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The generator range is 171.4 to 240 cents, placing it on the diatonic major second, usually representing a major second of some type (like [[8/7]]). The bright (chroma-positive) generator is, however, its major sixth complement (685.7 to 720 cents).
The generator range is 171.4 to 240 cents, placing it on the diatonic major second, usually representing a major second of some type (like [[8/7]]). The bright (chroma-positive) generator is, however, its major sixth complement (685.7 to 720 cents).


Because this diatonic is a major sixth-repeating scale, each tone has a 5/3 major sixth above it. The scale has one augmented chord, two major chords, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale.
Because this diatonic is a major sixth-repeating scale, each tone has a major sixth above it. The scale has one augmented chord, two major chords, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale.


[[Basic]] diatonic is in [[9ed5/3]], which is a very good major sixth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[9ed5/3]], which is a very good major 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 (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 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"
|+Normalized
|+Normalized
! colspan="2" |Notation
!Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 22: Line 21:
|-
|-
!Diatonic
!Diatonic
!19eds
!14eds
!23eds
!9eds
!22eds
!13eds
!17eds
|-
|Do#, Fa#, Sol#
|1\19, 46.154¢
|1\14, 63.158¢
|2\23, 77.419¢
| rowspan="2" |1\9, 100¢
|3\22, 124.138¢
|2\13, 141.176¢
|3\17, 163.636¢
|-
|Reb, Solb, Lab
|3\19, 138.462¢
|2\14, 126.316¢
|3\23, 116.129¢
|2\22, 82.759¢
|1\13, 70.588¢
|1\17, 54.545¢
|-
|'''Re, Sol, La'''
|'''4\19,''' '''184.615¢'''
|'''3\14,''' '''189.474¢'''
|'''5\23,''' '''193.548¢'''
|'''2\9,''' '''200¢'''
|'''5\22,''' '''206.897¢'''
|'''3\13,''' '''211.765¢'''
|'''4\17,''' '''218.182¢'''
|-
|Re#, Sol#, La#
|5\19, 230.769¢
|4\14, 252.632¢
|7\23, 270.968¢
| rowspan="2" |3\9, 300¢
|8\22, 331.034¢
|5\13, 352.941¢
|7\17, 381.818¢
|-
|Mib, Lab, Sib
|7\19, 323.077¢
|5\14, 315.789¢
|8\23, 309.677¢
|7\22, 289.655¢
|4\13, 282.353¢
|5\17, 272.727¢
|-
|Mi, La, Si
|8\19, 369.231¢
|6\14, 378.947¢
|10\23, 387.097¢
|4\9, 400¢
|10\22, 413.793¢
|6\13, 423.529¢
|8\17, 436.36&¢
|-
|Mi#, La#, Si#
|9\19, 415.385¢
| rowspan="2" |7\14, 442.105¢
|12\23, 464.516¢
|5\9, 500¢
|13\22, 537.931¢
|8\13, 564.706¢
|11\17, 600¢
|-
|Fab, Sibb, Dob
|10\19, 461.538¢
|11\23, 425.806¢
|4\9, 400¢
|9\22, 372.414¢
|5\13, 352.941¢
|6\17, 327.273¢
|-
|Fa, Sib, Do
|11\19, 507.692¢
|8\14, 505.263¢
|13\23, 503.226¢
|5\9, 500¢
|12\22, 496.552¢
|7\13, 494.118¢
|9\17, 490.909¢
|-
|Fa#, Si, Do#
|12\19, 553.846¢
|9\14, 568.421¢
|15\23, 580.645¢
| rowspan="2" |6\9, 600¢
|15\22, 620.690¢
|9\13, 635.294¢
|12\17, 654.545¢
|-
|Solb, Dob,  Reb
|14\19, 646.154¢
|10\14, 631.579¢
|16\23, 619.355¢
|14\22, 579.310¢
|8\13, 564.706¢
|10\17, 545.455¢
|-
|'''Sol, Do, Re'''
