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User:Moremajorthanmajor/2L 1s (perfect fourth-equivalent): Difference between revisions

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There are 4 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple,  quadruple or quintuple fourth (minor seventh, tenth, thirteenth or sixteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth notation and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.
There are 4 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple,  quadruple or quintuple fourth (minor seventh, tenth, thirteenth or sixteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth notation and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.
{| class="wikitable"
{| class="wikitable"
|+Cents<ref name=":05">Fractions repeating more than 4 digits written as continued fractions</ref>
|+Cents
! colspan="2" |Notation
! colspan="2" |Notation
!Supersoft
!Supersoft
Line 39: Line 39:
|3\9, 163.{{Overline|63}}
|3\9, 163.{{Overline|63}}
|-
|-
|Reb, Lab
| Reb, Lab
|Lab
|Lab
|3\11, 138.462
|3\11, 138.462
Line 64: Line 64:
|7\13, 270.967
|7\13, 270.967
| rowspan="2" |'''3\5,''' '''300'''
| rowspan="2" |'''3\5,''' '''300'''
|8\12, 331.034
| 8\12, 331.034
|5\7, 352.941
|5\7, 352.941
|7\9, 381.{{Overline|81}}
|7\9, 381.{{Overline|81}}
Line 78: Line 78:
|-
|-
|Mi, Si
|Mi, Si
|Si
| Si
|8\11, 369.231
|8\11, 369.231
|6\8, 378.947
|6\8, 378.947
Line 98: Line 98:
|-
|-
|Dob, Solb
|Dob, Solb
|Dob
| Dob
|10\11, 461.538
|10\11, 461.538
|11\13, 425.806
|11\13, 425.806
Line 175: Line 175:
|-
|-
|Mi#, Si#
|Mi#, Si#
|Mi#
| Mi#
|20\11, 923.077
|20\11, 923.077
| rowspan="2" |15\8, 947.378
| rowspan="2" |15\8, 947.378
|25\13
|25\13, 967.742
967; 1, 2.875
|10\5, 1000
|10\5
|25\12, 1034.483
1000
|15\7, 1058.824
|25\12
|20\9, 1090.{{Overline|90}}
1034; 2, 14
|15\7
1058; 1, 4.{{Overline|6}}
|20\9
1090.{{Overline|90}}
|-
|-
|Dob, Solb
|Dob, Solb
|Solb
|Solb
|21\11
|21\11, 969.231
969; 4.{{Overline|3}}
|24\13, 929.033
|24\13
|9\5, 900
929; 31
|21\12, 868.966
|9\5
|11\7, 776.471
900
|15\9, 818.{{Overline|18}}
|21\12
868; 1, 28
|11\7
776; 2.125
|15\9
818.{{Overline|18}}
|-
|-
!Do, Sol
!Do, Sol
!Sol
!Sol
!22\11
!22\11, 1015.385
1015; 2.6
!16\8, 1010.526
!16\8
!26\13, 1006.452
1010; 1.9
!10\5, 1000
!26\13
!24\12, 993.103
1006; 2, 4.{{Overline|6}}
!14\7, 988.235
!10\5
!18\9,981.{{Overline|81}}
1000
!24\12
993; 9.{{Overline|6}}
!14\7
988; 4.25
!18\9
981.{{Overline|81}}
|}
|}
{| class="wikitable"
{| class="wikitable"
! colspan="4" |Notation
! colspan="2" |Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 233: Line 215:
!Mahur
!Mahur
!Bijou
!Bijou
!Hyperionic
!Subsextal
!~11ed4/3
!~11ed4/3
!~8ed4/3
! ~8ed4/3
!~13ed4/3
!~13ed4/3
!~5ed4/3
!~5ed4/3
Line 245: Line 225:
|G#
|G#
|0#, E#
|0#, E#
|1#
|1\11, 46.154
|0#
|1\8, 63.158
|1\11
|2\13, 77.419
46; 6.5
| rowspan="2" |1\5, 100
|1\8
|3\12, 124.138
63; 6.{{Overline|3}}
|2\7, 141.176
|2\13
|3\9, 163.{{Overline|63}}
