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User:Moremajorthanmajor/4L 1s (major sixth-equivalent): Difference between revisions

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Line 33: Line 33:
|Do#, Sol#
|Do#, Sol#
|Α#
|Α#
|1\19
|1\19, 46.154¢
46.154
|1\14, 63.158¢
|1\14
|2\23, 77.419¢
63.158
| rowspan="2" |1\9, 100¢
|2\23
|3\22, 124.138¢
77.419
|2\13, 141.1765¢
| rowspan="2" |1\9
|3\17, 163.{{Overline|63}}¢
100
|3\22
124.138
|2\13
141.1765
|3\17
163.{{Overline|63}}
|-
|-
|Reb, Lab
|Reb, Lab
|Βb
|Βb
|3\19
|3\19, 138.4615¢
138.4615
|2\14, 126.316¢
|2\14
|3\23, 116.129¢
126.316
|2\22, 82.759¢
|3\23
|1\13, 70.588¢
116.129
|1\17, 54.{{Overline|54}}¢
|2\22
82.759
|1\13
70.588
|1\17
54.{{Overline|54}}
|-
|-
|'''Re, La'''
|'''Re, La'''
|'''Β'''
|'''Β'''
|'''4\19'''
|'''4\19,''' '''184.615¢'''
'''184.615'''
|'''3\14,''' '''189.474¢'''
|'''3\14'''
|'''5\23,''' '''193.548¢'''
'''189.474'''
|'''2\9,''' '''200¢'''
|'''5\23'''
|'''5\22,''' '''206.897¢'''
'''193.548'''
|'''3\13,''' '''211.765¢'''
|'''2\9'''
|'''4\17,''' '''218.{{Overline|18}}¢'''
'''200'''
|'''5\22'''
'''206.897'''
|'''3\13'''
'''211.765'''
|'''4\17'''
'''218.{{Overline|18}}'''
|-
|-
|Re#, La#
|Re#, La#
|Β#
|Β#
|5\19
|5\19, 230.769¢
230.769
|4\14, 252.632¢
|4\14
|7\23, 270.968¢
252.632
| rowspan="2" |3\9, 300¢
|7\23
|8\22, 331.0345¢
270.968
|5\13, 352.941¢
| rowspan="2" |3\9
|7\17, 381.{{Overline|81}}¢
300
|8\22
331.0345
|5\13
352.941
|7\17
381.{{Overline|81}}
|-
|-
|Mib, Sib
|Mib, Sib
|Γb
|Γb
|7\19
|7\19, 323.077¢
323.077
|5\14, 315.7895¢
|5\14
|8\23, 309.677¢
315.7895
|7\22l 289.655¢
|8\23
|4\13, 282.353¢
309.677
|5\17, 272.{{Overline|72}}¢
|7\22
289.655
|4\13
282.353
|5\17
272.{{Overline|72}}
|-
|-
|Mi, Si
|Mi, Si
|Γ
|Γ
|8\19
|8\19, 369.231¢
369.231
|6\14, 378.947¢
|6\14
|10\23, 387.097¢
378.947
|4\9, 400¢
|10\23
|10\22, 413.793¢
387.097
|6\13, 423.529¢
|4\9
|8\17, 436.{{Overline|36}}¢
400
|10\22
413.793
|6\13
423.529
|8\17
436.{{Overline|36}}
|-
|-
|Mi#, Si#
|Mi#, Si#
|Γ#
|Γ#
|9\19
|9\19, 415.385¢
415.385
| rowspan="2" |7\14, 442.105¢
| rowspan="2" |7\14
|12\23, 464.516¢
442.105
|5\9, 500¢
|12\23
|13\22, 537.931¢
464.516
|8\13, 564.706¢
|5\9
|11\17, 600¢
500
|13\22
537.931
|8\13
564.706
|11\17
600
|-
|-
|Fab, Dob
|Fab, Dob
|Δb
|Δb
|10\19
|10\19, 461.5385¢
461.5385
|11\23, 425.8065¢
|11\23
|4\9, 400¢
425.8065
|9\22, 372.414¢
|4\9
|5\13, 352.941¢
400
|6\17, 327.{{Overline|27}}¢
|9\22
372.414
|5\13
352.941
|6\17
327.{{Overline|27}}
|-
|-
|Fa, Do
|Fa, Do
|Δ
|Δ
|11\19
|11\19, 507.692¢
507.692
|8\14, 505.263¢
|8\14
|13\23, 503.226¢
505.263
|5\9, 500¢
|13\23
|12\22, 496.552¢
503.226
|7\13, 494.118¢
|5\9
|9\17, 490.{{Overline|90}}¢
500
|12\22
496.552
|7\13
494.118
|9\17
490.{{Overline|90}}
|-
|-
|Fa#, Do#
|Fa#, Do#
|Δ#
|Δ#
|12\19
|12\19, 553.846¢
553.846
|9\14, 568.421¢
|9\14
|15\23, 580.645¢
568.421
| rowspan="2" |6\9, 600¢
|15\23
|15\22, 620.690¢
580.645
|9\13, 635.294¢
| rowspan="2" |6\9
|12\17, 654.{{Overline|54}}¢
600
|15\22
620.690
|9\13
635.294
|12\17
654.{{Overline|54}}
|-
|-
|Solb, Reb
|Solb, Reb
|Εb
|Εb
|14\19
|14\19, 646.154¢
646.154
|10\14, 631.579¢
|10\14
|16\23, 619.355¢
631.579
|14\22, 579.310¢
|16\23
|8\13, 564.706¢