|'''15\19,''' '''692.308¢'''
|'''11\14,''' '''694.737¢'''
|'''18\23,''' '''696.774¢'''
|'''7\9,''' '''700¢'''
|'''17\22,''' '''703.448¢'''
|'''10\13,''' '''705.882¢'''
|'''13\17,''' '''709.091¢'''
|-
|Sol#, Do#, Re#
|16\19, 738.462¢
|12\14, 757.895¢
|20\23, 774.194¢
| rowspan="2" |8\9, 800¢
|20\22, 827.586¢
|12\13, 847.059¢
|16\17, 872.727¢
|-
|Dob, Fab, Solb
|18\19, 830.769¢
|13\14, 821.053¢
|21\23, 812.903¢
|19\22, 786.207¢
|11\13, 776.647¢
|14\17, 763.636¢
|-
!Do, Fa, Sol
!19\19, 876.923¢
!14\14, 884.211¢
!23\23, 890.323¢
!9\9, 900¢
!22\22, 910.345¢
!13\13, 917.647¢
!17\17, 927.273¢
|}
{| class="wikitable"
|+Normalized
!Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
! Superhard
|-
!Scala Francisci
!Scala Francisci
!19eds
!19eds
Line 29: Line 178:
!22eds
!22eds
!13eds
!13eds
!17eds
! 17eds
|-
|-
|Do#, Sol#
| Α#
|Α#
| 1\19, 46.154¢
|1\19
|1\14, 63.158¢
46.154
|2\23, 77.419¢
|1\14
| rowspan="2" |1\9, 100¢
63.158
| 3\22, 124.138¢
|2\23
|2\13, 141.176¢
77.419
|3\17, 163.636¢
| rowspan="2" |1\9
100
|3\22
124.138
|2\13
141.1765
|3\17
163.{{Overline|63}}
|-
|-
|Reb, Lab
|Βb
|Βb
|3\19
|3\19, 138.462¢
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, 54.545¢
|2\22
82.759
|1\13
70.588
|1\17
54.{{Overline|54}}
|-
|-
|'''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,''' '''218.182¢'''
'''200'''
|'''5\22'''
'''206.897'''
|'''3\13'''
'''211.765'''
|'''4\17'''
'''218.{{Overline|18}}'''
|-
|-
|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, 331.034¢
270.968
|5\13, 352.941¢
| rowspan="2" |3\9
| 7\17, 381.818¢
300
|8\22
331.0345
|5\13
352.941
|7\17
381.{{Overline|81}}
|-
|-
|Mib, Sib
|Γb
|Γb
|7\19
|7\19, 323.077¢
323.077
|5\14, 315.789¢
|5\14
|8\23, 309.677¢
315.7895
|7\22, 289.655¢
|8\23
|4\13, 282.353¢
309.677
|5\17, 272.727¢
|7\22
289.655
|4\13
282.353
|5\17
272.{{Overline|72}}
|-
|-
|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, 436.36&¢
400
|10\22
413.793
|6\13
423.529
|8\17
436.{{Overline|36}}
|-
|-
|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
|Δb
|Δb
|10\19
|10\19, 461.538¢
461.5385
|11\23, 425.806¢
|11\23
|4\9, 400¢
425.8065
|9\22, 372.414¢
|4\9
|5\13, 352.941¢
400
|6\17, 327.273¢
|9\22
372.414
|5\13
352.941
|6\17
327.{{Overline|27}}
|-
|-
|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, 490.909¢
500
|12\22
496.552
|7\13
494.118
|9\17
490.{{Overline|90}}
|-
|-
|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, 654.545¢
600
|15\22
620.690
|9\13
635.294
|12\17
654.{{Overline|54}}
|-
|-
|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, 545.455¢
|14\22
579.310
|8\13
564.706
|10\17
545.{{Overline|45}}
|-
|-
|'''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,''' '''709.091¢'''
'''700'''
|'''17\22'''
'''703.448'''
|'''10\13'''
'''705.882'''
|'''13\17'''
'''709.{{Overline|09}}'''
|-
|-
|Sol#, Re#
|Ε#
|Ε#
|16\19
|16\19, 738.462¢
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\17, 872.727¢
800
|20\22
827.586
|12\13
847.059
|16\14
872.{{Overline|72}}
|-
|-