77; 2, 2.6
| rowspan="2" |1\5
 
100
|3\12
124; 7.25
|2\7
141; 5.{{Overline|6}}
|3\9
163.{{Overline|63}}
|-
|-
|Jf, Af
|Jf, Af
|1b, 1d
|1b, 1d
|2f
|3\11, 138.462
|1f
|2\8, 126.316
|3\11
| 3\13, 116.129
138; 3.25
|2\12, 82.759
|2\8
|1\7, 70.588
126; 3.1{{Overline|6}}
|1\9, 54.{{Overline|54}}
|3\13
116; 7.75
|2\12
82; 1.3{{Overline|18}}
|1\7
70; 1.7
|1\9
54.{{Overline|54}}
|-
|-
|'''J, A'''
|'''J, A'''
|'''1'''
|'''1'''
|'''2'''
|'''4\11,''' '''184.615'''
|'''1'''
|'''3\8,''' '''189.474'''
|'''4\11'''
|'''5\13,''' '''193.548'''
'''184; 1.625'''
|'''2\5,''' '''200'''
|'''3\8'''
|'''5\12,''' '''206.897'''
'''189; 2.{{Overline|1}}'''
|'''3\7,''' '''211.765'''
|'''5\13'''
|'''4\9,''' '''218.{{Overline|18}}'''
'''193; 1, 1, 4.{{Overline|6}}'''
|'''2\5'''
'''200'''
|'''5\12'''
'''206; 1, 8.{{Overline|6}}'''
|'''3\7'''
'''211; 1, 3.25'''
|'''4\9'''
'''218.{{Overline|18}}'''
|-
|-
|J#, A#
|J#, A#
|1#
|1#
|2#
|5\11, 230.769
|1#
|4\8, 252.632
|5\11
|7\13, 270.968
230; 1.3
| rowspan="2" |'''3\5,''' '''300'''
|4\8
|8\12, 331.034
252; 1.58{{Overline|3}}
|5\7, 352.941
|7\13
|7\9, 381.{{Overline|81}}
270; 1.0{{Overline|3}}
| rowspan="2" |'''3\5'''
'''300'''
|8\12
331; 29
|5\7
352; 1.0625
|7\9
381.{{Overline|81}}
|-
|-
|'''Af, Bf'''
|'''Af, Bf'''
|'''2b, 2d'''
|'''2b, 2d'''
|'''3f'''
|'''7\11,''' '''323.077'''
|2f
|'''5\8,''' '''315.789'''
|'''7\11'''
|'''8\13,''' '''309.677'''
'''323; 13'''
|'''7\12,''' '''289.655'''
|'''5\8'''
|'''4\7,''' '''282.353'''
'''315; 1.2{{Overline|6}}'''
|'''5\9,''' '''272.{{Overline|72}}'''
|'''8\13'''
'''309; 1, 2.1'''
|'''7\12'''
'''289; 1, 1.9'''
|'''4\7'''
'''282; 2.8{{Overline|3}}'''
|'''5\9'''
'''272.{{Overline|72}}'''
|-
|-
|A, B
|A, B
|2
|2
|3
|8\11, 369.231
|'''2'''
|6\8, 378.947
|8\11
|10\13, 387.097
369; 4.{{Overline|3}}
|4\5, 400
|6\8
|10\12, 413.793
378; 1.0{{Overline|5}}
|6\7, 423.529
|10\13
|8\9, 436.{{Overline|36}}
387; 10.{{Overline|3}}
|4\5
400
|10\12
413; 1, 3.8{{Overline|3}}
|6\7
423; 1.{{Overline|8}}
|8\9
436.{{Overline|36}}
|-
|-
|A#, B#
|A#, B#
|2#
|2#
|3#
|9\11, 415.385
|2#
| rowspan="2" |7\8, 442.105
|9\11
|12\13, 464.516
415; 2.6
|5\5, 500
| rowspan="2" |7\8
|13\12, 537.069
442; 9.5
|8\7, 564.705
|12\13
|11\9, 600
464; 1.9375
|5\5
500
|13\12
537; 14.5
|8\7
564; 1.41{{Overline|6}}
|11\9
600
|-
|-
|Bb, Cf
|Bb, Cf
|3b, 3d
|3b, 3d
|4f
|10\11, 461.538
|'''3f'''
|11\13, 425.806
|10\11
| 4\5, 400
461; 1, 1.1{{Overline|6}}
|9\12, 372.414
|11\13
|5\7, 352.941
425; 1.24
|6\9, 327.{{Overline|27}}
|4\5
400
|9\12
372; 2.41{{Overline|6}}
|5\7
352; 1.0625
|6\9
327.{{Overline|27}}
|-
|-
!B, C
!B, C
!3
!3
!4
!'''11\11,''' '''507.692'''
!3
!'''8\8,''' '''505.263'''
!'''11\11'''
!'''13\13,''' '''503.226'''
'''507; 1.{{Overline|4}}'''
!5\5, 500
!'''8\8'''
!'''12\12,''' '''496.552'''
'''505; 3.8'''
!'''7\7,''' '''494.118'''
!'''13\13'''
!'''9\9,''' '''490.{{Overline|90}}'''
'''503; 4, 2.{{Overline|3}}'''
!'''5\5'''
'''500'''
!'''12\12'''
'''496; 1.8125'''
!'''7\7'''
'''494; 8.5'''
