, 1100
1122; 1, 1, 2, 1, 1
|26\53, 1075.862
|11\22
|18\31, 1270.588
1100
|19\40, 1036.364
|26\53
1075; 1, 6, 4
|18\31
1270; 1, 1, 2, 3
|19\40
1036.{{Overline|36}}
|-
|-
|き
|き
|26\48
|26\48, 1200
1200
|19\35, 1200
|19\35
|31\57, 1200
1200
|12\22, 1200
|31\57
|29\53, 1200
1200
|17\31, 1200
|12\22
|22\40, 1200
1200
|29\53
1200
|17\31
1200
|22\40
1200
|-
|-
|き#
|き#
|27\48
|27\48, 1246.154
1246; 6, 2
|20\35, 1263.158
|20\35
|33\57, 1277.419
1263: 6, 3
| rowspan="2" |13\22, 1300
|33\57
|32\53, 1324.138
1277; 2, 2, 1, 1
|18\31, 1270.588
| rowspan="2" |13\22
|25\40, 1363.636
1300
|32\53
1324; 7, 4
|18\31
1270; 1, 1, 2, 3
|25\40
1363.{{Overline|63}}
|-
|-
|せ (しb)
|せ (しb)
|29\48
|29\48, 1338.462
1338; 2, 6
|21\35, 1326.316
|21\35
|34\57, 1316.129
1326; 3, 6
|31\53, 1282.759
|34\57
|19\31, 1341.176
1316; 7, 1, 3
| 23\40, 1254.545
|31\53
1282; 1, 3, 7
|19\31
1341; 5, 1, 2
|23\40
1254.{{Overline|54}}
|-
|-
|し
|し
|30\48
|30\48, 1384.615
1384; 1, 1, 1, 1, 2
|22\35, 1389.474
|22\35
|36\57, 1393.548
1389; 2, 9
|14\22, 1400
|36\57
|34\53, 1406.897
1393; 1, 1, 4, 1, 2
|20\31, 1411.765
|14\22
|26\40, 1418.182
1400
|34\53
1406; 1, 8, 1, 2
|20\31
1411; 1, 3, 4
|26\40
1418.{{Overline|18}}
|-
|-
|し#
|し#
|31\48
|31\48, 1430.769
1430; 1, 3, 3
|23\35, 1452.632
|23\35
|38\57, 1470.968
1452; 1, 1, 1, 2, 2
| rowspan="2" |15\22, 1500
|38\57
|37\53, 1531.034
1470; 1, 30
|22\31, 1552.941
| rowspan="2" |15\22
|29\40, 1581.818
1500
|37\53
1531; 29
|22\31
1552; 1, 16
|29\40
1581.{{Overline|81}}
|-
|-
|て (ちb)
|て (ちb)
|33\48
|33\48, 1523.077
1523; 13
|24\35, 1515.789
|24\35
|39\57, 1509.677
1515; 1, 3, 1, 3
|36\53, 1489.655
|39\57
|21\31, 1482.353
1509; 1, 2, 10
|27\40, 1472.727
|36\53
1389; 1, 1, 1, 9
|21\31
1482; 2, 1, 5
|27\40
1472.{{Overline|72}}
|-
|-
|ち
|ち
|34\48
|34\48, 1569.231
1569; 4, 3
|25\35, 1578.947
|25\35
|41\57, 1587.097
1578; 1, 18
|16\22, 1600
|41\57
| 39\53, 1613.793
1587; 10, 3
|23\31, 1623.529
|16\22
|30\40, 1636.364
1600
|39\53
1613; 1, 3, 1, 5
|23\31
1623; 1, 1, 8
|30\40
1636.{{Overline|36}}
|-
|-
|ち#
|ち#
|35\48
|35\48, 1615.385
1615; 2, 2, 2
| rowspan="2" |26\35, 1642.105
| rowspan="2" |26\35
|43\57, 1664.516
1642; 9, 2
|17\22, 1700
|43\57
|42\53, 1737.069
1664; 1, 1, 15
|25\31, 1764.706
|17\22
|33\40, 1800
1700
|42\53
1737; 13, 2
|25\31
1764; 1, 2, 2, 2
|33\40
1800
|-
|-
|ね (にb)
|ね (にb)
|36\48
|36\48, 1661.538
1661; 1, 1, 6
|42\57, 1625.806
|42\57
|16\22, 1600
1625; 1, 4, 6
|38\53, 1572.414
|16\22
|22\31, 1552.941
1600
|28\40, 1527.273
|38\53
1572; 2, 2, 2, 2
|22\31
1552; 1, 16
|28\40
1527.{{Overline|27}}
|-
|-
|'''に'''
|'''に'''
|'''37\48'''
|'''37\48,''' '''1707.692'''
'''1707; 1, 2, 4'''
|'''27\35,''' '''1705.263'''
|'''27\35'''
|'''44\57,''' '''1703.226'''
'''1705; 3, 1, 4'''
|'''17\22, 1700'''
|'''44\57'''
|'''41\53,''' '''1696.552'''
'''1703; 4, 2, 3'''
|'''24\31,''' '''1694.118'''
|'''17\22'''
|'''31\40,''' '''1690.909'''
'''1700'''
|'''41\53'''
'''1696; 1, 1, 4, 3'''
|'''24\31'''
'''1694; 8, 2'''
|'''31\40'''
'''1690.{{Overline|90}}'''
|-
|-
|に#
|に#
|38\48
|38\48, 1753.846
1753; 1, 5, 2
|28\35, 1768.421
|28\35
|46\57, 1780.645
1768; 2, 2, 1, 2
| rowspan="2" | 18\22, 1800
|46\57
|44\53, 1820.690
1780; 1, 1, 4, 2
|26\31, 1835.294
| rowspan="2" |18\22
|34\40, 1854.545
1800
|44\53
1820; 1, 2, 4, 2
|26\31
1835; 3, 2, 2
|34\40
1854.{{Overline|54}}
|-
|-
|へ (ひb)
|へ (ひb)
|40\48
|40\48, 1846.158
1846; 6, 2
|29\35, 1831.579
|29\35
|47\57, 1819.355
1831; 1, 1, 2, 1, 2
| 43\53, 1779.310
|47\57
|25\31, 1764.706
1819; 2, 4, 2
|32\40, 1745.455
|43\53
1779; 9, 1, 2
|25\31
1764; 1, 2, 2, 2
|32\40
1745.{{Overline|45}}
|-
|-
|ひ
|ひ
|41\48
|41\48, 1892.308
1892; 3, 4
| 30\35, 1894.737
|30\35
|49\57, 1896.774
1894; 1, 2, 1, 4
|19\22, 1900
|49\57
|46\53, 1903.448
1896; 1, 3, 2, 3
|27\31, 1905.882
|19\22
|35\40, 1909.091
1900
|46\53
1903; 2, 4, 3
|27\31
1905; 1, 7, 2
|35\40
1909.{{Overline|09}}
|-
|-
|ひ#
|ひ#
|42\48
|42\48, 1938.462
1938; 2, 6
|31\35, 1957.895
|31\35
|51\57, 1974.194
1957; 1, 8, 2
| rowspan="2" |20\22, 2000
|51\57
| 49\53, 2027.586
1974; 5, 6
|29\31, 2047.059
| rowspan="2" |20\22
|38\40, 2072.727
2000
|49\53
2027; 1, 1, 2, 2, 2
|29\31
2047; 17
|38\40
2072.{{Overline|72}}
|-
|-
|め (みb)
|め (みb)
|44\48
|44\48, 2030.769
2030; 1, 3, 3
|32\35, 2021.053
|32\35
|52\57, 2012.903
2021; 19
|48\53, 1986.207
|52\57
|28\31, 1976.471
2012; 1, 9, 3
|36\40, 1963.636
|48\53
1986; 4, 1, 5
|28\31
1976; 2, 8
|36\40
1963.{{Overline|63}}
|-
|-
|み
|み
|45\48
|45\48, 2076.923
2076; 1, 12
|33\35, 2084.211
|33\35
|54\57, 2090.323
2084; 4, 1, 3
|21\22, 2100
|54\57
|51\53, 2110.345
2090; 3, 10
|30\31, 2117.647
|21\22
|39\40, 2127.273
2100
|51\53
2110; 2, 1, 9
|30\31
2117; 1, 1, 1, 5
|39\40
2127.{{Overline|27}}
|-
|-
|み#
|み#
|46\48
|46\48, 2123.077
2123; 13
| rowspan="2" | 34\35, 2147.368
| rowspan="2" |34\35
|56\57, 2167.742
2147; 2, 1, 2, 2
|22\22, 2200
|56\57
|54\53, 2234.483
2167; 1, 2, 1, 7
|32\31, 2258.824
|22\22
|42\40, 2290.909
2200
|54\53
2234; 2, 14
|32\31
2258; 1, 4, 1, 2
|42\40
2290.{{Overline|90}}
|-
|-
|こ (くb)
|こ (くb)
|47\48
|47\48, 2169.231
2169; 4, 3
|55\57, 2129.032
|55\57
|21\22, 2100
2129; 31
|50\53, 2068.966
|21\22
|29\31, 2047.059
2100
|37\40, 2018.182
|50\53
2068; 1, 28
|29\31
2047; 17
|37\40
2018.{{Overline|18}}
|-
|-
!く
!く
!48\48
!48\48, 2215.385
2215; 2, 2, 2
!35\35, 2210.526
!35\35
!57\57, 2206.452
2210; 1, 1, 9
!'''22\22, 2200'''
!57\57
!53\53, 2193.103
2206; 2, 4, 1, 2
!31\31, 2188.235
!22\22
!40\40, 2181.818
2200
!53\53
2193; 9, 1, 2
!31\31
2188; 4, 4
!40\40
2181.{{Overline|81}}
|}
==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):
|か (く#)
|49\48, 2261.538
|36\35, 2273.684
|59\57, 2283.871
| rowspan="2" |23\22, 2300
|56\53, 2317.241
|33\31, 2329.418
|43\40, 2345.455
|-
|-
|0
|そ (すb)
|く
|51\48, 2353.846
|perfect unison
|37\35, 2336.842
|0
|60\57, 2322.581
|く
|55\53, 2275.862
|“perfect” minor fourteenth
|32\31, 2258.854
|41\40, 2236.363
|-
|-
|1
|す
|に
|52\48, 2400
|natural eleventh
|38\35, 2400
| -1