|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, 763.636¢
|19\22
786.207
|11\13
776.647
|14\17
763.{{Overline|63}}
|-
|-
!Do, Sol
!Ϛ/Ϝ
!Ϛ/Ϝ
!19\19
!19\19, 876.923¢
876.923
!14\14, 884.211¢
!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, 927.273¢
900
!22\22
910.345
!13\13
917.647
!17\17
927.{{Overline|27}}
|-
|-
|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, 1052.824¢
| rowspan="2" |10\9
|20\17, 1090.909¢
1000
|25\22
1034.483
|15\13
1052.8235
|20\17
1090.{{Overline|90}}
|-
|-
|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, 981.818¢
|24\22
993.103
|14\13
988.235
|18\17
981.{{Overline|81}}
|-
|-
|'''Re, La'''
|'''Ζ'''
|'''Ζ'''
|'''23\19'''
|'''23\19, 1061.538¢'''
'''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,''' '''1145.455¢'''
'''1100'''
|'''27\22'''
'''1117.241'''
|'''16\13'''
'''1129.412'''
|'''21\17'''
'''1145.{{Overline|45}}'''
|-
|-
|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, 1309.091¢
1200
|30\22
1241.379
|18\13
1270.588
|24\14
1309.{{Overline|09}}
|-
|-
|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
|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, 1341.176¢
|13\9
|25\17, 1363.636¢
1300
|32\22
1324.138
|19\13
1341.1765
|25\17
1363.{{Overline|63}}
|-
|-
|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, 1527.272¢
1400
|35\22
1448.276
|21\13
1482.353
|28\17
1527.{{Overline|27}}
|-
|-
|Fab, Dob
|Θb
|Θb
|29\19
|29\19, 1338.462¢
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, 1254.545¢
|31\22
1282.759
|18\13
1270.588
|23\17
1254.{{Overline|54}}
|-
|-
|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, 1418.182¢
1400
|34\22
1406.897
|20\13
1411.765
|26\17
1418.{{Overline|18}}
|-
|-
|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, 1531.035¢
1470.968
|22\13, 1552.941¢
| rowspan="2" |15\9
|29\17, 1581.182¢
1500
|37\22
1531.0345
|22\13
1552.941
|29\17
1581.{{Overline|81}}
|-
|-
|Solb, Reb
|Ιb
|Ιb
|33\19
|33\19, 1523.077¢
1523.077
|24\14, 1515.789¢
|24\14
|39\23, 1509.677¢
1515.7895
|36\22, 1489.655¢
|39\23
|21\13, 1482.353¢
1509.677
|27\17, 1472.727¢
|36\22
1489.655
|21\13
1482.353
|27\17
1472.{{Overline|72}}
|-
|-
|'''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,''' '''1636.363¢'''
'''1600'''
|'''39\22'''
'''1613.793'''
|'''23\13'''
'''1623.529'''
|'''30\17'''
'''1636.{{Overline|36}}'''
|-
|-
|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
|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, 1490.909¢
|41\22
1696.552
|20\13
1694.118
|31\17
1490.{{Overline|90}}
|-
|-
!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, 1835.294¢
!18\9
!34\17, 1854.545¢
1800
!44\22
1820.690
!26\13
1835.2941
!34\17
1854.{{Overline|54}}
|}
|}
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
Line 533: Line 453:
|-
|-
|0
|0
|Do, Sol
|Do, Fa, Sol
|sextave (major sixth)
|sextave (major sixth)
|0
|0
|Do, Sol
|Do, Fa, Sol
|perfect unison
|perfect unison
|-
|-
|1
|1
|Sol, Re
|Sol, Do, Re
|perfect fifth
|perfect fifth
| -1
| -1
|Re, La
|Re, Sol, La
