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User:Moremajorthanmajor/4L 1s (5/3-equivalent): Difference between revisions

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[[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
==Notation==
==Notation==
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[8L 2s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
{| class="wikitable"
{| class="wikitable"
|+
|+
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|Α#
|Α#
|1\19
|1\19
46.15385
46.154
|1\14
|1\14
63.1579
63.158
|2\23
|2\23
77.41935
77.419
| rowspan="2" |1\9
| rowspan="2" |1\9
100
100
|3\22
|3\22
[[Tel:124.1379|124.1379]]
124.138
|2\13
|2\13
[[Tel:141.1765|141.1765]]
141.1765
|3\17
|3\17
163.{{Overline|63}}
163.{{Overline|63}}
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|Βb
|Βb
|3\19
|3\19
[[Tel:138.4615|138.4615]]
138.4615
|2\14
|2\14
[[Tel:126.3158|126.3158]]
126.316
|3\23
|3\23
116.129
116.129
|2\22
|2\22
82.7586
82.759
|1\13
|1\13
70.5882
70.588
|1\17
|1\17
54.{{Overline|54}}
54.{{Overline|54}}
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|'''Β'''
|'''Β'''
|'''4\19'''
|'''4\19'''
'''[[Tel:184.6154|184.6154]]'''
'''184.615'''
|'''3\14'''
|'''3\14'''
'''[[Tel:189.4736|189.4736]]'''
'''189.474'''
|'''5\23'''
|'''5\23'''
'''[[Tel:193.5484|193.5484]]'''
'''193.548'''
|'''2\9'''
|'''2\9'''
'''200'''
'''200'''
|'''5\22'''
|'''5\22'''
'''206.89655'''
'''206.897'''
|'''3\13'''
|'''3\13'''
'''[[Tel:211.7647|211.7647]]'''
'''211.765'''
|'''4\17'''
|'''4\17'''
'''218.{{Overline|18}}'''
'''218.{{Overline|18}}'''
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|Β#
|Β#
|5\19
|5\19
[[Tel:230.7692|230.7692]]
230.769
|4\14
|4\14
[[Tel:252.6316|252.6316]]
252.632
|7\23
|7\23
[[Tel:270.9677|270.9677]]
270.968
| rowspan="2" |3\9
| rowspan="2" |3\9
300
300
|8\22
|8\22
[[Tel:331.0345|331.0345]]
331.0345
|5\13
|5\13
[[Tel:352.9412|352.9412]]
352.941
|7\17
|7\17
381.{{Overline|81}}
381.{{Overline|81}}
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|Γb
|Γb
|7\19
|7\19
[[Tel:323.0769|323.0769]]
323.077
|5\14
|5\14
[[Tel:315.7895|315.7895]]
315.7895
|8\23
|8\23
[[Tel:309.6774|309.6774]]
309.677
|7\22
|7\22
[[Tel:289.6552|289.6552]]
289.655
|4\13
|4\13
[[Tel:282.3529|282.3529]]
282.353
|5\17
|5\17
272.{{Overline|72}}
272.{{Overline|72}}
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|Γ
|Γ
|8\19
|8\19
[[Tel:369.2308|369.2308]]
369.2301
|6\14
|6\14
[[Tel:378.9474|378.9474]]
378.947
|10\23
|10\23
[[Tel:387.0968|387.0968]]
387.097
|4\9
|4\9
400
400
|10\22
|10\22
[[Tel:413.7931|413.7931]]
413.793
|6\13
|6\13
[[Tel:423.5294|423.5294]]
423.529
|8\17
|8\17
436.{{Overline|36}}
436.{{Overline|36}}
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|Γ#
|Γ#
|9\19
|9\19
[[Tel:415.3846|415.3846]]
415.385
| rowspan="2" |7\14
| rowspan="2" |7\14
[[Tel:442.1053|442.1053]]
442.105
|12\23
|12\23
[[Tel:464.5161|464.5161]]
464.516
|5\9
|5\9
500
500
Line 144: Line 143:
537.931
537.931
|8\13
|8\13
[[Tel:564.7059|564.7059]]
564.706
|11\17
|11\17
600
600
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|Δb
|Δb
|10\19
|10\19
[[Tel:461.5385|461.5385]]
461.5385
|11\23
|11\23
425.80645
425.8065
|4\9
|4\9
400
400
|9\22
|9\22
[[Tel:372.4138|372.4138]]
372.414
|5\13
|5\13
[[Tel:352.9412|352.9412]]
352.941
|6\17
|6\17
327.{{Overline|27}}
327.{{Overline|27}}
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|Δ
|Δ
|11\19
|11\19
[[Tel:507.6923|507.6923]]
507.692
|8\14
|8\14
[[Tel:505.2632|505.2632]]
505.263