|62\57, 2400
|ぬ
| 24\22, 2400
|natural fourth
|58\53, 2400
|34\31, 2400
|44\40, 2400
|-
|-
|2
|さ (す#)
|き
|53\48, 2446.154
|perfect octave
|39\35, 2463.158
| -2
|64\57, 2477.419
|け (ゆb)
| rowspan="2" |25\22, 2500
|minor seventh
|61\53, 2524.138
|36\31, 2541.176
|47\40, 2563.636
|-
|-
|3
|と (つb)
|ふ
|55\48, 2538.462
|natural fifth
|40\35, 2526.316
| -3
|65\57, 2516.129
|て (ちb)
|60\53, 2482.759
|minor tenth
|35\31, 2570.588
|45\40, 2454.545
|-
|-
|4
|つ
|す
|56\48, 2584.615
|major second
|41\35, 2589.474
| -4
|67\57, 2593.548
|め (みb)
|26\22, 2600
|minor thirteenth
|63\53, 2606.897
|37\31, 2611.765
|48\40, 2618.182
|-
|-
|5
|た (つ#)
|ひ
|57\48, 2630.792
|natural twelfth (tritave)
| rowspan="2" | 42\35, 2652.632
| -5
|69\57, 2670.968
|と (つb)
|27\22, 2700
|minor third
|66\53, 2731.034
|39\31, 2752.941
|51\40, 2781.818
|-
|の (ぬb)
|58\48, 2676.923
|68\57, 2632.258
|26\22, 2600
|62\53, 2565.517
|36\31, 2541.176
|46\40, 2509.091
|-
|'''ぬ'''
|'''59\48, 2723.077'''
|'''43\35, 2715.789'''
|'''70\57, 2709.677'''
|'''27\22, 2700'''
|'''65\53, 2689.655'''
|'''38\31, 2682.353'''
|'''49\40, 2672.72'''
|-
|な (ぬ#)
|60\48, 2769.321
|44\35, 2778.947
|72\57, 2787.097
| rowspan="2" |28\22, 2800
|68\53, 2813.739
|40\31, 2823.529
|52\40, 2836.363
|-
|ほ (ふb)
|62\48, 2861.538
|45\35, 2842.105
|73\57, 2825.806
|67\53, 2772.414
|39\31, 2752.941
|51\40, 2781.818
|-
|ふ
|63\48, 2907.692
|46\35, 2905.263
|75\57, 2903.226
|29\22, 2900
|70\53, 2896.552
|41\31, 2894.118
|53\40, 2890.909
|-
|は (ふ#)
|64\48, 2953.846
|47\35, 2968.421
|77\57, 2980.645
| rowspan="2" |30\22, 3000
|73\53, 3020.690
|43\31, 3035.294
|56\40, 3054.545
|-
|-
|6
|し
|major ninth
| -6
|も (むb)
|も (むb)
|minor sixth
|66\48, 3046.154
|48\35, 3031.579
|78\57, 3019.355
|72\53, 2979.310
|42\31, 2964.706
|54\40, 2945.455
|-
|-
|7
|む
|む
|major sixth
|67\48, 3092.308
| -7
|49\35, 3094.737
|せ (しb)
| 80\57, 3096.774
|minor ninth
| 31\22, 3100
|75\53, 3103.448
|44\31, 3105.882
|57\40, 3109.090
|-
|-
|8
|よ (む#)
|つ
|68\48, 3138.462
|major third
|50\35, 3157.895
| -8
|82\57, 3174.194
|へ (ひb)
| rowspan="2" |32\22, 3200
|diminished twelfth
|78\53, 3227.586
|46\31, 3247.059
|60\40, 3272.727
|-
|-
|9
|け (ゆb)
|み
|70\48, 3230.769
|major thirteenth
|51\35, 3221.053
| -9
|83\57, 3212.903
|そ (すb)
|77\53, 3186.207
|minor second
|45\31, 3176.471
|58\40, 3163.636
|-
|ゆ
|71\48, 3276.923
|52\35, 3284.211
|85\57, 3290.323
|33\22, 3300
|80\53, 3310.345
|47\31, 3317.647
|61\40, 3327.273
|-
|-
|10
|や (ゆ#)
|ち
|72\48, 3323.077
|major tenth
| rowspan="2" |53\35, 3347.368
| -10
|86\57, 3329.032
|ほ (ふb)
|34\22, 3400
|diminished fifth
|83\53, 3434.483
|49\31, 3458.824
|64\40, 3490.909
|-
|-
|11
|ゆ
|major seventh
| -11
|ま (きb)
|ま (きb)
|diminished octave
|73\48, 3369.231
|87\57, 3367.742
|33\22, 3300
|79\53, 3268.966
|46\31, 3247.059
|59\40, 3218.182
|-
|き
|74\48, 3415.385
|54\35, 3410.526
|88\57, 3406.452
|34\22, 3400
|82\53, 3393.103
|48\31, 3388.235
|62\40, 3381.818
|-
|-
|12
|き#
|な (ぬ#)
|75\48, 3461.538
|augmented fourth
|55\35, 3473.684
| -12
|90\57, 3483.871
|ね (にb)
| rowspan="2" |35\22, 3500
|diminished eleventh
|85\53, 3517.241
|50\31, 3529.421
|65\40, 3545.455
|-
|-
| 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
|せ (しb)
|77\48, 3553.846
|56\35, 3536.842
|92\57, 3522.581
|84\53, 3475.862
|49\31, 3458.824
| 63\40, 3436.364
|-
|-
|13
| し
|か (く#)
|78\48, 3600
|augmented unison
|57\35, 3600
| -13
|93\57, 3600
|こ (くb)
| 36\22, 3600
|diminished fourteenth
|87\53, 3600
|51\31, 3600
|66\40, 3600
|-
|し#
|79\48, 3646.154
|58\35, 3663.158
|95\57, 3677.419
| rowspan="2" | 37\22, 3700
|90\53, 3724.138
| 53\31, 3741.176
| 69\40, 3763.636
|-
|て (ちb)
|81\48, 3738.462
|59\35, 3726.316
|96\57, 3716.129
|89\53, 3682.759
|52\31, 3670.588
|67\40, 3654.545
|-
|-
|14
|ち
|に#
|82\48, 3784.615
|augmented eleventh
|60\35, 3789.474
| -14
|98\57, 3793.458
|の (ぬb)
|38\22, 3800
|diminished fourth
| 92\53, 3806.897
| 54\31, 3811.765
|70\40, 3818.182
|-
|-
|15
|ち#
|き#
|83\48, 3830.077
|augmented octave
| rowspan="2" |61\35, 3852.632
| -15
|100\57, 3870.968
|けb (ゆbb)
|39\22, 3900
|diminished seventh
|95\53, 3931.034
|56\31, 3952.941
|73\40, 3981.818
|-
|-
|16
|ね (にb)
|は (ふ#)
|84\48, 3876.923
|augmented fifth
|99\57, 3832.258
| -16
|38\22, 3800
|てb (ちbb)
|91\53, 3765.517
|diminished tenth
|53\31, 3741.176
| 68\40, 3709.091
|-
|-
|17
|'''に'''
|さ (す#)
|'''85\48, 3923.077'''
|augmented second
|'''62\35, 3915.789'''
| -17
|'''101\57, 3909.677'''
|めb (みbb)
|'''39\22, 3900'''
|diminished thirteenth
|'''94\53, 3889.655'''
|'''55\31, 3882.353'''
|'''71\40, 3872.727'''
|-
|-
|18
|に#
|に#
|augmented twelfth
|86\48, 3969.231
| -18
|63\35, 3978.947
|とb (つbb)
|103\57, 3987.097
|diminished third
| rowspan="2" |40\22, 4000
| 97\53, 4013.793
| 57\31, 4023.529
| 74\40, 4036.364
|-
|へ (ひb)
|88\48, 4061.538
|64\35, 4042.105
|104\57, 4025.846
|96\53, 3972.414
|56\31, 3952.941
|69\40, 3763.636
|-
|-
|19
|ひ
|し#
|89\48, 4107.692
|augmented ninth
|65\35, 4105.263
| -19
|106\57, 4103.226
|もb (むbb)
|41\22, 4100
|diminished sixth
|99\53, 4096.552
|58\31, 4094.118
|75\40, 4090.909
|-
|-
|20
|ひ#
|よ (む#)
|90\48, 4153.846
|augmented sixth
|66\35, 4168.421
| -20
|108\57, 4180.645
|せb (しbb)
| rowspan="2" |42\22, 4200
|diminished ninth
|102\53, 4220.690
|60\31, 4235.294
|78\40, 4254.545
|-
|-
|21
|め (みb)
|た (つ#)
|92\48, 4246.154
|augmented third
|67\35, 4231.579
| -21
|110\57, 4219.355
|へb (ひbb)
|101\53, 4179.310
|doubly diminished twelfth
|59\31, 4164.706
|76\40, 4145.455
|-
|み
| 93\48, 4292.308
|68\35, 4294.737
|111\57, 4296.774
|43\22, 4300
| 104\53, 4303.448
|61\31, 4305.882
|79\40, 4309.091
|-
|み#
|94\48, 4338.462
| rowspan="2" |69\35, 4357.895
|113\57, 4374.194
|44\22, 4400
|107\53, 4427.586
|63\31, 4447.059
|82\40, 4472.727
|-
|こ (くb)
|95\48, 4384.615
|112\57, 4335.484
|43\22, 4300
|103\53, 4262.931
|60\31, 4235.294
|77\40, 4200
|-
!く
!96\48, 4430.769
!70\35, 4421.053
!114\57, 4412.903
!44\22, 4400
!106\53, 4386.207
!62\31, 4376.471
!80\40, 4363.636
|}
|}


