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

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There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (major sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol;  Fa, Sol, La, Si, Do 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.
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (major sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol;  Fa, Sol, La, Si, Do 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"
!Notation
|+Normalized
! colspan="2" |Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 19: Line 20:
!Superhard
!Superhard
|-
|-
!Diatonic
!Scala Francisci
!Scala Francisci
!19eds
!19eds
Line 28: Line 30:
!17eds
!17eds
|-
|-
|Do#, Fa#, Sol#
|Α#
|Α#
|1\19, 46.154
|1\19, 46.154¢
|1\14, 63.158
|1\14, 63.158¢
|2\23, 77.419
|2\23, 77.419¢
| rowspan="2" |1\9, 100
| rowspan="2" |1\9, 100¢
|3\22, 124.138
|3\22, 124.138¢
|2\13, 141.176
|2\13, 141.176¢
|3\17, 163.636
|3\17, 163.636¢
|-
|-
|Reb, Solb, Lab
|Βb
|Βb
|3\19, 138.462
|3\19, 138.462¢
|2\14, 126.316
|2\14, 126.316¢
|3\23, 116.129
|3\23, 116.129¢
|2\22, 82.759
|2\22, 82.759¢
|1\13, 70.588
|1\13, 70.588¢
|1\17, 54.545
|1\17, 54.545¢
|-
|-
|'''Re, Sol, La'''
|'''Β'''
|'''Β'''
|'''4\19,''' '''184.615'''
|'''4\19,''' '''184.615¢'''
|'''3\14,''' '''189.474'''
|'''3\14,''' '''189.474¢'''
|'''5\23,''' '''193.548'''
|'''5\23,''' '''193.548¢'''
|'''2\9,''' '''200'''
|'''2\9,''' '''200¢'''
|'''5\22,''' '''206.897'''
|'''5\22,''' '''206.897¢'''
|'''3\13,''' '''211.765'''
|'''3\13,''' '''211.765¢'''
|'''4\17,''' '''218.182'''
|'''4\17,''' '''218.182¢'''
|-
|-
|Re#, Sol#, La#
|Β#
|Β#
|5\19, 230.769
|5\19, 230.769¢
|4\14, 252.632
|4\14, 252.632¢
|7\23, 270.968
|7\23, 270.968¢
| rowspan="2" |3\9, 300
| rowspan="2" |3\9, 300¢
|8\22, 331.035
|8\22, 331.034¢
|5\13, 352.941
|5\13, 352.941¢
|7\17, 381.818
|7\17, 381.818¢
|-
|-
|Mib, Lab, Sib
|Γb
|Γb
|7\19, 323.077
|7\19, 323.077¢
|5\14, 315.789
|5\14, 315.789¢
|8\23, 309.677
|8\23, 309.677¢
|7\22, 289.655
|7\22, 289.655¢
|4\13, 282.353
|4\13, 282.353¢
|5\17, 272.727
|5\17, 272.727¢
|-
|-
|Mi, La, Si
|Γ
|Γ
|8\19, 369.231
|8\19, 369.231¢
|6\14, 378.947
|6\14, 378.947¢
|10\23, 387.097
|10\23, 387.097¢
|4\9, 400
|4\9, 400¢
|10\22, 413.793
|10\22, 413.793¢
|6\13, 423.529
|6\13, 423.529¢
|8\17, 436.364
|8\17, 436.36&¢
|-
|-
|Mi#, La#, Si#
|Γ#
|Γ#
|9\19, 415.385
|9\19, 415.385¢
| rowspan="2" |7\14, 442.105
| rowspan="2" |7\14, 442.105¢
|12\23, 464.516
|12\23, 464.516¢
|5\9, 500
|5\9, 500¢
|13\22, 537.931
|13\22, 537.931¢
|8\13, 564.706
|8\13, 564.706¢
|11\17, 600
|11\17, 600¢
|-
|-
|Fab, Sibb, Dob
|Δb
|Δb
|10\19, 461.538
|10\19, 461.538¢
|11\23, 425.806
|11\23, 425.806¢
|4\9, 400
|4\9, 400¢
|9\22, 372.414
|9\22, 372.414¢
|5\13, 352.941
|5\13, 352.941¢
|6\17, 327.273
|6\17, 327.273¢
|-
|-
|Fa, Sib, Do
|Δ
|Δ
|11\19, 507.692
|11\19, 507.692¢
|8\14, 505.263
|8\14, 505.263¢
|13\23, 503.226
|13\23, 503.226¢
|5\9, 500
|5\9, 500¢
|12\22, 496.552