|13\23
|13\23
[[Tel:503.2259|503.2259]]
503.226
|5\9
|5\9
500
500
|12\22
|12\22
[[Tel:496.5517|496.5517]]
496.552
|7\13
|7\13
494.11765
494.118
|9\17
|9\17
490.{{Overline|90}}
490.{{Overline|90}}
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|Δ#
|Δ#
|12\19
|12\19
553.84615
553.846
|9\14
|9\14
568.42105
568.421
|15\23
|15\23
[[Tel:580.6452|580.6452]]
580.645
| rowspan="2" |6\9
| rowspan="2" |6\9
600
600
|15\22
|15\22
[[Tel:620.6897|620.6897]]
620.690
|9\13
|9\13
[[Tel:635.2941|635.2941]]
635.294
|12\17
|12\17
654.{{Overline|54}}
654.{{Overline|54}}
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|Εb
|Εb
|14\19
|14\19
646.15385
646.154
|10\14
|10\14
631.57895
631.579
|16\23
|16\23
[[Tel:619.3548|619.3548]]
619.355
|14\22
|14\22
[[Tel:579.3103|579.3103]]
579.310
|8\13
|8\13
[[Tel:564.7059|564.7059]]
564.706
|10\17
|10\17
545.{{Overline|45}}
545.{{Overline|45}}
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|'''Ε'''
|'''Ε'''
|'''15\19'''
|'''15\19'''
'''[[Tel:692.3077|692.3077]]'''
'''692.308'''
|'''11\14'''
|'''11\14'''
'''[[Tel:694.7368|694.7368]]'''
'''694.737'''
|'''18\23'''
|'''18\23'''
'''[[Tel:696.7742|696.7742]]'''
'''696.774'''
|'''7\8'''
|'''7\9'''
'''700'''
'''700'''
|'''17\22'''
|'''17\22'''
'''[[Tel:703.4483|703.4483]]'''
'''703.448'''
|'''10\13'''
|'''10\13'''
'''705.88235'''
'''705.882'''
|'''13\17'''
|'''13\17'''
'''709.{{Overline|09}}'''
'''709.{{Overline|09}}'''
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|Ε#
|Ε#
|16\19
|16\19
[[Tel:738.4615|738.4615]]
738.4615
|12\14
|12\14
[[Tel:757.8947|757.8947]]
757.8947
|20\23
|20\23
774.19355
774.194
| rowspan="2" |8\8
| rowspan="2" |8\9
800
800
|20\22
|20\22
[[Tel:827.5862|827.5862]]
827.586
|12\13
|12\13
[[Tel:847.0588|847.0588]]
847.059
|16\14
|16\14
872.{{Overline|72}}
872.{{Overline|72}}
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|Ϛb/Ϝb
|Ϛb/Ϝb
|18\19
|18\19
[[Tel:830.7692|830.7692]]
830.769
|13\14
|13\14
[[Tel:821.0526|821.0526]]
821.053
|21\23
|21\23
[[Tel:812.9032|812.9032]]
812.903
|19\22
|19\22
[[Tel:786.2069|786.2069]]
786.207
|11\13
|11\13
[[Tel:776.6471|776.6471]]
776.647
|14\17
|14\17
763.{{Overline|63}}
763.{{Overline|63}}
Line 264: Line 263:
!Ϛ/Ϝ
!Ϛ/Ϝ
!19\19
!19\19
[[Tel:876.9231|876.9231]]
876.923
!14\14
!14\14
[[Tel:884.2105|884.2105]]
884.2105
!23\23
!23\23
[[Tel:890.3226|890.3226]]
890.323
!9\9
!9\9
900
900
!22\22
!22\22
[[Tel:910.3448|910.3448]]
910.345
!13\13
!13\13
[[Tel:917.6471|917.6471]]
917.647
!17\17
!17\17
927.{{Overline|27}}
927.{{Overline|27}}
Line 281: Line 280:
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|20\19
|20\19
[[Tel:923.0769|923.0769]]
923.077
|15\14
|15\14
[[Tel:947.3684|947.3684]]
947.368
|24\23
|24\23
[[Tel:929.0323|929.0323]]
929.032
| rowspan="2" |10\9
| rowspan="2" |10\9
1000
1000
|25\22
|25\22
1034.4829
1034.483
|15\13
|15\13
1052.8235
1052.8235
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|Ζb
|Ζb
|22\19
|22\19
1015.3847
1015.385
|16\14
|16\14
1010.5263
1010.526
|26\23
|26\23
1006.4516
1006.452
|24\22
|24\22
993.10345
993.103
|14\13
|14\13
[[Tel:988.2353|988.2353]]
988.235
|18\17
|18\17
981.{{Overline|81}}
981.{{Overline|81}}
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'''1061.5385'''
'''1061.5385'''
|'''17\14'''
|'''17\14'''
'''1071.6842'''
'''1071.684'''
|'''28\23'''
|'''28\23'''
'''1083.871'''
'''1083.871'''
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'''1100'''
'''1100'''
|'''27\22'''
|'''27\22'''
'''1117.2414'''
'''1117.241'''
|'''16\13'''