==Genchain==
The generator chain for this scale is as follows:
{| class="wikitable"
{| class="wikitable"
|+
|+Cents
|
!Notation
|
!Supersoft
|
!Soft
|
!Semisoft
|
!Basic
|
!Semihard
|へb (ひbb)
!Hard
|せb (しbb)
!Superhard
|もb (むbb)
|-
|とb (つbb)
|А#
|めb (みbb)
| 1\48, 46.154
|てb (ちbb)
|1\35, 63.158
|けb (ゆbb)
|2\57, 77.419
|→
| rowspan="2" | 1\22, 100
|3\53, 124.138
|2\31, 141.176
|3\40, 163.636
|-
|Бь
|3\48, 138.462
|2\35, 126.316
|3\57, 116.129
|2\53, 82.759
|1\31, 70.588
|1\40, 54.545
|-
|Б
| 4\48, 184.615
|3\35, 189.454
|5\57, 193.548
|2\22, 200
|5\53, 206.897
| 3\31, 211.765
|4\40, 218.182
|-
|Б#
|5\48, 230.769
|4\35, 252.632
|7\57, 270.968
| rowspan="2" |3\22, 300
|8\53, 331.034
|5\31, 352.941
|7\40, 381.818
|-
|-
|
|Вь
|
|7\48, 323.077
|
|5\35, 315.789
|
|8\57, 309.677
|
|7\53, 289.655
|
|4\31, 282.353
|dd12
| 5\40, 272.727
|d9
|d6
|d3
|d13
|d10
|d7
|
|-
|-
|の (ぬb)
|В
|こ (くb)
|8\48, 369.231
|ね (にb)
|6\35, 378.947
|ま (きb)
|10\57, 387.097
|ほ (ふb)
|4\22, 400
|そ (すb)
|10\53, 413.739
|へ (ひb)
| 6\31, 423.529
|せ (しb)
|8\40, 436.364
|も (むb)
|-
|と (つb)
|В#
|め (みb)
|9\48, 415.385
|て (ちb)
| rowspan="2" |7\35, 442.105
|け (ゆb)
|12\57, 464.516
|→
|5\22, 500
|13\53, 537.069
|8\31, 564.706
|11\40, 600
|-
|Гь
|10\48. 461.538
|11\57, 425.806
| 4\22, 400
|9\53, 372.414
|5\31, 352.941
|6\40, 327.273
|-
|Г
|'''11\48,''' '''507.692'''
|'''8\35,''' '''505.263'''
|'''13\57,''' '''503.226'''
|'''5\22,''' '''500'''
|'''12\53,''' '''496.552'''
|'''7\31,''' '''494.118'''
|'''9\40,''' '''490.909'''
|-
|-
|d4
| Г#
|d14
|12\48, 553.846
|d11
|9\35, 568.421
|d8
|15\57, 580.645
|d5
| rowspan="2" |6\22, 600
|m2
|15\53, 620.690
|d12
|9\31, 635.294
|m9
|12\40, 654.545
|m6
|m3
|m13
|m10
|m7
|
|-
|-
|ぬ
|Дь
|く
|14\48, 646.154
|に
|10\35, 631.579
|き
|16\57, 619.355
|ふ
|14\53, 579.310
|す
|8\31, 564.706
|ひ
|10\40, 545.455
|し
|-
|む
|Д
|つ
|15\48, 692.308
|み
|11\35, 694.737
|ち
|18\57, 696.774
|ゆ
|7\22, 700
|→
|17\53, 703.448
|10\31, 705.882
|13\40, 709.091
|-
|Д#
|16\48, 738.462
|12\35, 757.895
|20\57, 774.194
| rowspan="2" |8\22, 800
| 20\53, 827.586
|12\31, 847.059
|16\40, 872.727
|-
|-
|N4
|Еь
|P1
|18\48, 830.769
|N11
|13\35, 821.053
|P8
|21\57, 812.903
|N5
|19\53, 786.261
|M2
| 11\31, 776.471
|N12
|14\40, 763.636
|M9
|M6
|M3
|M13
|M10
|M7
|
|-
|-
|な (ぬ#)
|Е
|か (く#)
|19\48, 876.923
|に#
|14\35, 884.211
|き#
|23\57, 890.323
|は (ふ#)
|9\22, 900
|さ (す#)
|22\53, 910.345
|に#
|13\31, 917.647
|し#
|17\40, 927.273
|よ (む#)
|-
|た (つ#)
|Е#
|
|20\48, 923.077
|
|15\35, 947.638
|
|25\57, 967.742
|
| rowspan="2" |10\22, 1000
|25\53, 1034.483
|15\31, 1058.824
|20\40, 1090.909
|-
|Ёь
|22\48, 1015.385
|16\35, 1010.526
|26\57, 1006.452
|24\53, 993.103
|14\31, 988.235
|18\40, 981.818
|-
| Ё
|23\48, 1061.538
|17\35, 1073.684
|28\57, 1083.871
|11\22, 1100
|27\53, 1117.241
| 16\31, 1129.412
|21\40, 1145.45
|-
|Ё#
|24\48, 1107.692
| rowspan="2" |18\35, 1136.842
|30\57, 1161.290
|12\22, 1200
|30\29, 1241.176
|15\31, 1058.824
|24\40, 1309.091
|-
|Жь
|25\48, 1153.846
|29\57, 1122.581
| 11\22, 1100
|26\53, 1075.862
|18\31, 1270.588
|19\40, 1036.364
|-
|Ж
|26\48, 1200
|19\35, 1200
|31\57, 1200
|12\22, 1200
|29\53, 1200
| 17\31, 1200
|22\40, 1200
|-
|Ж#
|27\48, 1246.154
| 20\35, 1263.158
|33\57, 1277.419
| rowspan="2" |13\22, 1300
|32\53, 1324.138
|18\31, 1270.588
|25\40, 1363.636
|-
|Зь
|29\48, 1338.462
|21\35, 1326.316
|34\57, 1316.129
|31\53, 1282.759
|19\31, 1341.176
|23\40, 1254.545
|-
|-
|A4
|З
|A1
|30\48, 1384.615
|A11
|22\35, 1389.474
|A8
|36\57, 1393.548
|A5
| 14\22, 1400
|A2
|34\53, 1406.897
|A12
|20\31, 1411.765
|A9
|26\40, 1418.182
|A6
|-
|A3
|З#
|
|31\48, 1430.769
|
|23\35, 1452.632
|
|38\57, 1470.968
|
| rowspan="2" |15\22, 1500
|}
|37\53, 1531.034
 