!'''9\9'''
'''490.{{Overline|90}}'''
|-
|-
|B#, C#
|B#, C#
|3#
|3#
|4#
|12\11, 553.846
|3#
|9\8, 568.421
|12\11
|15\13, 580.645
553; 1.{{Overline|18}}
| rowspan="2" |6\5, 600
|9\8
|15\12, 620.690
568; 2.375
|9\7, 635.294
|15\13
|12\9, 654.{{Overline|54}}
580; 1.55
| rowspan="2" |6\5
600
|15\12
620; 1.45
|9\7
635; 3.4
|12\9
654.{{Overline|54}}
|-
|-
|Cf, Qf
|Cf, Qf
|4b, 4d
|4b, 4d
|5f
|14\11, 646.154
|4f
|10\8, 631.579
|14\11
|16\13, 619.355
646; 6.5
|14\12, 579.310
|10\8
|8\7, 564.706
631; 1.{{Overline|72}}
|10\9, 545.{{Overline|45}}
|16\13
619; 2.{{Overline|81}}
|14\12
579; 3.{{Overline|2}}
|8\7
564; 1.41{{Overline|6}}
|10\9
545.{{Overline|45}}
|-
|-
|'''C, Q'''
|'''C, Q'''
|'''4'''
|'''4'''
|'''5'''
|'''15\11,''' '''692.308'''
|'''4'''
|'''11\8''' '''694.737'''
|'''15\11'''
|'''18\13,''' '''696.774'''
'''692; 3.25'''
|'''7\5,''' '''700'''
|'''11\8'''
|'''17\12,''' '''703.448'''
'''694; 1, 2.8'''
|'''10\7,''' '''705.882'''
|'''18\13'''
|'''13\9,''' '''709.{{Overline|09}}'''
'''696; 1.291{{Overline|6}}'''
|'''7\5'''
'''700'''
|'''17\12'''
'''703; 2, 2.1{{Overline|6}}'''
|'''10\7'''
'''705; 1.1{{Overline|3}}'''
|'''13\9'''
'''709.{{Overline|09}}'''
|-
|-
|C#, Q#
|C#, Q#
|4#
|4#
|5#
|16\11, 738.462
|4#
|12\8, 757.895
|16\11
| 20\13, 774.194
738; 2.1{{Overline|6}}
| rowspan="2" |'''8\5,''' '''800'''
|12\8
|20\12, 827.586
757; 1, 8.5
|12\7, 847.059
|20\13
|16\9, 872.{{Overline|72}}
774; 5.1{{Overline|6}}
| rowspan="2" |'''8\5'''
'''800'''
|20\12
827; 1, 1.41{{Overline|6}}
|12\7
847; 17
|16\9
872.{{Overline|72}}
|-
|-
|'''Qf, Df'''
|'''Qf, Df'''
|'''5b, 5d'''
|'''5b, 5d'''
|'''6f'''
|'''18\11,''' '''830.769'''
|5f
|'''13\8,''' '''821.053'''
|'''18\11'''
|'''21\13,''' '''812.903'''
'''830; 1.3'''
|'''19\12,''' '''786.207'''
|'''13\8'''
|'''11\7,''' '''776.471'''
'''821; 19'''
|'''14\9,''' '''763.{{Overline|63}}'''
|'''21\13'''
'''812; 1, 9.{{Overline|3}}'''
|'''19\12'''
'''786; 4.8{{Overline|3}}'''
|'''11\7'''
'''776; 2.125'''
|'''14\9'''
'''763.{{Overline|63}}'''
|-
|-
|Q, D
|Q, D
|5
|5
|6
|19\11, 876.923
|'''5'''
|14\8, 884.211
|19\11
|23\13, 890.323
876; 1.08{{Overline|3}}
|9\5, 900
|14\8
|22\12, 910.345
884; 4.75
|13\7, 917.647
|23\13
|17\9, 927.{{Overline|27}}
890; 3.1
|9\5
900
|22\12
910; 2.9
|13\7
917; 1.{{Overline|54}}
|17\9
927.{{Overline|27}}
|-
|-
|Q#, D#
|Q#, D#
|5#
|5#
|6#
|20\11, 923.077
|5#
| rowspan="2" |15\8, 947.368
|20\11
|25\13, 967.742
923: 13
|10\5, 1000
| rowspan="2" |15\8
|25\12, 1034.483
947; 2, 1.4
|15\7, 1058.824
|25\13
|20\9, 1090.{{Overline|90}}
967; 1, 2.875
|10\5
1000
|25\12
1034; 2, 14
|15\7
1058; 1, 4.{{Overline|6}}
|20\9
1090.{{Overline|90}}
|-
|-
|Df, Sf
|Df, Sf
|6b, 6d
|6b, 6d
|7f
|21\11, 969.231
|'''6f'''
|24\13, 929.033
|21\11
|9\5, 900
969; 4.{{Overline|3}}
|21\12, 868.966
|24\13
|11\7, 776.471
929; 31
|15\9, 818.{{Overline|18}}
|9\5
900
|21\12
868; 1, 28
|11\7
776; 2.125
|15\9
818.{{Overline|18}}
|-
|-
!D, S
!D, S
!6
!6
!7
!22\11, 1015.385
!6
!16\8, 1010.526