|12\22, 496.552¢
|7\13, 494.118
|7\13, 494.118¢
|9\17, 490.909
|9\17, 490.909¢
|-
|-
|Fa#, Si, Do#
|Δ#
|Δ#
|12\19, 553.846
|12\19, 553.846¢
|9\14, 568.421
|9\14, 568.421¢
|15\23, 580.645
|15\23, 580.645¢
| rowspan="2" |6\9, 600
| rowspan="2" |6\9, 600¢
|15\22, 620.690
|15\22, 620.690¢
|9\13, 635.294
|9\13, 635.294¢
|12\17, 654.545
|12\17, 654.545¢
|-
|-
|Solb, Dob,  Reb
|Εb
|Εb
|14\19, 646.154
|14\19, 646.154¢
|10\14, 631.579
|10\14, 631.579¢
|16\23, 619.355
|16\23, 619.355¢
|14\22, 579.310
|14\22, 579.310¢
|8\13, 564.706
|8\13, 564.706¢
|10\17, 545.455
|10\17, 545.455¢
|-
|-
|'''Sol, Do, Re'''
|'''Ε'''
|'''Ε'''
|'''15\19,''' '''692.308'''
|'''15\19,''' '''692.308¢'''
|'''11\14,''' '''694.737'''
|'''11\14,''' '''694.737¢'''
|'''18\23,''' '''696.774'''
|'''18\23,''' '''696.774¢'''
|'''7\9,''' '''700'''
|'''7\9,''' '''700¢'''
|'''17\22,''' '''703.448'''
|'''17\22,''' '''703.448¢'''
|'''10\13,''' '''705.882'''
|'''10\13,''' '''705.882¢'''
|'''13\17,''' '''709.091'''
|'''13\17,''' '''709.091¢'''
|-
|-
|Sol#, Do#, Re#
|Ε#
|Ε#
|16\19, 738.462
|16\19, 738.462¢
|12\14, 757.895
|12\14, 757.895¢
|20\23, 774.194
|20\23, 774.194¢
| rowspan="2" |8\9, 800
| rowspan="2" |8\9, 800¢
|20\22, 827.586
|20\22, 827.586¢
|12\13, 847.059
|12\13, 847.059¢
|16\17, 872.727
|16\17, 872.727¢
|-
|-
|Dob, Fab, Solb
|Ϛb/Ϝb
|Ϛb/Ϝb
|18\19, 830.769
|18\19, 830.769¢
|13\14, 821.053
|13\14, 821.053¢
|21\23, 812.903
|21\23, 812.903¢
|19\22, 786.207
|19\22, 786.207¢
|11\13, 776.647
|11\13, 776.647¢
|14\17, 763.636
|14\17, 763.636¢
|-
|-
!Do, Fa, Sol
!Ϛ/Ϝ
!Ϛ/Ϝ
!19\19, 876.923
!19\19, 876.923¢
!14\14, 884.211
!14\14, 884.211¢
!23\23, 890.323
!23\23, 890.323¢
!9\9, 900
!9\9, 900¢
!22\22, 910.345
!22\22, 910.345¢
!13\13, 917.647
!13\13, 917.647¢
!17\17, 927.273
!17\17, 927.273¢
|-
|-
|Do#, Fa#, Sol#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|20\19, 923.077
|20\19, 923.077¢
|15\14, 947.368
|15\14, 947.368¢
|24\23, 929.032
|24\23, 929.032¢
| rowspan="2" |10\9, 1000
| rowspan="2" |10\9, 1000¢
|25\22, 1034.483
|25\22, 1034.483¢
|15\13, 1052.824
|15\13, 1052.824¢
|20\17, 1090.909
|20\17, 1090.909¢
|-
|-
|Reb, Solb, Lab
|Ζb
|Ζb
|22\19, 1015.385
|22\19, 1015.385¢
|16\14, 1010.526
|16\14, 1010.526¢
|26\23, 1006.452
|26\23, 1006.452¢
|24\22, 993.103
|24\22, 993.103¢
|14\13, 988.235
|14\13, 988.235¢
|18\17, 981.818
|18\17, 981.818¢
|-
|-
|'''Re, Sol, La'''
|'''Ζ'''
|'''Ζ'''
|'''23\19, 1061.538'''
|'''23\19, 1061.538¢'''
|'''17\14,''' '''1071.684'''
|'''17\14,''' '''1071.684¢'''
|'''28\23,''' '''1083.871'''
|'''28\23,''' '''1083.871¢'''
|'''11\9,''' '''1100'''
|'''11\9,''' '''1100¢'''
|'''27\22,''' '''1117.241'''
|'''27\22,''' '''1117.241¢'''
|'''16\13,''' '''1129.412'''
|'''16\13,,''' '''1129.412¢'''
|'''21\17,''' '''1145.455'''
|'''21\17,''' '''1145.455¢'''
|-
|-
|Re#, Sol#, La#
|Ζ#
|Ζ#
|24\19, 1107.692
|24\19, 1107.692¢
|18\14, 1136.842
|18\14, 1136.842¢
|30\23, 1161.290
|30\23, 1161.290¢
| rowspan="2" |12\9, 1200
| rowspan="2" |12\9, 1200¢