|22\31, 1552.941
==Modes==
|29\40, 1581.818
The mode names are based on the diatonic scale:
|-
{| class="wikitable"
|Иь
|+
| 33\48, 1523.077
!Mode
|24\35, 1515.789
!Scale
|39\57, 1509.677
![[Modal UDP Notation|UDP]]
|36\53, 1489.655
! colspan="12" |Interval type
|21\31, 1482.353
|27\40, 1472.727
|-
|И
|34\48, 1569.231
|25\35, 1578.947
|41\57, 1587.097
|16\22, 1600
|39\53, 1613.793
| 23\31, 1623.529
|30\40, 1636.364
|-
|И#
|35\48, 1615.385
| rowspan="2" |26\35, 1642.105
|43\57, 1664.516
|17\22, 1700
|42\53, 1737.069
|25\31, 1764.706
|33\40, 1800
|-
|Йь
|36\48, 1661.538
|42\57, 1625.806
|16\22, 1600
|38\53, 1572.414
|22\31, 1552.941
|28\40, 1527.273
|-
|Й
|'''37\48,''' '''1707.692'''
|'''27\35,''' '''1705.263'''
|'''44\57,''' '''1703.226'''
|'''17\22, 1700'''
|'''41\53,''' '''1696.552'''
|'''24\31,''' '''1694.118'''
|'''31\40,''' '''1690.909'''
|-
|Й#
|38\48, 1753.846
|28\35, 1768.421
|46\57, 1780.645
| rowspan="2" |18\22, 1800
|44\53, 1820.690
|26\31, 1835.294
|34\40, 1854.545
|-
|-
!name
|Кь
!pattern
|40\48, 1846.158
!notation
|29\35, 1831.579
!2nd
|47\57, 1819.355
!3rd
|43\53, 1779.310
!4th
|25\31, 1764.706
!5th
|32\40, 1745.455
!6th
|-
!7th
|К
!8th
|41\48, 1892.308
!9th
|30\35, 1894.737
!10th
|49\57, 1896.774
!11th
|19\22, 1900
!12th
|46\53, 1903.448
!13th
|27\31, 1905.882
|35\40, 1909.091
|-
|К#
|42\48, 1938.462
| 31\35, 1957.895
|51\57, 1974.194
| rowspan="2" |20\22, 2000
|49\53, 2027.586
|29\31, 2047.059
| 38\40, 2072.727
|-
|Ль
|44\48, 2030.769
|32\35, 2021.053
|52\57, 2012.903
|48\53, 1986.207
|28\31, 1976.471
|36\40, 1963.636
|-
|-
|Lydian Dominant ♮11
|Л
|LLLsLLsLLsLLs
|45\48, 2076.923
|<nowiki>12|0</nowiki>
|33\35, 2084.211
|M
|54\57, 2090.323
|M
|21\22, 2100
|A
|51\53, 2110.345
|P
|30\31, 2117.647
|M
|39\40, 2127.273
|M
|P
|M
|M
|P
|P
|M
|-
|-
|Major b14
|Л#
|LLsLLLsLLsLLs
|46\48, 2123.077
|<nowiki>11|1</nowiki>
| rowspan="2" |34\35, 2147.368
|M
|56\57, 2167.742
|M
|22\22, 2200
|P
|54\53, 2234.483
|P
|32\31, 2258.824
|M
|42\40, 2290.909
|M
|-
|P
| Мь
|M
|47\48, 2169.231
|M
|55\57, 2129.032
|P
|21\22, 2100
|P
|50\53, 2068.966
|M
|29\31, 2047.059
|37\40, 2018.182
|-
|-
|Mixolydian
!М
|LLsLLsLLLsLLs
!48\48, 2215.385
|<nowiki>10|2</nowiki>
!35\35, 2210.526
|M
!57\57, 2206.452
|M
!'''22\22, 2200'''
|P
!53\53, 2193.103
|P
!31\31, 2188.235
|M
!40\40, 2181.818
|m
|P
|M
|M
|P
|P
|M
|-
|-
|Mixolydian b10 (Persian)
|М#
|LLsLLsLLsLLLs
|49\48, 2261.538
|<nowiki>9|3</nowiki>
|36\35, 2273.684
|M
|59\57, 2283.871
|M
| rowspan="2" |23\22, 2300
|P
|56\53, 2317.241
|P
|33\31, 2329.418
|M
|43\40, 2345.455
|m
|P
|M
|m
|P
|P
|M
|-
|-
|Aeolian Dominant ♮6
|Нь
|LLsLLsLLsLLsL
|51\48, 2353.846
|<nowiki>8|4</nowiki>
|37\35, 2336.842
|M
|60\57, 2322.581
|M
|55\53, 2275.862
|P
|32\31, 2258.854
|P
|41\40, 2236.363
|M
|m
|P
|M
|m
|P
|P
|m
|-
|-
|Dorian b13
|Н
|LsLLLsLLsLLsL
|52\48, 2400
|<nowiki>7|5</nowiki>
|38\35, 2400
|M
|62\57, 2400
|m
|24\22, 2400
|P
|58\53, 2400
|P
|34\31, 2400
|M
|44\40, 2400
|m
|-
|P
| Н#
|M
|53\48, 2446.154
|m
|39\35, 2463.158
|P
|64\57, 2477.419
|P
| rowspan="2" |25\22, 2500
|m
|61\53, 2524.138
|36\31, 2541.176
|47\40, 2563.636
|-
|Оь
|55\48, 2538.462
|40\35, 2526.316
|65\57, 2516.129
|60\53, 2482.759
|35\31, 2570.588
|45\40, 2454.545
|-
|О
|56\48, 2584.615
|41\35, 2589.474
|67\57, 2593.548
|26\22, 2600
|63\53, 2606.897
|37\31, 2611.765
|48\40, 2618.182
|-
|О#
|57\48, 2630.792
| rowspan="2" |42\35, 2652.632
|69\57, 2670.968
|27\22, 2700
| 66\53, 2731.034
|39\31, 2752.941
|51\40, 2781.818
|-
|Пь
|58\48, 2676.923
|68\57, 2632.258
|26\22, 2600
|62\53, 2565.517
|36\31, 2541.176
|46\40, 2509.091
|-
|'''П'''
|'''59\48, 2723.077'''
|'''43\35, 2715.789'''
|'''70\57, 2709.677'''
|'''27\22, 2700'''
|'''65\53, 2689.655'''
|'''38\31, 2682.353'''
|'''49\40, 2672.72'''
|-
|П#
|60\48, 2769.321
|44\35, 2778.947
|72\57, 2787.097
| rowspan="2" |28\22, 2800
|68\53, 2813.739
|40\31, 2823.529
|52\40, 2836.363
|-
|-
|Minor
|Рь
|LsLLsLLLsLLsL
|62\48, 2861.538
|<nowiki>6|6</nowiki>
|45\35, 2842.105
|M
|73\57, 2825.806
|m
|67\53, 2772.414
|P
|39\31, 2752.941
|P
|51\40, 2781.818
|m
|-
|m
|Р
|P
|63\48, 2907.692
|M
|46\35, 2905.263
|m
|75\57, 2903.226
|P
|29\22, 2900
|P
|70\53, 2896.552
|m
|41\31, 2894.118
|53\40, 2890.909
|-
| Р#
|64\48, 2953.846
|47\35, 2968.421
|77\57, 2980.645
| rowspan="2" |30\22, 3000
|73\53, 3020.690
|43\31, 3035.294
|56\40, 3054.545
|-
|Сь
|66\48, 3046.154
|48\35, 3031.579
|78\57, 3019.355
|72\53, 2979.310
|42\31, 2964.706
| 54\40, 2945.455
|-
|-
|Phrygian ♮2
|С
|LsLLsLLsLLLsL
|67\48, 3092.308
|<nowiki>5|7</nowiki>
|49\35, 3094.737
|M
|80\57, 3096.774
|m
|31\22, 3100
|P
|75\53, 3103.448
|P
|44\31, 3105.882
|m
| 57\40, 3109.090
|m
|P
|m
|m
|P
|P
|m
|-
|-
|Locrian ♮2 ♮5
|С#
|LsLLsLLsLLsLL
|68\48, 3138.462
|<nowiki>4|8</nowiki>
|50\35, 3157.895
|M
|82\57, 3174.194
|m
| rowspan="2" |32\22, 3200
|P
| 78\53, 3227.586
|P
|46\31, 3247.059
|m
|60\40, 3272.727
|m
|-
|P
|Ть
|m
|70\48, 3230.769
|m
|51\35, 3221.053
|P
| 83\57, 3212.903
|P
|77\53, 3186.207
|m
|45\31, 3176.471
|58\40, 3163.636
|-
|-
|Locrian ♮5
|Т
|sLLLsLLsLLsLL
|71\48, 3276.923
|<nowiki>3|9</nowiki>
|52\35, 3284.211
|m
| 85\57, 3290.323
|m
|33\22, 3300
|P
|80\53, 3310.345
|P
|47\31, 3317.647
|m
|61\40, 3327.273
|m
|P
|m
|m
|P
|P
|m
|-
|-
|Locrian
|Т#
|sLLsLLLsLLsLL
|72\48, 3323.077
|<nowiki>2|10</nowiki>
| rowspan="2" |53\35, 3347.368
|m
|86\57, 3329.032
|m
|34\22, 3400
|P
|83\53, 3434.483
|d
|49\31, 3458.824
|m
|64\40, 3490.909
|m
|P
|m
|m
|P
|P
|m
|-
|-
|Locrian b8
|Уь
|sLLsLLsLLLsLL
|73\48, 3369.231
|<nowiki>1|11</nowiki>
|87\57, 3367.742
|m
|33\22, 3300
|m
|79\53, 3268.966
|P
| 46\31, 3247.059
|d
|59\40, 3218.182
|m
|m
|d
|m
|m
|P
|d
|m
|-
|-
|Locrian b8 b11
|У
|sLLsLLsLLsLLL
|74\48, 3415.385
|<nowiki>0|12</nowiki>
|54\35, 3410.526
|m
|88\57, 3406.452
|m
|34\22, 3400
|P
|82\53, 3393.103
|d
|48\31, 3388.235
|m
|62\40, 3381.818
|m
|-
|d
|У#
|m
|75\48, 3461.538
|m
|55\35, 3473.684
|d
|90\57, 3483.871
|d
| rowspan="2" |35\22, 3500
|m
|85\53, 3517.241
|50\31, 3529.421
|65\40, 3545.455
|-
|Фь
| 77\48, 3553.846
|56\35, 3536.842
| 92\57, 3522.581
|84\53, 3475.862
|49\31, 3458.824
|63\40, 3436.364
|-
|Ф
|78\48, 3600
|57\35, 3600
|93\57, 3600
|36\22, 3600
|87\53, 3600
| 51\31, 3600
|66\40, 3600
|-
|Ф#
|79\48, 3646.154
|58\35, 3663.158
|95\57, 3677.419
| rowspan="2" |37\22, 3700
|90\53, 3724.138
|53\31, 3741.176
|69\40, 3763.636
|-
|Хь
|81\48, 3738.462
|59\35, 3726.316
|96\57, 3716.129
|89\53, 3682.759
|52\31, 3670.588
|67\40, 3654.545
|-
|Х
|82\48, 3784.615
|60\35, 3789.474
|98\57, 3793.458
|38\22, 3800
|92\53, 3806.897
|54\31, 3811.765
|70\40, 3818.182
|-
| Х#
|83\48, 3830.077
| rowspan="2" |61\35, 3852.632
|100\57, 3870.968
|39\22, 3900
|95\53, 3931.034
| 56\31, 3952.941
|73\40, 3981.818
|-
|Ць
|84\48, 3876.923
|99\57, 3832.258
|38\22, 3800
|91\53, 3765.517
|53\31, 3741.176
|68\40, 3709.091
|-
|'''Ц'''
|'''85\48, 3923.077'''
|'''62\35, 3915.789'''
|'''101\57, 3909.677'''
|'''39\22, 3900'''
|'''94\53, 3889.655'''
|'''55\31, 3882.353'''
|'''71\40, 3872.727'''
|-
|Ц#
|86\48, 3969.231
|63\35, 3978.947
|103\57, 3987.097
| rowspan="2" |40\22, 4000
|97\53, 4013.793
|57\31, 4023.529
|74\40, 4036.364
|-
|Чь
|88\48, 4061.538
|64\35, 4042.105
|104\57, 4025.846
|96\53, 3972.414
|56\31, 3952.941
|69\40, 3763.636
|-
|Ч
|89\48, 4107.692
|65\35, 4105.263
|106\57, 4103.226
|41\22, 4100
|99\53, 4096.552
|58\31, 4094.118
|75\40, 4090.909
|-
|Ч#
|90\48, 4153.846
|66\35, 4168.421
| 108\57, 4180.645
| rowspan="2" |42\22, 4200
|102\53, 4220.690
|60\31, 4235.294
|78\40, 4254.545
|-
|Шь
|92\48, 4246.154
|67\35, 4231.579
|110\57, 4219.355
|101\53, 4179.310
|59\31, 4164.706
|76\40, 4145.455
|-
|Ш
|93\48, 4292.308
|68\35, 4294.737
|111\57, 4296.774
|43\22, 4300
|104\53, 4303.448
|61\31, 4305.882
|79\40, 4309.091
|-
|Ш#
|94\48, 4338.462
| rowspan="2" |69\35, 4357.895
|113\57, 4374.194
|44\22, 4400
|107\53, 4427.586
|63\31, 4447.059
|82\40, 4472.727
|-
|Аь
| 95\48, 4384.615
|112\57, 4335.484
|43\22, 4300
|103\53, 4262.931
|60\31, 4235.294
|77\40, 4200
|-
!А
!96\48, 4430.769
!70\35, 4421.053
!114\57, 4412.903
!44\22, 4400
!106\53, 4386.207
!62\31, 4376.471
!80\40, 4363.636
|}
|}