|major second
|major second
|-
|-
|2
|2
|Fa, Do
|Fa, Sib, Do
|perfect fourth
|perfect fourth
| -2
| -2
|Mi, Si
|Mi, La, Si
|major third
|major third
|-
|-
|3
|3
|Mib, Sib
|Mib, Lab, Sib
|minor third
|minor third
| -3
| -3
|Fa#, Do#
|Fa#, Si, Do#
|augmented fourth
|augmented fourth
|-
|-
|4
|4
|Reb, Lab
|Reb, Solb, Lab
|minor second
| minor second
| -4
| -4
|Sol#, Re#
|Sol#, Do#, Re#
|augmented fifth
|augmented fifth
|-
|-
Line 570: Line 490:
|-
|-
|5
|5
|Dob, Solb
|Dob, Fab, Solb
|diminished sextave
|diminished sextave
| -5
| -5
|Do#, Sol#
|Do#, Fa#, Sol#
|augmented unison (chroma)
|augmented unison (chroma)
|-
|-
|6
|6
|Solb, Reb
|Solb, Dob, Reb
|diminished fifth
| diminished fifth
| -6
| -6
|Re#, La#
|Re#, Sol#, La#
|augmented second
|augmented second
|-
|-
|7
|7
|Fab, Dob
| Fab, Sibb, Dob
|diminished fourth
|diminished fourth
| -7
| -7
|Mi#, Si#
|Mi#, La#, Si#
|augmented third
|augmented third
|-
|-
|8
|8
|Mibb, Sibb
|Mibb, Labb, Sibb
|diminished third
|diminished third
| -8
| -8
|Fax, Dox
|Fax, Si#, Dox
|doubly augmented fourth
| doubly augmented fourth
|}
|}
==Genchain==
==Genchain==
Line 601: Line 521:
{| class="wikitable"
{| class="wikitable"
|Mibb
|Mibb
Labb
Sibb
Sibb
|Fab
|Fab
Sibb
Dob
Dob
|Solb
|Solb
Dob
Reb
Reb
|Dob
|Dob
Fab
Solb
Solb
|Reb
|Reb
Solb
Lab
Lab
|Mib
|Mib
Lab
Sib
Sib
|Fa
|Fa
Sib
Do
| Sol
Do
Do
|Sol
 
Re
Re
|Do
|Do
Fa
Sol
Sol
|Re
|Re
Sol
La
La
|Mi
|Mi
La
Si
Si
|Fa#
|Fa#
Si
Do#
Do#
|Sol#
|Sol#
Do#
Re#
Re#
|Do#
|Do#
Fa#
Sol#
Sol#
|Re#
|Re#
Sol#
La#
La#
|Mi#
|Mi#
La#
Si#
Si#
|Fax
|Fax
Si#
Dox
Dox
|-
|-
Line 654: Line 608:
|}
|}
==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 711: Line 665:
==Temperaments==
==Temperaments==
The most basic rank-2 temperament interpretation of this diatonic is '''Dorianic''', which has pental 4:5:6 or septimal 14:18:21 chords spelled <code>root-(2g)-(p-1g)</code> (p = the major sixth, g = the whole tone). The name "Dorianic" comes from the Dorian major mode having the minor sixth as its characteristic interval.
The most basic rank-2 temperament interpretation of this diatonic is '''Dorianic''', which has pental 4:5:6 or septimal 14:18:21 chords spelled <code>root-(2g)-(p-1g)</code> (p = the major sixth, g = the whole tone). The name "Dorianic" comes from the Dorian major mode having the minor sixth as its characteristic interval.
==='''Dorianic-Meantone'''===
==='''Dorianic[5]-Meantone'''===
[[Subgroup]]: 5/3.4/3.3/2
[[Subgroup]]: 5/3.4/3.3/2


[[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[5]-Superpyth'''===
[[Subgroup]]: 12/7.4/3.3/2
[[Subgroup]]: 12/7.4/3.3/2


[[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]]: [[4ed12/7]], [[9ed12/7]], [[13ed12/7]], [[17ed12/7]]


==Scale tree==
==Scale tree==
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Generator
!Generator
(bright)
(bright)
!Normalised
!Normalised
Line 744: Line 698:
|-
|-
|1\5
|1\5
|
|
|171.429
|171.429
|1
|1
Line 753: Line 705:
|-
|-
|6\29
|6\29
|
|180.000
|
|180
|6
|6
|5
|5
Line 762: Line 712:
|-
|-
|5\24
|5\24
|
|181.818
|
|181.{{Overline|81}}
|5
|5
|4
|4
Line 770: Line 718:
|
|
|-
|-
|
|14\67
|14\67
|
|182.609
|182.609
|14
|14
Line 779: Line 725:
|
|
|-
|-
|
|9\43
|9\43
|
|183.051
|183.051
|9
|9
Line 789: Line 733:
|-
|-
|4\19
|4\19
|
|
|184.615
|184.615
|4
|4
Line 797: Line 739:
|
|
|-
|-
|
|11\52
|11\52
|
|185.915
|185.915
|11
|11
Line 806: Line 746:
|
|
|-
|-
|
|7\33
|7\33
|
|186.667
|186.{{Overline|6}}
|7
|7
|5
|5
Line 815: Line 753:
|
|
|-
|-
|
|10\47
|10\47
|
|187.5
|187.5
|10
|10
Line 825: Line 761:
|-
|-
|3\14
|3\14
|
|
|189.474
|189.474
|3
|3
Line 833: Line 767:
|Dorianic-Meantone starts here
|Dorianic-Meantone starts here
|-
|-
|
|14\65
|14\65
|
|190.909
|190.{{Overline|90}}
|14
|14
|9
|9
Line 842: Line 774:
|
|
|-
|-
|
|11\51
|11\51
|
|191.304
|191.304
|11
|11
Line 851: Line 781:
|
|
|-
|-
|
|8\37
|8\37
|
|192.000
|192
|8
|8
|5
|5
Line 860: Line 788:
|
|
|-
|-
|
|5\23
|5\23
|
|193.548
|193.548
|5
|5
Line 869: Line 795:
|
|
|-
|-
|
|7\32
|7\32
|
|195.349
|195.349
|7
|7
Line 878: Line 802:
|
|
|-
|-
|
|9\41
|9\41
|
|196.364
|196.{{Overline|36}}
|9
|9
|5
|5
Line 887: Line 809:
|
|
|-
|-
|
|11\50
|11\50
|
|197.015
|197.015
|11
|11
Line 896: Line 816:
|
|
|-
|-
|
|13\59
|13\59
|
|197.468
|197.468
|13
|13
Line 905: Line 823:
|
|
|-
|-
|
|15\68
|15\68
|
|197.802
|197.802
|15
|15
Line 914: Line 830:
|
|
|-
|-
|
|17\77
|17\77
|
|198.058
|198.058
|17
|17
Line 923: Line 837:
|
|
|-
|-
|
|19\86
|19\86
|
|198.261
|198.261
|19
|19
Line 932: Line 844:
|
|
|-
|-
|
|21\95
|21\95
|
|198.425
|198.425
|21
|21
Line 941: Line 851:
|
|
|-
|-
|
|23\104
|23\104
|
|198.561
|198.561
|23
|23
Line 950: Line 858:
|
|
|-
|-
|2\9
|25\113
|198.675
|25
|13
|1.923
|
|
|-
|27\122
|198.773
|27
|14
|1.929
|
|
|200
|2
|1
|2.000
|Dorianic-Meantone ends, Dorianic-Pythagorean begins
|-
|-
|29\131
|198.857
|29
|15
|1.933
|
|
|21\94
|-
|31\140
|198.930
|31
|16
|1.9375
|
|
|201.6
|-
|21
|33\149
|10
|198.995
|2.100
|33
|17
|1.941
|
|
|-
|-
|35\158
|199.052
|35
|18
|1.944
|
|
|19\85
|
|201.77
|19
|9
|2.111
|
|-
|-
|
|2\9
|200
|2
|1
|2.000
|Dorianic-Meantone ends, Dorianic-Pythagorean begins
|-
|17\76
|17\76
|
|201.980
|201.98
|17
|17
|8
|8
Line 986: Line 914:
|
|
|-
|-
|
|15\67
|15\67
|
|202.247
|202.247
|15
|15
Line 995: Line 921:
|
|
|-
|-
|
|13\58
|13\58
|
|202.597
|202.597
|13
|13
Line 1,004: Line 928:
|
|
|-
|-
|
|11\49
|11\49
|
|203.076
|203.076
|11
|11
Line 1,013: Line 935:
|
|
|-
|-
|
|9\40
|9\40
|
|203.774
|203.774
|9
|9
Line 1,022: Line 942:
|
|
|-
|-
|
|7\31
|7\31
|
|204.838
|204.838
|7
|7
Line 1,031: Line 949:
|
|
|-
|-
|
|
|12\53
|12\53
|205.714
|205.714
Line 1,040: Line 956:
|
|
|-
|-
|
|5\22
|5\22
|
|206.897
|206.897
|5
|5
Line 1,049: Line 963:
|
|
|-
|-
|
|
|18\79
|18\79
|207.692
|207.692
Line 1,058: Line 970:
|
|
|-
|-
|13\57
|208.000
|13
|5
|2.600
|
|
|-
|8\35
|8\35
|
|208.696
|208.696
|8
|8
Line 1,067: Line 984:
|
|
|-
|-
|
|11\48
|11\48
|
|209.524
|209.524
|11
|11
Line 1,076: Line 991:
|
|
|-
|-
|
|14\61
|14\61
|
|210.000