619.355
|10\17, 545.{{Overline|45}}¢
|14\22
579.310
|8\13
564.706
|10\17
545.{{Overline|45}}
|-
|-
|'''Sol, Re'''
|'''Sol, Re'''
|'''Ε'''
|'''Ε'''
|'''15\19'''
|'''15\19,''' '''692.308¢'''
'''692.308'''
|'''11\14,''' '''694.737¢'''
|'''11\14'''
|'''18\23,''' '''696.774¢'''
'''694.737'''
|'''7\9,''' '''700¢'''
|'''18\23'''
|'''17\22,''' '''703.448¢'''
'''696.774'''
|'''10\13,''' '''705.882¢'''
|'''7\9'''
|'''13\17,''' '''709.{{Overline|09}}¢'''
'''700'''
|'''17\22'''
'''703.448'''
|'''10\13'''
'''705.882'''
|'''13\17'''
'''709.{{Overline|09}}'''
|-
|-
|Sol#, Re#
|Sol#, Re#
|Ε#
|Ε#
|16\19
|16\19, 738.4615¢
738.4615
|12\14, 757.895¢
|12\14
|20\23, 774.194¢
757.895
| rowspan="2" |8\9, 800¢
|20\23
|20\22, 827.586¢
774.194
|12\13, 847.059¢
| rowspan="2" |8\9
|16\14, 872.{{Overline|72}}¢
800
|20\22
827.586
|12\13
847.059
|16\14
872.{{Overline|72}}
|-
|-
|Dob, Solb
|Dob, Solb
|Ϛb/Ϝb
|Ϛb/Ϝb
|18\19
|18\19, 830.769¢
830.769
|13\14, 821.053¢
|13\14
|21\23, 812.903¢
821.053
|19\22, 786.207¢
|21\23
|11\13, 776.647¢
812.903
|14\17, 763.{{Overline|63}}¢
|19\22
786.207
|11\13
776.647
|14\17
763.{{Overline|63}}
|-
|-
!Do, Sol
!Do, Sol
!Ϛ/Ϝ
!Ϛ/Ϝ
!19\19
!19\19, 876.923¢
876.923
!14\14, 884.2105¢
!14\14
!23\23, 890.323¢
884.2105
!9\9, 900¢
!23\23
!22\22, 910.345¢
890.323
!13\13, 917.647¢
!9\9
!17\17, 927.{{Overline|27}}¢
900
!22\22
910.345
!13\13
917.647
!17\17
927.{{Overline|27}}
|-
|-
|Do#, Sol#
|Do#, Sol#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|20\19
|20\19, 923.077¢
923.077
|15\14, 947.368¢
|15\14
|24\23, 929.032¢
947.368
| rowspan="2" |10\9, 1000¢
|24\23
|25\22, 1034.483¢
929.032
|15\13, 1052.8235¢
| rowspan="2" |10\9
|20\17, 1090.{{Overline|90}}¢
1000
|25\22
1034.483
|15\13
1052.8235
|20\17
1090.{{Overline|90}}
|-
|-
|Reb, Lab
|Reb, Lab
|Ζb
|Ζb
|22\19
|22\19, 1015.385¢
1015.385
|16\14, 1010.526¢
|16\14
|26\23, 1006.452¢
1010.526
|24\22, 993.103¢
|26\23
|14\13, 988.235¢
1006.452
|18\17, 981.{{Overline|81}}¢
|24\22
993.103
|14\13
988.235
|18\17
981.{{Overline|81}}
|-
|-
|'''Re, La'''
|'''Re, La'''
|'''Ζ'''
|'''Ζ'''
|'''23\19'''
|'''23\19,1061.5385¢'''
'''1061.5385'''
|'''17\14,''' '''1071.684¢'''
|'''17\14'''
|'''28\23,''' '''1083.871¢'''
'''1071.684'''
|'''11\9,''' '''1100¢'''
|'''28\23'''
|'''27\22,''' '''1117.241¢'''
'''1083.871'''
|'''16\13,,''' '''1129.412¢'''
|'''11\9'''
|'''21\17,''' '''1145.{{Overline|45}}¢'''
'''1100'''
|'''27\22'''
'''1117.241'''
|'''16\13'''
'''1129.412'''
|'''21\17'''
'''1145.{{Overline|45}}'''
|-
|-
|Re#, La#
|Re#, La#
|Ζ#
|Ζ#
|24\19
|24\19, 1107.692¢
1107.692
|18\14, 1136.842¢
|18\14
|30\23, 1161.290¢
1136.842
| rowspan="2" |12\9, 1200¢
|30\23
|30\22, 1241.379¢
1161.290
|18\13, 1270.588¢
| rowspan="2" |12\9
|24\14, 1309.{{Overline|09}}¢
1200
|30\22
1241.379
|18\13
1270.588
|24\14
1309.{{Overline|09}}
|-
|-
|Mib, Sib
|Mib, Sib
|Ηb
|Ηb
|26\19
|26\19, 1200¢
1200
|19\14, 1200¢
|19\14
|31\23,1200¢
1200
|29\22, 1200¢
|31\23
|17\13, 1200¢
1200
|22\17, 1200¢
|29\22
1200
|17\13
1200
|22\17
1200
|-
|-
|Mi, Si
|Mi, Si
|Η
|Η
|27\19
|27\19, 1246.154¢
1246.154
|20\14, 1263.158¢
|20\14
|33\23, 1277.419¢
1263.158
|13\9, 1300¢
|33\23
|32\22, 1324.138¢
1277.419
|19\13, 1341.1765¢
|13\9