|30\22, 1241.379
|30\22, 1241.379¢
|18\13, 1270.588
|18\13, 1270.588¢
|24\14, 1309.091
|24\14, 1309.091¢
|-
|-
|Mib, Lab, Sib
|Ηb
|Ηb
|26\19, 1200
|26\19, 1200¢
|19\14, 1200
|19\14, 1200¢
|31\23,1200
|31\23,1200¢
|29\22, 1200
|29\22, 1200¢
|17\13, 1200
|17\13, 1200¢
|22\17, 1200
|22\17, 1200¢
|-
|-
|Mi, La, Si
|Η
|Η
|27\19, 1246.154
|27\19, 1246.154¢
|20\14, 1263.158
|20\14, 1263.158¢
|33\23, 1277.419
|33\23, 1277.419¢
|13\9, 1300
|13\9, 1300¢
|32\22, 1324.138
|32\22, 1324.138¢
|19\13, 1341.176
|19\13, 1341.176¢
|25\17, 1363.636
|25\17, 1363.636¢
|-
|-
|Mi#, La#, Si#
|Η#
|Η#
|28\19, 1292.308
|28\19, 1292.308¢
| rowspan="2" |21\14, 1326.316¢
| rowspan="2" |21\14, 1326.316¢
|35\23, 1354.839
|35\23, 1354.839¢
|14\9, 1400
|14\9, 1400¢
|35\22, 1448.276
|35\22, 1448.276¢
|21\13, 1482.353
|21\13, 1482.353¢
|28\17, 1527.272
|28\17, 1527.272¢
|-
|-
|Fab, Sibb, Dob
|Θb
|Θb
|29\19, 1338.462
|29\19, 1338.462¢
|34\23, 1316.129
|34\23, 1316.129¢
|13\9, 1300
|13\9, 1300¢
|31\22, 1282.759
|31\22, 1282.759¢
|18\13, 1270.588
|18\13, 1270.588¢
|23\17, 1254.545
|23\17, 1254.545¢
|-
|-
|Fa, Sib, Do
|Θ
|Θ
|30\19, 1384.615
|30\19, 1384.615¢
|22\14, 1389.474
|22\14, 1389.474¢
|36\23, 1393.548
|36\23, 1393.548¢
|14\9, 1400
|14\9, 1400¢
|34\22, 1406.897
|34\22, 1406.897¢
|20\13, 1411.765
|20\13, 1411.765¢
|26\17, 1418.182
|26\17, 1418.182¢
|-
|-
|Fa#, Si, Do#
|Θ#
|Θ#
|31\19, 1430.769
|31\19, 1430.769¢
|23\14, 1452.632
|23\14, 1452.632¢
|38\23, 1470.968
|38\23, 1470.968¢
| rowspan="2" |15\9, 1500
| rowspan="2" |15\9, 1500¢
|37\22, 1531.035
|37\22, 1531.0345¢
|22\13, 1552.941
|22\13, 1552.941¢
|29\17, 1581.182
|29\17, 1581.182¢
|-
|-
|Solb, Dob,  Reb
|Ιb
|Ιb
|33\19, 1523.077
|33\19, 1523.077¢
|24\14, 1515.789
|24\14, 1515.789¢
|39\23, 1509.677
|39\23, 1509.677¢
|36\22, 1489.655
|36\22, 1489.655¢
|21\13, 1482.353
|21\13, 1482.353¢
|27\17, 1472.727
|27\17, 1472.727¢
|-
|-
|'''Sol, Do, Re'''
|'''Ι'''
|'''Ι'''
|'''34\19,''' '''1569.231'''
|'''34\19,''' '''1569.231¢'''
|'''25\14,''' '''1578.947'''
|'''25\14,''' '''1578.947¢'''
|'''41\23,''' '''1587.097'''
|'''41\23,''' '''1587.097¢'''
|'''16\9,''' '''1600'''
|'''16\9,''' '''1600¢'''
|'''39\22,''' '''1613.793'''
|'''39\22,''' '''1613.793¢'''
|'''23\13,''' '''1623.529'''
|'''23\13,''' '''1623.529¢'''
|'''30\17,''' '''1636.363'''
|'''30\17,''' '''1636.363¢'''
|-
|-
|Sol#, Do#, Re#
|Ι#
|Ι#
|35\19, 1615.385
|35\19, 1615.385¢
|26\14, 1642.105
|26\14, 1642.105¢
|43\23, 1664.516
|43\23, 1664.516¢
| rowspan="2" |17\9, 1700
| rowspan="2" |17\9, 1700¢
|42\22, 1737.931
|42\22, 1737.931¢
|25\13, 1764.706
|25\13, 1764.706¢
|33\17, 1800
|33\17, 1800¢
|-
|-
|Dob, Fab, Solb
|Αb
|Αb
|37\19, 1707.692
|37\19, 1707.692¢
|27\14, 1705.263
|27\14, 1705.263¢
|44\23, 1703.226
|44\23, 1703.226¢
|41\22, 1696.552
|41\22, 1696.552¢
|20\13, 1694.118
|20\13, 1694.118¢
|31\17, 1490.909
|31\17, 1490.909¢
|-
|-
!Do, Fa, Sol
!Α
!Α
!38\19, 1753.846¢
!38\19, 1753.846¢
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