!22\11
!26\13, 1006.452
1015; 2.6
!10\5, 1000
!16\8
!24\12, 993.103
1010; 1.9
! 14\7, 988.235
!26\13
!18\9, 981.{{Overline|81}}
1006; 2, 4.{{Overline|6}}
!10\5
1000
!24\12
993; 9.{{Overline|6}}
!14\7
988; 4.25
!18\9
981.{{Overline|81}}
|-
|-
|D#, S#
|D#, S#
|6#
|6#
|7#
|23\11, 1061.538
|6#
|17\8, 1073.684
|23\11
|28\13, 1083.871
1061; 1, 1.1{{Overline|6}}
| rowspan="2" |11\5, 1100
|17\8
|27\12, 1117.241
1073; 1, 2.1{{Overline|6}}
|16\7, 1129.412
|28\13
|21\9, 1145.{{Overline|45}}
1083; 1.{{Overline|148}}
| rowspan="2" |11\5
1100
|27\12
1117; 4, 7
|16\7
1129; 2, 2.{{Overline|3}}
|24\9
1309.{{Overline|09}}
|-
|-
|Ef
|Ef
|7b, 7d
|7b, 7d
|8f
| 25\11, 1153.846
|7f
| 18\8, 1136.842
|25\11
|29\13, 1122.581
1153; 1.{{Overline|18}}
|26\12, 1075.862
|18\8
|15\7, 1058.824
1136; 1.1875
|19\9, 1036.{{Overline|36}}
|29\13
1122; 1.7{{Overline|2}}
|26\12
1075; 1.16
|15\7
1058; 1, 4.{{Overline|6}}
|19\9
1036.{{Overline|36}}
|-
|-
|'''E'''
|'''E'''
|'''7'''
|'''7'''
|'''26\11,''' '''1200'''
|'''19\8,''' '''1200'''
|'''31\13,''' '''1200'''
|'''12\5,''' '''1200'''
|'''29\12,''' '''1200'''
|'''17\7,''' '''1200'''
|'''22\9,''' '''1200'''
|-
|E#
|7#
|27\11, 1246.154
|20\8, 1263.158
|33\13, 1277.419
| rowspan="2" |'''13\5,''' '''1300'''
|32\12, 1324.138
|19\7, 1341.176
|25\9, 1363.{{Overline|63}}
|-
|'''Ff'''
|'''8b, Gd'''
|'''29\11,''' '''1338.462'''
|'''21\8,''' '''1326.316'''
|'''34\13,''' '''1316.129'''
|'''31\12,''' '''1282.759'''
|'''18\7,''' '''1270.588'''
|'''23\9,''' '''1254.{{Overline|54}}'''
|-
|F
|8, G
|30\11, 1384.615
|22\8, 1389.474
|36\13, 1393.548
|14\5, 1400
|34\12, 1406.897
|20\7, 1411.765
|26\9, 1418.{{Overline|18}}
|-
|F#
|8#, G#
|31\11, 1430.769
| rowspan="2" |23\8, 1452.632
|38\13, 1470.968
|15\5, 1500
|37\12, 1531.034
|22\7, 1552.941
|29\9, 1581.{{Overline|81}}
|-
|Gf
|9b, Ad
|32\11, 1476.923
|37\13, 1432.258
|14\5, 1400
|33\12, 1365.517
|19\7, 1341.176
|24\9, 1309.{{Overline|09}}
|-
!G
!'''9, A'''
!33\11, 1523.077
!24\8, 1515.789
!39\13, 1509.677
!15\5, 1500
!36\12, 1489.655
!21\7, 1482.353
!27\9, 1472.{{Overline|72}}
|-
|G#
|9#, A#
|34\11, 1569.231
| 25\8, 1578.947
|41\13, 1587.097
| rowspan="2" |16\5, 1600
|39\12, 1613.793
|23\7, 1623.529
|30\9, 1636.{{Overline|36}}
|-
|Jf, Af
|Xb, Bd
|36\11, 1661.538
|26\8, 1642.105
|42\13, 1625.806
|38\12, 1572.034
|22\7, 1552.941
|28\9, 1527.{{Overline|27}}
|-
|'''J, A'''
|'''X, B'''
|'''37\11,''' '''1707.692'''
|'''27\8,''' '''1705.263'''
|'''44\13,''' '''1703.226'''
|'''17\5,''' '''1700'''
|'''41\12,''' '''1696.552'''
|'''24\7,''' '''1694.118'''
|'''31\9,''' '''1690.{{Overline|90}}'''
|-
|J#, A#
|X#, B#
|38\11, 1753.846
|28\8, 1768.421
|46\13, 1780.645
| rowspan="2" |'''18\5,''' '''1800'''
|44\12, 1820.690
|26\7, 1835.294
|34\9, 1854.{{Overline|54}}
|-
|'''Af, Bf'''
|'''Eb, Dd'''
|'''40\11,''' '''1846.154'''
|'''29\8,''' '''1831.579'''
|'''47\13,''' '''1819.355'''
|'''43\12,''' '''1779.310'''
|'''25\7,''' '''1764.706'''
|'''32\9,''' '''1745.{{Overline|45}}'''