|25\17, 1363.{{Overline|63}}¢
1300
|32\22
1324.138
|19\13
1341.1765
|25\17
1363.{{Overline|63}}
|-
|-
|Mi#, Si#
|Mi#, Si#
|Η#
|Η#
|28\19
|28\19, 1292.308¢
1292.308
| rowspan="2" |21\14, 1326.316¢
| rowspan="2" |21\14
|35\23, 1354.839¢
1326.316
|14\9, 1400¢
|35\23
|35\22, 1448.276¢
1354.839
|21\13, 1482.353¢
|14\9
|28\17, 1527.{{Overline|27}}¢
1400
|35\22
1448.276
|21\13
1482.353
|28\17
1527.{{Overline|27}}
|-
|-
|Fab, Dob
|Fab, Dob
|Θb
|Θb
|29\19
|29\19, 1338.4615¢
1338.4615
|34\23, 1316.129¢
|34\23
|13\9, 1300¢
1316.129
|31\22, 1282.759¢
|13\9
|18\13, 1270.588¢
1300
|23\17, 1254.{{Overline|54}}¢
|31\22
1282.759
|18\13
1270.588
|23\17
1254.{{Overline|54}}
|-
|-
|Fa, Do
|Fa, Do
|Θ
|Θ
|30\19
|30\19, 1384.615¢
1384.615
|22\14, 1389.474¢
|22\14
|36\23, 1393.548¢
1389.474
|14\9, 1400¢
|36\23
|34\22, 1406.897¢
1393.548
|20\13, 1411.765¢
|14\9
|26\17, 1418.{{Overline|18}}¢
1400
|34\22
1406.897
|20\13
1411.765
|26\17
1418.{{Overline|18}}
|-
|-
|Fa#, Do#
|Fa#, Do#
|Θ#
|Θ#
|31\19
|31\19, 1430.769¢
1430.769
|23\14, 1452.632¢
|23\14
|38\23, 1470.968¢
1452.632
| rowspan="2" |15\9, 1500¢
|38\23
|37\22, 1531.0345¢
1470.968
|22\13, 1552.941¢
| rowspan="2" |15\9
|29\17, 1581.{{Overline|81}}¢
1500
|37\22
1531.0345
|22\13
1552.941
|29\17
1581.{{Overline|81}}
|-
|-
|Solb, Reb
|Solb, Reb
|Ιb
|Ιb
|33\19
|33\19, 1523.077¢
1523.077
|24\14, 1515.7895¢
|24\14
|39\23, 1509.677¢
1515.7895
|36\22, 1489.655¢
|39\23
|21\13, 1482.353¢
1509.677
|27\17, 1472.{{Overline|72}}¢
|36\22
1489.655
|21\13
1482.353
|27\17
1472.{{Overline|72}}
|-
|-
|'''Sol, Re'''
|'''Sol, Re'''
|'''Ι'''
|'''Ι'''
|'''34\19'''
|'''34\19,''' '''1569.231¢'''
'''1569.231'''
|'''25\14,''' '''1578.947¢'''
|'''25\14'''
|'''41\23,''' '''1587.097¢'''
'''1578.947'''
|'''16\9,''' '''1600¢'''
|'''41\23'''
|'''39\22,''' '''1613.793¢'''
'''1587.097'''
|'''23\13,''' '''1623.529¢'''
|'''16\9'''
|'''30\17,''' '''1636.{{Overline|36}}¢'''
'''1600'''
|'''39\22'''
'''1613.793'''
|'''23\13'''
'''1623.529'''
|'''30\17'''
'''1636.{{Overline|36}}'''
|-
|-
|Sol#, Re#
|Sol#, Re#
|Ι#
|Ι#
|35\19
|35\19, 1615.385¢
1615.385
|26\14, 1642.105¢
|26\14
|43\23, 1664.516¢
1642.105
| rowspan="2" |17\9, 1700¢
|43\23
|42\22, 1737.931¢
1664.516
|25\13, 1764.706¢
| rowspan="2" |17\9
|33\17, 1800¢
1700
|42\22
1737.931
|25\13
1764.706
|33\17
1800
|-
|-
|Dob, Solb
|Dob, Solb
|Αb
|Αb
|37\19
|37\19, 1707.692¢
1707.692
|27\14, 1705.263¢
|27\14
|44\23, 1703.226¢
1705.263
|41\22, 1696.552¢
|44\23
|20\13, 1694.118¢
1703.226
|31\17, 1490.{{Overline|90}}¢
|41\22
1696.552
|20\13
1694.118
|31\17
1490.{{Overline|90}}
|-
|-
!Do, Sol
!Do, Sol
!Α
!Α
!38\19
!38\19, 1753.846¢
1753.846
!28\14, 1768.421¢
!28\14
!46\23, 1780.645¢
1768.421
!18\9, 1800¢
!46\23
!44\22, 1820.690¢
1780.645
!26\13, 1835.2941¢
!18\9
!34\17, 1854.{{Overline|54}}¢
1800
!44\22
1820.690
!26\13
1835.2941
!34\17
1854.{{Overline|54}}
|}
|}
==Intervals==
==Intervals==
Line 654: Line 454:
|}
|}
==Modes==
==Modes==
The mode names are based on the major satellites of Uranus, in order of size:
The mode names are based on the classical modes:
{| class="wikitable"
{| class="wikitable"
!Mode
!Mode
Line 716: Line 516:
[[Comma]] list: [[81/80]]
[[Comma]] list: [[81/80]]