==Temperaments==
== Intervals==
The '''Shōsūshī''' temperament spells its major hexad 24:30:36:45:54:64 or 84:108:126:162:189:224 <code>root-2(4g-3p)-(3g-2p)-(11g-8p)-2(3g-2p)-(1g)</code> (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 <code>root-(-5g-p)-(3g-2p)-(-2g)-2(3g-2p)-(1g)</code> (p = 18/5 or 7/2, g = 8/3).
{| class="wikitable"
 
|+
===Shōsūshī-Meantone===
!Generators
[[Subgroup]]: 18/5.2.3
!Fourteenth notation
 
!Interval category name
[[Comma]] list: [[81/80]]
!Generators
 
!Notation of 7/2ish inverse
[[POL2]] generator: ~4/3 = 506.8820¢
!Interval category name
 
|-
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
| colspan="6" |The 13-note MOS has the following intervals (from some root):
 
|-
[[Vals]]: [[22ed18/5]], [[35ed18/5]], [[48ed18/5]], [[61ed18/5]]
|0
 
|く
===Shōsūshī-Superpyth===
|perfect unison
[[Subgroup]]: 7/2.2.3
|0
 
|く
[[Comma]] list: [[64/63]]
|“perfect” minor fourteenth
 
[[POL2]] generator: ~4/3 = 486.8323¢
 
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
 
[[Vals]]: [[22ed7/2]], [[31ed7/2]], [[40ed7/2]], [[49ed7/2]]
 