|'''16\13'''
'''1129.4118'''
'''1129.412'''
|'''21\17'''
|'''21\17'''
'''1145.{{Overline|45}}'''
'''1145.{{Overline|45}}'''
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|Ζ#
|Ζ#
|24\19
|24\19
1107.6923
1107.692
|18\14
|18\14
1136.8421
1136.842
|30\23
|30\23
1161.7097
1161.290
| rowspan="2" |12\9
| rowspan="2" |12\9
1200
1200
|30\22
|30\22
1241.3793
1241.379
|18\13
|18\13
1270.5882
1270.588
|24\14
|24\14
1309.{{Overline|09}}
1309.{{Overline|09}}
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|Η
|Η
|27\19
|27\19
1246.15385
1246.154
|20\14
|20\14
1263.1579
1263.158
|33\23
|33\23
1277.41935
1277.419
|13\9
|13\9
1300
1300
|32\22
|32\22
1324.1379
1324.138
|19\13
|19\13
1341.1765
1341.1765
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|Η#
|Η#
|28\19
|28\19
1292.3077
1292.308
| rowspan="2" |21\14
| rowspan="2" |21\14
1326.3158
1326.316
|35\23
|35\23
1354.8387
1354.839
|14\9
|14\9
1400
1400
|35\22
|35\22
1448.2759
1448.276
|21\13
|21\13
1482.3529
1482.353
|28\17
|28\17
1527.{{Overline|27}}
1527.{{Overline|27}}
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1300
1300
|31\22
|31\22
1282.7586
1282.759
|18\13
|18\13
1270.5882
1270.588
|23\17
|23\17
1254.{{Overline|54}}
1254.{{Overline|54}}
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|Θ
|Θ
|30\19
|30\19
1384.6154
1384.615
|22\14
|22\14
1389.4737
1389.474
|36\23
|36\23
1393.5484
1393.548
|14\9
|14\9
1400
1400
|34\22
|34\22
1406.89655
1406.897
|20\13
|20\13
1411.7647
1411.765
|26\17
|26\17
1418.{{Overline|18}}
1418.{{Overline|18}}
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|Θ#
|Θ#
|31\19
|31\19
1430.7692
1430.769
|23\14
|23\14
1452.6316
1452.632
|38\23
|38\23
1470.9677
1470.968
| rowspan="2" |15\9
| rowspan="2" |15\9
1500
1500
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1531.0345
1531.0345
|22\13
|22\13
1552.9412
1552.941
|29\17
|29\17
1581.{{Overline|81}}
1581.{{Overline|81}}
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|Ιb
|Ιb
|33\19
|33\19
1523.0769
1523.077
|24\14
|24\14
1515.7895
1515.7895
|39\23
|39\23
1509.6774
1509.677
|36\22
|36\22
1489.6551
1489.655
|21\13
|21\13
1482.3529
1482.353
|27\17
|27\17
1472.{{Overline|72}}
1472.{{Overline|72}}
Line 461: Line 459:
|'''Ι'''
|'''Ι'''
|'''34\19'''
|'''34\19'''
'''1569.2308'''
'''1569.231'''
|'''25\14'''
|'''25\14'''
'''1578.9474'''
'''1578.947'''
|'''41\23'''
|'''41\23'''
'''1587.0968'''
'''1587.097'''
|'''16\9'''
|'''16\9'''
'''1600'''
'''1600'''
|'''39\22'''
|'''39\22'''
'''1613.7931'''
'''1613.793'''
|'''23\13'''
|'''23\13'''
'''1623.5294'''
'''1623.529'''
|'''30\17'''
|'''30\17'''
'''1636.{{Overline|36}}'''
'''1636.{{Overline|36}}'''
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|Ι#
|Ι#
|35\19
|35\19
1615.3846
1615.385
|26\14
|26\14
1642.1053
1642.105
|43\23
|43\23
1664.5161
1664.516
| rowspan="2" |17\9
| rowspan="2" |17\9
1700
1700
Line 488: Line 486:
1737.931
1737.931
|25\13
|25\13
1764.7059
1764.706
|33\17
|33\17
1800
1800
Line 495: Line 493:
|Αb
|Αb
|37\19
|37\19
1707.6923
1707.692
|27\14
|27\14
1705.2632
1705.263
|44\23
|44\23
1703.2258
1703.226
|41\22
|41\22
1696.5517
1696.552
|20\13
|20\13
1694.11765
1694.118
|31\17
|31\17
1490.{{Overline|90}}
1490.{{Overline|90}}
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!Α
!Α
!38\19
!38\19
1753.84615
1753.846
!28\14
!28\14
1768.42105
1768.421
!46\23
!46\23
1780.6452
1780.645
!18\9
!18\9
1800
1800
!44\22
!44\22
1820.6897
1820.690
!26\13
!26\13
1835.2941
1835.2941
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