|-
|A, B
|E, D
|41\11, 1892.308
|30\8, 1894.737
|49\13, 1896.774
|19\5, 1900
|46\12, 1903.448
|27\7, 1905.882
|35\9, 1909.{{Overline|09}}
|-
|A#, B#
|E#, D#
|42\11, 1938.462
| rowspan="2" |31\8, 1957.895
|51\13, 1974.194
|20\5, 2000
|49\12, 2027.586
|29\7, 2047.059
|38\9, 2072.{{Overline|72}}
|-
|Bb, Cf
|0b, Ed
| 43\11, 1984.615
|50\13, 1935.484
|19\5, 1900
|45\12, 1862.069
|26\7, 1835.294
|33\9, 1800
|-
!B, C
! 0, E
!44\11, 2030.769
!32\8, 2021.053
!52\13, 2012.903
!20\5, 2000
!48\12, 1986.207
!28\7, 1976.471
!36\9, 1963.{{Overline|63}}
|}
{| class="wikitable"
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
! Basic
!Semihard
!Hard
!Superhard
|-
!Hyperionic
!Subsextal
!~11ed4/3
!~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
! ~7ed4\3
!~9ed4/3
|-
|1#
|0#
|1\11, 46.154
|1\8, 63.158
|2\13, 77.419
| rowspan="2" |1\5, 100
|3\12, 124.138
|2\7, 141.176
|3\9, 163.{{Overline|63}}
|-
|2f
|1f
| 3\11, 138.462
|2\8, 126.316
|3\13, 116.129
|2\12, 82.759
|1\7, 70.588
|1\9, 54.{{Overline|54}}
|-
|'''2'''
|'''1'''
|'''4\11,''' '''184.615'''
|'''3\8,''' '''189.474'''
|'''5\13,''' '''193.548'''
|'''2\5,''' '''200'''
|'''5\12,''' '''206.897'''
|'''3\7,''' '''211.765'''
|'''4\9,''' '''218.{{Overline|18}}'''
|-
|2#
|1#
| 5\11, 230.769
| 4\8, 252.632
|7\13, 270.967
| rowspan="2" |'''3\5,''' '''300'''
|8\12, 331.034
|5\7, 352.941
| 7\9, 381.{{Overline|81}}
|-
|'''3f'''
|2f
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.{{Overline|72}}'''
|-
|3
|'''2'''
| 8\11, 369.231
|6\8, 378.947
|10\13, 387.098
|4\5, 400
|10\12, 413.793
|6\7, 423.529
|8\9, 436.{{Overline|36}}
|-
|3#
| 2#
| 9\11, 415.385
| rowspan="2" | 7\8, 442.105
| 12\13, 464.516
|5\5, 500
|13\12, 537.069
|8\7, 564.705
|11\9, 600
|-
|4f
|'''3f'''
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
| 5\7, 352.941
|6\9, 327.{{Overline|27}}
|-
!4
!3
!'''11\11,''' '''507.692'''
!'''8\8,''' '''505.263'''
!'''13\13,''' '''503.226'''
! 5\5, 500
!'''12\12,''' '''496.552'''
!'''7\7,''' '''494.118'''
!'''9\9,''' '''490.{{Overline|90}}'''
|-
|4#
| 3#
|12\11, 553.846
| 9\8, 568.421
|15\13, 580.645
| rowspan="2" | 6\5, 600
| 15\12, 620.690
|9\7, 635.294
|12\9, 654.{{Overline|54}}
|-
|5f
|4f
|14\11, 646.154
|10\8, 631.579
|16\13, 619.355
|14\12, 579.310
|8\7, 564.706
|10\9, 545.{{Overline|45}}
|-
|'''5'''
|'''4'''
|'''15\11,''' '''692.308'''
|'''11\8'''  '''694.737'''
|'''18\13,''' '''696.774'''
|'''7\5,''' '''700'''
|'''17\12,''' '''703.448'''
|'''10\7,''' '''705.882'''
|'''13\9,''' '''709.{{Overline|09}}'''
|-
|5#
|4#
|16\11, 738.462
|12\8, 757.895
|20\13, 774.194
| rowspan="2" |'''8\5,''' '''800'''
|20\12, 827.586
| 12\7, 847.059
|16\9, 872.{{Overline|72}}
|-
|'''6f'''
|5f
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''21\13,''' '''812.903'''
|'''19\12,''' '''786.207'''
|'''11\7,''' '''776.471'''
|'''14\9,''' '''763.{{Overline|63}}'''
|-
|6
|'''5'''
|19\11, 876.923
|14\8, 884.211
|23\13, 890.323
|9\5, 900
|22\12, 910.345