==Scale tree==
The spectrum looks like this:
{| class="wikitable"
|+
! colspan="3" |Generator
!<u>Normalized<ref name=":0" /></u>
!L
!s
!L/s
!Comments
|-
|-
|3\13
|
|
|<u>514; 3, 2</u>
|1
|1
|1
|に
|1.000
|natural eleventh
|Equalised
| -1
|ぬ
|natural fourth
|-
| 2
| き
|perfect octave
| -2
|け (ゆb)
|minor seventh
|-
|-
|
|3
|17\74
|ふ
|
|natural fifth
|<u>510</u>
| -3
|6
|て (ちb)
|5
|minor tenth
|1.200
|
|-
|-
|
|14\61
|
|<u>509.{{Overline|09}}</u>
|5
|4
|4
|1.250
|す
|
|major second
| -4
|め (みb)
|minor thirteenth
|-
|-
|
|5
|
|ひ
|25\109
|natural twelfth (tritave)
|<u>508; 2, 9, 3</u>
| -5
|9
|と (つb)
|7
|minor third
|1.286
|
|-
|-
|
|6
|11\48
|し
|
|major ninth
|<u>507; 1, 3, 3</u>
| -6
|4
|も (むb)
|3
|minor sixth
|1.333
|
|-
|-
|
|
|19\83
|<u>506.{{Overline|6}}</u>
|7
|7
|5
|む
|1.400
|major sixth
|
| -7
| せ (しb)
|minor ninth
|-
|-
|
|8\35
|
|<u>505; 3, 1, 4</u>
|3
|2
|1.500
|Shōsūshī-Meantone starts here
|-
|
|
|21\92
|<u>504</u>
|8
|8
|5
|つ
|1.600
|major third
|
| -8
|へ (ひb)
|diminished twelfth
|-
|-
|
|9
|
|み
|13\57
|major thirteenth
|<u>503; 4, 2, 3</u>
| -9
|5
| そ (すb)
|3
| minor second
|1.667
|
|-
|-
|
|10
|
|ち
|18\79
|major tenth
|<u>502; 3, 14</u>
| -10
|7
|ほ (ふb)
|4
|diminished fifth
|1.750
|
|-
|-
|
|11
|
|ゆ
|23\101
|major seventh
|<u>501.{{Overline|81}}</u>
| -11
|9
|ま (きb)
|5
|diminished octave
|1.800
|-
|
|12
|な (ぬ#)
| augmented fourth
| -12
|ね (にb)
|diminished eleventh
|-
|-
|
| 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
|5\22
|
|<u>500</u>
|2
|1
|2.000
|Shōsūshī-Meantone ends, Shōsūshī-Pythagorean begins
|-
|-
|
|13
|
|か (く#)
|27\119
|augmented unison
|<u>498; 2, 6</u>
| -13
|11
|こ (くb)
|5
|diminished fourteenth
|2.200
|
|-
|-
|
| 14
|
|に#
|22\97
|augmented eleventh
|<u>498; 8, 1, 5</u>
| -14
|9
|の (ぬb)
|4
|diminished fourth
|2.250
|
|-
|-
|
|15
|
|き#
|17\75
|augmented octave
|<u>497; 1, 1, 3, 1, 1, 2</u>
| -15
|7
|けb (ゆbb)
|3
|diminished seventh
|2.333
|-
|
|16
|-
|は (ふ#)
|
|augmented fifth
|
| -16
|12\53
|てb (ちbb)
|<u>496; 1, 1, 4, 3</u>
|diminished tenth
|5
|-
|2
|17
|2.500
|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:
{| class="wikitable"
|+
|
|
|
|
|
|
|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:
{| class="wikitable"
|+
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
| Lydian♮11 b14
|LLLsLLsLLsLLs
|<nowiki>12|0</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Major b14
|LLsLLLsLLsLLs
|<nowiki>11|1</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
| M
|P
|P
|M
|-
|Mixolydian
|LLsLLsLLLsLLs
|<nowiki>10|2</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|M
|P
|P
|M
|-
|Mixolydian b10 (Persian)
|LLsLLsLLsLLLs
|<nowiki>9|3</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Hindu♮6
|LLsLLsLLsLLsL
|<nowiki>8|4</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian b13
|LsLLLsLLsLLsL
|<nowiki>7|5</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Minor
|LsLLsLLLsLLsL
|<nowiki>6|6</nowiki>
| M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Phrygian ♮2
|LsLLsLLsLLLsL
|<nowiki>5|7</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian ♮2 ♮5
|LsLLsLLsLLsLL
|<nowiki>4|8</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian ♮5
|sLLLsLLsLLsLL
|<nowiki>3|9</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Locrian
|sLLsLLLsLLsLL
|<nowiki>2|10</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Locrian b8
|sLLsLLsLLLsLL
|<nowiki>1|11</nowiki>
|m
|m
|P
|d
|m
|m
|d
|m
|m
|P
|d
|m
|-
|Locrian b8 b11
|sLLsLLsLLsLLL
|<nowiki>0|12</nowiki>
|m
|m
|P
|d
|m
|m
|d
|m
|m
|d
| d
|m
|}
Natural Dorian and Phrygian modes are shōsūshī MODMOS by one alteration, as are the close approximation to Lydian and the dominant version of Mixolydian and the analog to Harmonic Minor only has two step sizes:
{| class="wikitable"
|+
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
| Dorian
|LsLLLsLLsLLLs
|<nowiki>7|5 #13</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Mixolydian Dominant
|LLsLLsLLLsLsL
|<nowiki>6|6 #3 #10</nowiki>
|M
|M
|P
|P
|m
|m
|P
|M
|M
|P
|P
|m
|-
|Persian ♮7
|LLsLLLsLsLLLs
|<nowiki>5|7 #3 #6 #7</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Lydian Dominant ♮11
|LLLsLsLLLsLLs
|<nowiki>4|8 #3 #4 #5 #9 #10 #12 #13</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Locrian b4 b8 b11
|sLsLLLsLLsLLL
|<nowiki>3|9 b4 b5 b8 b11</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|-
|Lydian b14
|LLLsLLsLLLsLs
|<nowiki>2|10 #5 #6 #7 #9 #10 #12 #13</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|A
|P
|M
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>1|11 #8 b11</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|d
|d
|m
|-
|Phrygian b8
|sLLLsLsLLLsLL
|<nowiki>0|12 #5 #11 #12</nowiki>
|m
|m
|P
|P
|m
|m
|d
|m
|m
|P
|P
|m
|-
|Locrian ♮2
|LsLsLLLsLLsLL
|<nowiki>12|0 b3 b5 b6 b7 b9 b10 b12 b13</nowiki>
|M
|m
|P
|d
|m
|m
|P
|m
|m
|P
|P
|M
|-
|Phrygian
|sLLLsLLsLLLsL
|<nowiki>11|1 b2 b3 b6 b7</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Minor b12
|LsLLsLLLsLsLL
|<nowiki>10|2 b3 b6 b10 b12 b13</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|d
|m
|-
|Phrygian ♮2 ♮6
|LsLLLsLsLLLsL
|<nowiki>9|3 b3 b9 b13</nowiki>
|M
|m
|P
|P
|M
|m
|P
|m
|m
|P
|P
|m
|-
|Hindu
|LLsLsLLLsLLsL
|<nowiki>8|4 b6</nowiki>
|M
|M
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|}
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
! 4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Harmonic Minor
|LsLLsLLLsLLLs
|<nowiki>6|6 #13</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|P
|M
|-
|Dorian♮10 b13
|LsLLLsLLLsLsL
|<nowiki>5|7 #6 #10</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|M
|P
|P
|M
|-
|Ionian Dominant
|LLsLLLsLLsLsL
|<nowiki>4|8 #3 #4 #5 #6 #7 #9 #10 #12</nowiki>
|M
| M
|P
|P
|M
|M
|P
|M
|M
|P
|P
|m
|-
|Lydian b10 ♮11 b14
|LLLsLLsLsLLLs
|<nowiki>3|9 #2 #3 #4 #6 #7 #9 #10 #11 #12 #13</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Locrian bb7 b8
|sLLsLsLLLsLLL
|<nowiki>2|10 bb7 b8</nowiki>
|m
|m
|P
|d
|m
|d
|d
|m
|m
|P
|d
|m
|-
|Locrian b4 b8 b11
|sLsLLLsLLLsLL
|<nowiki>1|11 b4 b11</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|-
|Lydian #8 b14
|LLLsLLLsLLsLs
|<nowiki>0|12 #2 #3 #4 #5 #6 #7 x8 #9 #10 x11 #12 #13</nowiki>
|M
|M
| P
|P
|M
|M
|A
|M
|M
|A
|P
|M
|-
| Locrian♮5 b11
|sLLLsLLsLsLLL
|<nowiki>12|0 b2 b3 b6 b7 b9 b10 b11 b12 b13</nowiki>
|m
|m
|P
| P
|m
|m
|P
|m
|m
|d
| d
|m
|-
|Minor b8 b9 b12
|LsLLsLsLLLsLL
|<nowiki>11|1 b3 b6 b7 b8 b9 b12</nowiki>
|M
|m
|P
|P
|m
|m
|d
|m
|m
|P
|d
|m
|-
|Minor b5 b9
|LsLsLLLsLLLsL
|<nowiki>10|2 b3 b5 b6 b7 b9</nowiki>
|M
|m
|P
|d
|M
|m
|P
|m
|m
|P
|d
| m
|-
|Phrygian♮9
|sLLLsLLLsLLsL
|<nowiki>9|3 b2 b3 b6 b13 </nowiki>
|m
|m
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian b12 b13
|LsLLLsLLsLsLL
|<nowiki>8|4 b2 b3 b6 b13</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|m
|m
|-
|Persian Dominant b9
|LLsLLsLsLLLsL
|<nowiki>7|5 #3 b9 b10</nowiki>
|M
|m
|P
|P
|M
|m
|P
|m
|m
|P
|P
|M
|}
{| class="wikitable"
|+
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Phrygian
|sLLLsLLsLLLsL
|<nowiki>5|7 b2</nowiki>
|m
|m
|P
|P
|m
|m
|P
| m
|m
|P
|P
|m
|-
|Minor b12
|LsLLsLLLsLsLL
|<nowiki>4|8 #9 b12</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|d
|m
|-
|Phrygian ♮2 ♮6
|LsLLLsLsLLLsL
|<nowiki>3|9 #2 #6</nowiki>
|M
|m
|P
|P
|M
|m
|P
| m
|m
|P
|P
|m
|-
|Hindu
|LLsLsLLLsLLsL
|<nowiki>2|10 #2 #5 #9 #12</nowiki>
|M
|M
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian
|LsLLLsLLsLLLs
|<nowiki>1|11 #2 #5 #8 #9 #12</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Mixolydian Dominant
|LLsLLsLLLsLsL
|<nowiki>0|12 #2 #3 #5 #8 #9 #10 #11 #12</nowiki>
|M
|M
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Persian ♮7
|LLsLLLsLsLLLs
|<nowiki>12|0 b4 b10</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Lydian Dominant ♮11
|LLLsLsLLLsLLs
|<nowiki>11|1 #4 b7</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Locrian b4 b8 b11
|sLsLLLsLLsLLL
|<nowiki>10|2 b2 b3 b4 b5 b6 b8 b9 b10 b11 b12 b13</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|-
|Lydian b14
|LLLsLLsLLLsLs
|<nowiki>9|3 #4 #7</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|A
|P
|M
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>8|4 b2 b3 b5 b6 b8 b9 b11 b12 b13</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
| d
|d
|m
|-
|Phrygian b8
|sLLLsLsLLLsLL
|<nowiki>7|5 b2 b5 b6 b8 b9 b11 b12 b13</nowiki>
|m
|m
|P
|P
|m
|m
|d
|m
|m
|P
|P
|m
|-
|Minor b5 b9 b12
|LsLsLLLsLLsLL
|<nowiki>6|6 b5 b9 b12</nowiki>
| M
|m
|P
|P
|m
|m
|P
|m
|m
| P
|P
|M
|}
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Lydian b14
|LLLsLLsLLLsLs
|<nowiki>12|0 #11</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|A
|P
|M
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>11|1 b2 b3 b5 b6 b7 b9 b10 b12 b13</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|d
|d
|m
|-
|Phrygian b8
|sLLLsLsLLLsLL
|<nowiki>10|2 b2 b3 b4 b8 b9 b10 b12 b13</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|d
|d
|m
|-
|Minor b5 b9 b12
|LsLsLLLsLLsLL
|<nowiki>9|3 b3 b5 b6 b9 b12 b13</nowiki>
|m
|m
|P
|P
|m
|m
|d
|m
|m
|P
|P
|m
|-
|Phrygian
|sLLLsLLsLLLsL
|<nowiki>8|4 b6 b9 </nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|M
|-
|Minor b12
|LsLLsLLLsLsLL
|<nowiki>7|5 b6 b12</nowiki>
|m
|m
|P
|P
|m
|m
|P
|M
|m
|P
|d
|m
|-
|Minor b9
|LsLLLsLsLLLsL
|<nowiki>6|6 b9</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Hindu
|LLsLsLLLsLLsL
|<nowiki>5|7 #3 #9</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian
|LsLLLsLLsLLLs
|<nowiki>4|8 #6 #9 #10</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Mixolydian Dominant
|LLsLLsLLLsLsL
|<nowiki>3|9 #2 #3 #6 #9 #10 #12</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|M
|P
|P
|M
|-
|Persian ♮7
|LLsLLLsLsLLLs
|<nowiki>2|10 #2 #3 #5 #6 #7 #9 #12 #13</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Lydian Dominant ♮11
|LLLsLsLLLsLLs
|<nowiki>1|11 #2 #3 #4 #5 #6 #8 #9 #10 #12</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Locrian b4 b8 b11
|sLsLLLsLLsLLL
|<nowiki>0|12 b4</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|}
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
! 8th
!9th
!10th
!11th
!12th
!13th
|-
|Lydian b14
|LLLsLLsLLLsLs
|<nowiki>12|0 #11</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|A
|P
| M
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>11|1 b2 b3 b5 b6 b7 b9 b10 b12 b13</nowiki>
|m
|m
|P
|d
|m
|m
| P
|m
|m
|d
| d
|m
|-
|Phrygian b8
|sLLLsLsLLLsLL
|<nowiki>10|2 b2 b3 b4 b8 b9 b10 b12 b13</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
| d
|d
|m
|-
|Minor b5 b9 b12
|LsLsLLLsLLsLL
|<nowiki>9|3 b3 b5 b6 b9 b12 b13</nowiki>
|m
|m
|P
|P
|m
|m
|d
|m
|m
|P
|P
|m
|-
|Phrygian
|sLLLsLLsLLLsL
|<nowiki>8|4 b6 b9 </nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|M
|-
|Minor b12
|LsLLsLLLsLsLL
|<nowiki>7|5 b6 b12</nowiki>
|m
|m
|P
|P
|m
|m
|P
|M
|m
|P
|d
|m
|-
|Minor b9
|LsLLLsLsLLLsL
|<nowiki>6|6 b9</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Hindu
|LLsLsLLLsLLsL
|<nowiki>5|7 #3 #9</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian
|LsLLLsLLsLLLs
|<nowiki>4|8 #6 #9 #10</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Mixolydian Dominant
|LLsLLsLLLsLsL
|<nowiki>3|9 #2 #3 #6 #9 #10 #12</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|M
|P
|P
|M
|-
|Persian ♮7
|LLsLLLsLsLLLs
|<nowiki>2|10 #2 #3 #5 #6 #7 #9 #12 #13</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Lydian Dominant♮11
|LLLsLsLLLsLLs
|<nowiki>1|11 #2 #3 #4 #5 #6 #8 #9 #10 #12</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Locrian b4 b8 b11
|sLsLLLsLLsLLL
|<nowiki>0|12 b4</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|}
{| class="wikitable"
|+
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Mixolydian Dominant
|LLsLLsLLLsLsL
|<nowiki>10|2 b13</nowiki>
|M
|M
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Persian ♮7
|LLsLLLsLsLLLs
|<nowiki>9|3 #7</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Major #4 b14
|LLLsLsLLLsLLs
|<nowiki>8|4 #3 #4 #7 #10 #13 </nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Locrian b4 b8 b11
|sLsLLLsLLsLLL
|<nowiki>7|5 b2 b4 b5 b6 b8 b9 b10 b11 b12</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|-
|Lydian b14
|LLLsLLsLLLsLs
|<nowiki>6|6 #3 #4 #6 #7 #10 #11 #13</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|A
|P
|M
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>5|7 b2 b5 b6 b9 b11</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|d
|d
|m
|-
|Phrygian b8
|sLLLsLsLLLsLL
|<nowiki>4|8 b8 #12</nowiki>
|m
|m
|P
|P
|m
|m
|d
|m
|m
|P
|P
|m
|-
|Locrian♮2
|LsLsLLLsLLsLL
|<nowiki>3|9 #5 #6 #7 #8 #9 #10 #12</nowiki>
|M
|m
|P
|d
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Phrygian
|sLLLsLLsLLLsL
|<nowiki>2|10 #5 #12</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Minor b12
|LsLLsLLLsLsLL
|<nowiki>1|11 #2 #5 #6 #8 #9 #12</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|d
|m
|-
|Phrygian♮2 ♮6
|LsLLLsLsLLLsL
|<nowiki>0|12 #2 #5 #8 #11 #12</nowiki>
|M
|m
|P
|P
|M
|m
|P
|m
|m
|P
|P
|m
|-
|Hindu
|LLsLsLLLsLLsL
|<nowiki>12|0 b3 b4 b7 b10</nowiki>
|M
|M
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Dorian
|LsLLLsLLsLLLs
|<nowiki>11|1 b3 b7 b10</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|}
 