[[POL2]] generator: ~9/8 = 193.8419
[[POL2]] generator: ~9/8 = 193.8419¢


[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]


[[Optimal ET sequence]]: 5ed5/3, 9ed5/3, 14ed5/3
[[Optimal ET sequence]]: [[5ed5/3]], [[9ed5/3]], [[14ed5/3]]
==='''Dorianic-Superpyth'''===
==='''Dorianic-Superpyth'''===
[[Subgroup]]: 12/7.4/3.3/2
[[Subgroup]]: 12/7.4/3.3/2
Line 726: Line 526:
[[Comma]] list: [[64/63]]
[[Comma]] list: [[64/63]]


[[POL2]] generator: ~9/8 = 216.5781
[[POL2]] generator: ~9/8 = 216.5781¢


[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]


[[Optimal ET sequence]]: 4ed14/9, 13ed14/9, 17ed14/9
[[Optimal ET sequence]]: [[4ed14/9]], [[13ed14/9]], [[17ed14/9]]


==Scale tree==
==Scale tree==
Line 958: Line 758:
|2.000
|2.000
|Dorianic-Meantone ends, Dorianic-Pythagorean begins
|Dorianic-Meantone ends, Dorianic-Pythagorean begins
|-
|
|21\94
|
|201.6
|21
|10
|2.100
|
|-
|
|19\85
|
|201.77
|19
|9
|2.111
|
|-
|
|17\76
|
|201.98
|17
|8
|2.125
|
|-
|-
|
|
Line 1,190: Line 963:
|21
|21
|5
|5
|R.200
|4.200
|
|
|-
|-
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/4L_1s_(major_sixth-equivalent)"