|13\7, 917.647
|17\9, 927.{{Overline|27}}
|-
|6#
|5#
|20\11, 923.077
| rowspan="2" | 15\8, 947.368
|25\13, 967.742
|10\5, 1000
|25\12, 1034.483
|15\7, 1058.824
|20\9, 1090.{{Overline|90}}
|-
|7f
|'''6f'''
|21\11, 969.231
|24\13, 929.032
|9\5, 900
|21\12, 868.966
|11\7, 776.471
|15\9, 818.{{Overline|18}}
|-
!7
!6
!22\11, 1015.385
!16\8, 1010.526
!26\13, 1006.452
!10\5, 1000
!24\12, 993.103
!14\7, 988.235
!18\9, 981.{{Overline|81}}
|-
|7#
|6#
|23\11, 1061.538
|17\8, 1073.684
|28\13, 1083.871
| rowspan="2" |11\5, 1100
|27\12, 1117.241
|16\7, 1129.412
|21\9, 1145.{{Overline|45}}
|-
|8f
| 7f
|25\11, 1153.846
|18\8, 1136.842
|29\13, 1122.581
| 26\12, 1075.862
|15\7, 1058.824
|19\9, 1036.{{Overline|36}}
|-
|'''8'''
|'''8'''
|7
|7
|'''26\11'''
|'''26\11,''' '''1200'''
'''1200'''
|'''19\8,''' '''1200'''
|'''19\8'''
|'''31\13,''' '''1200'''
'''1200'''
|'''12\5,''' '''1200'''
|'''31\13'''
|'''29\12,''' '''1200'''
'''1200'''
|'''17\7,''' '''1200'''
|'''12\5'''
|'''22\9,''' '''1200'''
'''1200'''
|'''29\12'''
'''1200'''
|'''17\7'''
'''1200'''
|'''22\9'''
'''1200'''
|-
|-
|E#
|7#
|8#
|8#
|7#
|7#
|27\11
|27\11, 1246.154
1246; 6,5
|20\8, 1263.158
|20\8
|33\13, 1277.419
1263; 6.{{Overline|3}}
| rowspan="2" |'''13\5,''' '''1300'''
|33\13
|32\12, 1324.138
1277; 2, 2.6
|19\7, 1341.176
| rowspan="2" |'''13\5'''
|25\9, 1363.{{Overline|63}}
'''1300'''
|32\12
1324; 7.25
|19\7
1341; 5.{{Overline|6}}
|25\9
1363.{{Overline|63}}
|-
|-
|'''Ff'''
|'''8b, Gd'''
|'''9f'''
|'''9f'''
|8f
|8f
|'''29\11'''
|'''29\11,''' '''1338.462'''
'''1338; 3.25'''
|'''21\8,''' '''1326.316'''
|'''21\8'''
|'''34\13,''' '''1316.129'''
'''1326; 3.16̄'''
|'''31\12,''' '''1282.759'''
|'''34\13'''
|'''18\7,''' '''1270.588'''
'''1316; 7.75'''
|'''23\9,''' '''1254.{{Overline|54}}'''
|'''31\12'''
'''1282; 1.3{{Overline|18}}'''
|'''18\7'''
'''1270; 1.7'''
|'''23\9'''
'''1254.{{Overline|54}}'''
|-
|-
|F
|8, G
|9
|9
|'''8'''
|'''8'''
|30\11
|30\11, 1384.615
1384; 1.625
|22\8, 1389.474
|22\8
|36\13, 1393.548
1389; 2.1̄
|14\5, 1400
|36\13
|34\12, 1406.897
1393; 1, 1, 4.{{Overline|6}}
|20\7, 1411.765
|14\5
|26\9, 1418.{{Overline|18}}
1400
|34\12
1406; 1, 8.{{Overline|6}}
|20\7
1411; 1, 3.25
|26\9
1418.{{Overline|18}}
|-
|-
|F#
|8#, G#
|9#
|9#
|8#
|8#
|31\11
| 31\11, 1430.769
1430; 1.3
| rowspan="2" | 23\8, 1452.632
| rowspan="2" |23\8
|38\13, 1470.968
1452; 1.58{{Overline|3}}
|15\5, 1500
|38\13
|37\12, 1531.034
1470; 1.0{{Overline|3}}
|22\7, 1552.941
|15\5
|29\9, 1581.{{Overline|81}}
1500
|37\12
1531; 29
|22\7
1552; 1.0625
|29\9
1581.{{Overline|81}}
|-
|-
|Gf
|9b, Ad
|Af
|Af
|9f
|9f
|32\11
|32\11, 1476.923
1476; 1.08{{Overline|3}}
| 37\13, 1432.258
|37\13
|14\5, 1400
1432: 3.875
|33\12, 1365.517
|14\5
|19\7, 1341.176
1400
|24\9, 1309.{{Overline|09}}
|33\12
1365; 1.9{{Overline|3}}
|19\7
1341; 5.{{Overline|3}}
|24\9
1309.{{Overline|09}}
|-
|-
!G
!'''9, A'''
!A
!A
!9
!9
!33\11
!33\11, 1523.077
1523; 13
!24\8, 1515.789
!24\8
!39\13, 1509.677
1515; 1.2{{Overline|6}}