===Cyclic Permutation Order===
{| class="wikitable"
|+
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Mixolydian b10 (Persian)
|LLsLLsLLsLLLs
|<nowiki>9|3</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Phrygian♮2
|LsLLsLLsLLLsL
|<nowiki>5|7</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian b8
|sLLsLLsLLLsLL
|<nowiki>1|11</nowiki>
|m
|m
|P
|d
|m
|m
|d
|m
|m
|P
|d
|m
|-
|Mixolydian
|LLsLLsLLLsLLs
|<nowiki>10|2</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|M
|P
|P
|M
|-
|Minor
|LsLLsLLLsLLsL
|<nowiki>6|6</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|P
|m
|-
|Locrian
|sLLsLLLsLLsLL
|<nowiki>2|10</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Major b14
|LLsLLLsLLsLLs
|<nowiki>11|1</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Dorian b13
|LsLLLsLLsLLsL
|<nowiki>7|5</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Locrian♮5
|sLLLsLLsLLsLL
|<nowiki>3|9</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Lydian♮11 b14
|LLLsLLsLLsLLs
|<nowiki>12|0</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Hindu♮6
|LLsLLsLLsLLsL
|<nowiki>8|4</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Locrian♮2♮5
|LsLLsLLsLLsLL
|<nowiki>4|8</nowiki>
|M
|m
|P
|P
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Locrian b8 b11
|sLLsLLsLLsLLL
|<nowiki>0|12</nowiki>
|m
|m
|P
|d
|m
|m
|d
|m
|m
|d
|d
|m
|}
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Persian♮7
|LLsLLLsLsLLLs
|<nowiki>9|3 #7</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|m
|P
|P
|M
|-
|Phrygian♮2♮6
|LsLLLsLsLLLsL
|<nowiki>5|7 #6</nowiki>
|M
|m
|P
|P
|M
|m
|P
|m
|m
|P
|P
|m
|-
|Phrygian
|sLLLsLsLLLsLL
|<nowiki>5|7 b2</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Major #4 b14
|LLLsLsLLLsLLs
|<nowiki>11|1 #4</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Hindu
|LLsLsLLLsLLsL
|<nowiki>8|4 b6</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|m
|P
|P
|m
|-
|Locrian♮2
|LsLsLLLsLLsLL
|<nowiki>2|10 #2</nowiki>
|M
|m
|P
|d
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Locrian b4 b8 b11
|sLsLLLsLLsLLL
|<nowiki>0|12 b4</nowiki>
|m
|m
|d
|d
|m
|m
|d
|m
|m
|d
|d
|m
|-
|Dorian
|LsLLLsLLsLLLs
|<nowiki>7|5 #13</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>2|10 b11</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|d
|d
|m
|-
|Lydian b14
|LLLsLLsLLLsLs
|<nowiki>12|0 #11</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|A
|P
|M
|-
|Mixolydian Dominant
|LLsLLsLLLsLsL
|<nowiki>10|2 b13</nowiki>
|M
|M
|P
|P
|M
|m
|P
|M
|M
|P
|P
|m
|-
|Minor b12
|LsLLsLLLsLsLL
|<nowiki>6|6 b12</nowiki>
|m
|m
|P
|P
|m
|m
|P
|m
|m
|P
|d
|m
|-
|Locrian b11
|sLLsLLLsLsLLL
|<nowiki>2|10 b11</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|d
|d
|m
|}
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="12" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
!6th
!7th
!8th
!9th
!10th
!11th
!12th
!13th
|-
|Persian #4
|LLLsLsLLsLLLs
|<nowiki>9|3 #4</nowiki>
|M
|M
|A
|P
|M
|m
|P
|M
|m
|P
|P
|M
|-
|Hindu b9
|LLsLsLLsLLLsL
|<nowiki>8|4 b6 b9, 5|7 #3</nowiki>
|M
|M
|P
|P
|m
|m
|P
|m
|m
|P
|P
|m
|-
|Locrian♮2
|LsLsLLsLLLsLL
|<nowiki>2|10 #2</nowiki>
|M
|m
|P
|d
|m
|m
|d
|m
|m
|P
|d
|m
|-
|Locrian bb7 b8
|sLsLLsLLLsLLL
|<nowiki>1|11 bb7</nowiki>
|m
|m
|P
|d
|m
|d
|d
|m
|m
|P
|d
|m
|-
|Harmonic Minor
|LsLLsLLLsLLLs
|<nowiki>6|6 #13</nowiki>
|M
|m
|P
|P
|m
|m
|P
|M
|m
|P
|P
|M
|-
|Locrian ♮12
|sLLsLLLsLLLsL
|<nowiki>2|10 #12</nowiki>
|m
|m
|P
|d
|m
|m
|P
|m
|m
|P
|M
|m
|-
|Major #11 b14
|LLsLLLsLLLsLs
|<nowiki>11|1 #11</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|A
|P
|M
|-
|Dorian♮10 b13
|LsLLLsLLLsLsL
|<nowiki>7|5 #10</nowiki>
|M
|m
|P
|P
|M
|m
|P
|M
|M
|P
|P
|m
|-
|Locrian♮5♮9
|sLLLsLLLsLsLL
|<nowiki>3|9 #9</nowiki>
|m
|m
|P
|P
|m
|m
|P
|M
|m
|P
|d
|m
|-
|Lydian #8♮11 b14
|LLLsLLLsLsLLs
|<nowiki>12|0 #8</nowiki>
|M
|M
|A
|P
|M
|M
|P
|M
|M
|P
|P
|M
|-
|Ionian Dominant
|LLsLLLsLsLLsL
|<nowiki>11|1 b13, 8|4 #7</nowiki>
|M
|M
|P
|P
|M
|M
|P
|M
|M
|P
|P
|m
|-
|Locrian♮2♮5♮6
|LsLLLsLsLLsLL
|<nowiki>4|8 #6</nowiki>
|M
|m
|P
|P
|M
|m
|P
|m
|m
|P
|d
|m
|-
|Locrian♮5 b8 b11
|sLLLsLsLLsLLL
|<nowiki>0|12 #5</nowiki>
|m
|m
|P
|P
|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 <code>root-2(4g-3p)-(3g-2p)-(11g-8p)-2(3g-2p)-(1g)</code> (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 <code>root-(-5g-p)-(3g-2p)-(-2g)-2(3g-2p)-(1g)</code> (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]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
 