|210
|14
|14
|5
|5
Line 1,086: Line 999:
|-
|-
|3\13
|3\13
|
|
|211.765
|211.765
|3
|3
Line 1,094: Line 1,005:
|Dorianic-Pythagorean ends, Dorianic-Superpyth begins
|Dorianic-Pythagorean ends, Dorianic-Superpyth begins
|-
|-
|
|22\95
|22\95
|
|212.903
|212.903
|22
|22
Line 1,103: Line 1,012:
|
|
|-
|-
|
|19\82
|19\82
|
|213.084
|213.084
|19
|19
Line 1,112: Line 1,019:
|
|
|-
|-
|
|16\69
|16\69
|
|213.333
|213.{{Overline|3}}
|16
|16
|5
|5
Line 1,121: Line 1,026:
|
|
|-
|-
|
|13\56
|13\56
|
|213.699
|213.699
|13
|13
Line 1,130: Line 1,033:
|
|
|-
|-
|
|10\43
|10\43
|
|214.286
|214.286
|10
|10
Line 1,139: Line 1,040:
|
|
|-
|-
|
|7\30
|7\30
|
|215.385
|215.385
|7
|7
Line 1,148: Line 1,047:
|
|
|-
|-
|
|11\47
|11\47
|
|216.393
|216.393
|11
|11
Line 1,157: Line 1,054:
|
|
|-
|-
|
|15\64
|15\64
|
|216.867
|216.867
|15
|15
Line 1,166: Line 1,061:
|
|
|-
|-
|
|19\81
|19\81
|
|217.143
|217.143
|19
|19
Line 1,176: Line 1,069:
|-
|-
|4\17
|4\17
|
|218.182
|
|218.{{Overline|18}}
|4
|4
|1
|1
Line 1,184: Line 1,075:
|
|
|-
|-
|
|21\89
|21\89
|
|219.130
|219.13
|21
|21
|5
|5
|R.200
|4.200
|
|
|-
|-
|
|17\72
|17\72
|
|219.355
|219.355
|17
|17
Line 1,202: Line 1,089:
|
|
|-
|-
|
|13\55
|13\55
|
|219.718
|219.718
|13
|13
Line 1,211: Line 1,096:
|
|
|-
|-
|
|9\38
|9\38
|
|220.408
|220.408
|9
|9
Line 1,220: Line 1,103:
|
|
|-
|-
|
|14\59
|14\59
|
|221.053
|221.053
|14
|14
Line 1,230: Line 1,111:
|-
|-
|5\21
|5\21
|
|222.222
|
|222.{{Overline|2}}
|5
|5
|1
|1
Line 1,238: Line 1,117:
|Dorianic-Superpyth ends
|Dorianic-Superpyth ends
|-
|-
|
|11\46
|11\46
|
|223.729
|223.729
|11
|11
Line 1,247: Line 1,124:
|
|
|-
|-
|
|17\71
|17\71
|
|224.176
|224.176
|17
|17
Line 1,257: Line 1,132:
|-
|-
|6\25
|6\25
|
|225.000
|
|225
|6
|6
|1
|1
Line 1,266: Line 1,139:
|-
|-
|1\4
|1\4
|
|240.000
|
|240
|1
|1
|0
|0
Line 1,275: Line 1,146:
|}
|}


== See also ==
==See also==
[[4L 1s (5/3-equivalent)]] - idealized meantone tuning
[[4L 1s (5/3-equivalent)]] - idealized meantone tuning
[[4L 1s (27/16-equivalent)]] - Pythagorean tuning
[[4L 1s (22/13-equivalent)]] - Neogothic tuning


[[4L 1s (12/7-equivalent)]] - idealized Archytas tuning
[[4L 1s (12/7-equivalent)]] - idealized Archytas tuning
[[8L 2s (e-equivalent)|8L 2s ([math]e[/math]-equivalent)]] - natural tuning
[[8L 2s (2000/729-equivalent)]] - 1/2 comma meantone tuning
[[8L 2s (11/4-equivalent)]] - idealized low tuning, low undecimal tuning
[[8L 2s (45/16-equivalent)]] - 1/6 comma meantone tuning
[[8L 2s (14/5-equivalent)]] - low septimal (meantone) tuning
[[8L 2s (729/256-equivalent)]] - Pythagorean tuning
[[8L 2s (20/7-equivalent)]] - idealized high tuning, high septimal tuning
[[8L 2s (81/28-equivalent)]] - 1/6 comma Archytas tuning
[[8L 2s (32/11-equivalent)]] - high undecimal tuning
[[8L 2s (2000/729-equivalent)|8L 2s (1024/343-equivalent)]] - 1/2 comma Archytas tuning
[[8L 2s (3/1-equivalent)]] - warped Pythagorean tuning
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/4L_1s_(major_sixth-equivalent)"