!15\5, 1500
!39\13
!36\12, 1489.655
1509; 1, 2.1
!21\7, 1482.353
!15\5
!27\9, 1472.{{Overline|72}}
1500
!36\12
1489; 1, 1.9
!21\7
1482; 2.8{{Overline|3}}
!27\9
1472.{{Overline|72}}
|-
|-
|G#
|9#, A#
|A#
|A#
|9#
|9#
|34\11
|34\11, 1569.231
1569; 4.{{Overline|3}}
|25\8, 1578.947
|25\8
|41\13, 1587.097
1578; 1.05̄
| rowspan="2" |16\5, 1600
|41\13
|39\12, 1613.793
1587; 10.{{Overline|3}}
|23\7, 1623.529
| rowspan="2" |16\5
|30\9, 1636.{{Overline|36}}
1600
|39\12
1613; 1, 3.8{{Overline|3}}
|23\7
1623; 1.{{Overline|8}}
|30\9
1636.{{Overline|36}}
|-
|-
|Jf, Af
|Xb, Bd
|Bf
|Bf
|Xb
|Xb
|36\11
|36\11, 1661.538
1661; 1, 1.1{{Overline|6}}
|26\8, 1642.105
|26\8
|42\13, 1625.806
1642; 9.5
|38\12, 1572.034
|42\13
|22\7, 1552.941
1625; 1.24
|28\9, 1527.{{Overline|27}}
|38\12
1572; 29
|22\7
1552; 1.0625
|28\9
1527.{{Overline|27}}
|-
|-
|'''J, A'''
|'''X, B'''
|'''B'''
|'''B'''
|'''X'''
|'''X'''
|'''37\11'''
|'''37\11,''' '''1707.692'''
'''1707; 1.{{Overline|4}}'''
|'''27\8,''' '''1705.263'''
|'''27\8'''
|'''44\13,''' '''1703.226'''
'''1705; 3.8'''
|'''17\5,''' '''1700'''
|'''44\13'''
|'''41\12,''' '''1696.552'''
'''1703; 4, 2.3̄'''
|'''24\7,''' '''1694.118'''
|'''17\5'''
|'''31\9,''' '''1690.{{Overline|90}}'''
 
'''1700'''
|'''41\12'''
'''1696; 1.8125'''
|'''24\7'''
'''1694; 8.5'''
|'''31\9'''
'''1690.{{Overline|90}}'''
|-
|-
|J#, A#
|X#, B#
|B#
|B#
|X#
|X#
|38\11
|38\11, 1753.846
1753; 1.{{Overline|18}}
|28\8, 1768.421
|28\8
|46\13, 1780.645
1768; 2.375
| rowspan="2" |'''18\5,''' '''1800'''
|46\13
|44\12, 1820.690
1780; 1.55
|26\7, 1835.294
| rowspan="2" |'''18\5'''
|34\9, 1854.{{Overline|54}}
'''1800'''
|44\12
1820; 1.45
|26\7
1835; 3,4
|34\9
1854.{{Overline|54}}
|-
|-
|'''Af, Bf'''
|'''Eb, Dd'''
|'''Cf'''
|'''Cf'''
|'''ɛf'''
|'''ɛf'''
|'''40\11'''
|'''40\11,''' '''1846.154'''
'''1846; 6.5'''
|'''29\8,''' '''1831.579'''
|'''29\8'''
|'''47\13,''' '''1819.355'''
 
|'''43\12,''' '''1779.310'''
'''1831; 1.{{Overline|72}}'''
|'''25\7,''' '''1764.706'''
|'''47\13'''
|'''32\9,''' '''1745.{{Overline|45}}'''
'''1819; 2.{{Overline|81}}'''
|'''43\12'''
'''1779; 3.{{Overline|2}}'''
|'''25\7'''
'''1764; 1, 3.25'''
|'''32\9'''
'''1745.{{Overline|45}}'''
|-
|-
|A, B
|E, D
|C
|C
|ɛ
|ɛ
|41\11
|41\11, 1892.308
1892; 3.25
|30\8, 1894.737
|30\8
|49\13, 1896.774
1894; 1, 2.8
|19\5, 1900
|49\13
|46\12, 1903.448
1896; 1.291{{Overline|6}}
|27\7, 1905.882
|19\5
|35\9, 1909.{{Overline|09}}
1900
|46\12
1903; 2, 2.1{{Overline|6}}
|27\7
1905; 1, 7.5
|35\9
1909.{{Overline|09}}
|-
|-
|A#, B#
|E#, D#
|C#
|C#
|ɛ#
|ɛ#
|42\11
|42\11, 1938.462
1938; 2.1{{Overline|6}}
| rowspan="2" |31\8, 1957.895
| rowspan="2" |31\8
|51\13, 1974.194
1957; 1, 8.5
|20\5, 2000
|51\13
|49\12, 2027.586
1974; 5.1{{Overline|6}}
|29\7, 2047.059
|20\5
|38\9, 2072.{{Overline|72}}
2000
|49\12
2027; 1, 1.41{{Overline|6}}
|29\7
2047; 17
|38\9
2072.{{Overline|72}}
|-
|-
|Bb, Cf
|0b, Ed
|Df
|Df
|Af
|Af
|43\11
|43\11, 1984.615
1984; 1.625
|50\13, 1935.484
|50\13
|19\5, 1900