[[Vals]]: [[22ed18/5]], [[35ed18/5]], [[48ed18/5]], [[61ed18/5]]
 
===Shōsūshī-Superpyth===
[[Subgroup]]: 7/2.2.3
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~4/3 = 486.8323¢
 
[[Mapping]]: [{{Val|1 1 2}}, {{Val|0 -2 -5}}]
 
[[Vals]]: [[22ed7/2]], [[31ed7/2]], [[40ed7/2]], [[49ed7/2]]
 
==Scale tree==
The spectrum looks like this:
{| class="wikitable"
|+
!Generator
!<u>Normalized</u>
!L
!s
!L/s
!Comments
|-
|3\13
|<u>514.286</u>
|1
|1
|1.000
|Equalised
|-
|17\74
|<u>510.000</u>
|6
|5
|1.200
|
|-
|14\61
|<u>509.091</u>
|5
|4
|1.250
|
|-
|25\109
|<u>508.474</u>
|9
|7
|1.286
|
|-
|11\48
|<u>507.692</u>
|4
|3
|1.333
|
|-
|19\83
|<u>506.{{Overline|6}}</u>
|7
|5
|1.400
|
|-
|8\35
|<u>505.263</u>
|3
|2
|1.500
|Shōsūshī-Meantone starts here
|-
|21\92
|<u>504.000</u>
|8
|5
|1.600
|
|-
|13\57
|<u>503.226</u>
|5
|3
|1.667
|
|-
|18\79
|<u>502.326</u>
|7
|4
|1.750
|
|-
|23\101
|<u>501.818</u>
|9
|5
|1.800
|
|-
|5\22
|<u>500.000</u>
|2
|1
|2.000
|Shōsūshī-Meantone ends, Shōsūshī-Pythagorean begins
|-
|42\185
|<u>499.010</u>
|17
|8
|2.125
|
|-
|37\163
|<u>498.876</u>
|15
|7
|2.143
|
|-
|32\141
|<u>498.701</u>
|13
|6
|2.167
|
|-
|27\119
|<u>498.462</u>
|11
|5
|2.200
|
|-
|22\97
|<u>498.113</u>
|9
|4
|2.250
|
|-
|17\75
|<u>497.561</u>
|7
|3
|2.333
|
|-
|12\53
|<u>496.552</u>
|5
|2
|2.500
|Shōsūshī-Neogothic heartland is from here…
|Shōsūshī-Neogothic heartland is from here…
|-
|-
|
|
|19\84
|19\84
|<u>495; 1, 1, 1, 7</u>
|<u>495.652</u>
|8
|8
|3
|3
Line 1,346: Line 4,176:
|…to here
|…to here
|-
|-
|
|7\31
|7\31
|
|<u>494.118</u>
|<u>494; 8, 2</u>
|3
|3
|1
|1
Line 1,355: Line 4,183:
|Shōsūshī-Pythagorean ends, Shōsūshī-Superpyth begins
|Shōsūshī-Pythagorean ends, Shōsūshī-Superpyth begins
|-
|-
|
|
|30\133
|30\133
|<u>493; 6, 1, 1, 1, 3</u>
|<u>493.159</u>
|13
|13
|4
|4
Line 1,364: Line 4,190:
|
|
|-
|-
|
|
|23\102
|23\102
|<u>492.8{{Overline|3}}</u>
|<u>492.857</u>
|10
|10
|3
|3
Line 1,373: Line 4,197:
|
|
|-
|-
|
|
|16\71
|16\71
|<u>492; 3, 4</u>
|<u>492.308</u>
|7
|7
|2
|2
Line 1,382: Line 4,204:
|
|
|-
|-
|
|
|25\111
|25\111
|<u>491; 1, 4, 12</u>
|<u>491.803</u>
|11
|11
|3
|3
Line 1,391: Line 4,211:
|
|
|-
|-
|
|9\40
|9\40
|
|<u>490.909</u>
|<u>490.{{Overline|90}}</u>
|4
|4
|1
|1
Line 1,400: Line 4,218:
|
|
|-
|-
|
|
|20\89
|20\89
|<u>489; 1, 3, 1, 9</u>
|<u>489.796</u>
|9
|9
|2
|2
Line 1,409: Line 4,225:
|
|
|-
|-
|
|11\49
|11\49
|
|<u>488.889</u>
|<u>488.{{Overline|8}}</u>
|5
|5
|1
|1
Line 1,418: Line 4,232:
|Shōsūshī-Superpyth ends
|Shōsūshī-Superpyth ends
|-
|-
|
|13\58
|13\58
|
|<u>487.500</u>
|<u>487.5</u>
|6
|6
|1
|1
Line 1,428: Line 4,240:
|-
|-
|2\9
|2\9
|
|<u>480.000</u>
|
|<u>480</u>
|1
|1
|0
|0
Line 1,437: Line 4,247:
|}
|}


== See also ==
==See also==
[[9L 4s (7/2-equivalent)]] - septimal tuning
[[9L 4s (7/2-equivalent)]] - septimal Shōsūshī tuning
 
[[9L 4s (39/11-equivalent)]] - neogothic Shōsūshī tuning
 
[[9L 4s (25/7-equivalent)]] - St. James Scale
 
[[9L 4s (18/5-equivalent)]] - classical Shōsūshī tuning
 
[[18L 8s (112/9-equivalent)]] - septimal Petrushka minor tuning


[[9L 4s (39/11-equivalent)]] - neogothic tuning
[[18L 8s (88/7-equivalent)]] and [[18L 8s (4π-equivalent)|18L 8s (4[math]π[/math]-equivalent)]] - neogothic Petrushka minor tuning


[[9L 4s (18/5-equivalent)]] - classical tuning<references />
[[18L 8s (64/5-equivalent)]] - classical Petrushka minor tuning<references />
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/9L_4s_(minor_fourteenth-equivalent)"