1935; 2.0{{Overline|6}}
|45\12, 1862.069
|19\5
|26\7, 1835.294
1900
|33\9, 1800
|45\12
1862; 14.5
|26\7
1835; 3,4
|33\9
1800
|-
|-
!B, C
!0, E
!D
!D
!A
!A
!44\11
!44\11, 2030.769
2030; 1.3
!32\8, 2021.053
!32\8
!52\13, 2012.903
 
!20\5, 2000
2021; 19
!48\12, 1986.207
!52\13
!28\7, 1976.471
2012; 1, 9.{{Overline|3}}
!36\9, 1963.{{Overline|63}}
!20\5
2000
!48\12
1986; 4.8{{Overline|3}}
!28\7
1976; 2.125
!36\9
1963.{{Overline|63}}
|-
|-
|B#, C#
|0#, E#
|D#
|D#
|A#
|A#
|45\11
|45\11, 2076.923
2076; 1.08{{Overline|3}}
|33\8, 2084.211
|33\8
| 54\13, 2090.323
2084; 4.75
| rowspan="2" |21\5, 2100
|54\13
|51\12, 2110.345
2090; 3.1
|30\7, 2117.647
| rowspan="2" |21\5
|39\9, 2127.{{Overline|27}}
2100
|51\12
2110; 2.9
|30\7
2117; 1.{{Overline|54}}
|39\9
2127.{{Overline|27}}
|-
|-
|Cf, Qf
|1b, 1d
|Ef
|Ef
|Bf
|Bf
|47\11
|47\11, 2169.231
2169; 4.{{Overline|3}}
|34\8, 2147.368
|34\8
|55\13, 2129.032
2147; 2, 1.4
|50\12, 2068.966
|55\13
|29\7, 2047.059
2129; 31
|37\9, 2018.{{Overline|18}}
|50\12
2068; 1, 28
|29\7
2047; 17
|37\9
2018.{{Overline|18}}
|-
|-
|'''C, Q'''
|'''1'''
|'''E'''
|'''E'''
|'''B'''
|'''B'''
|'''48\11'''
|'''48\11,''' '''2215.385'''
'''2215; 2.6'''
|'''35\8,''' '''2210.526'''
|'''35\8'''
|'''57\13,''' '''2206.452'''
'''2210; 1.9'''
|'''22\5,''' '''2200'''
|'''57\13'''
|'''53\12,''' '''2193.103'''
'''2206; 2, 4.{{Overline|6}}'''
|'''31\7,''' '''2188.235'''
|'''22\5'''
|'''40\9,''' '''2181.{{Overline|81}}'''
'''2200'''
|'''53\12'''
'''2193; 9.{{Overline|6}}'''
|'''31\7'''
'''2188; 4.25'''
|'''40\9'''
'''2181.{{Overline|81}}'''
|-
|-
|C#, Q#
|1#
|E#
|E#
|B#
|B#
|49\11
|49\11, 2261.538
2261; 1, 1.1{{Overline|6}}
|36\8, 2273.684
|36\8
|59\13, 2283.871
2273; 1, 2.1{{Overline|6}}
| rowspan="2" |'''23\5,''' '''2300'''
|59\13
|56\12, 2317.241
2083; 1.{{Overline|148}}
|33\7, 2329.412
| rowspan="2" |'''23\5'''
|43\9, 2345.{{Overline|45}}
'''2300'''
|56\12
2327; 4, 7
|33\7
2329; 2, 2.{{Overline|3}}
|43\9
2345.{{Overline|45}}
|-
|-
|'''Qf, Df'''
|'''2b, 2d'''
|'''Ff'''
|'''Ff'''
|'''Cf'''
|'''Cf'''
|'''51\11'''
|'''51\11,''' '''2353.846'''
'''2353; 1.{{Overline|18}}'''
|'''37\8,''' '''2336.842'''
|'''37\8'''
|'''61\13,''' '''2322.581'''
'''2336; 1.1875'''
|'''55\12,''' '''2275.864'''
|'''61\13'''
|'''32\7,''' '''2258.824'''
'''2322; 1.7{{Overline|2}}'''
|'''41\9,''' '''2236.{{Overline|36}}'''
|'''55\12'''
'''2275; 1.16'''
|'''32\7'''
'''2258; 1, 4.{{Overline|6}}'''
|'''41\9'''
'''2236.{{Overline|36}}'''
|-
|-
|Q, D
|2
|F
|F
|C
|C
|52\11
| 52\11, 2400
2400
|38\8, 2400
|38\8
|62\13, 2400
2400
|24\5, 2400
|62\13
| 58\12, 2400
2400
|34\7, 2400
|24\5
| 44\9, 2400
2400
|58\12
2400
|34\7
2400
|44\9
2400
|-
|-
|Q#, D#
|2#
|F#
|F#
|C#
|C#
|53\11
|53\11, 2446.154
2446; 6.5
| rowspan="2" |39\8, 2463.158
| rowspan="2" |39\8
|64\13, 2477.419
2463; 6.{{Overline|3}}
|25\5, 2500
|64\13
|61\12, 2524.138
2477; 2, 2.6
|36\7, 2541.176
|25\5
|47/9, 2563.{{Overline|63}}
2500
|61\12
2524; 7.25
|36\7
2541; 5.{{Overline|6}}
|47/9
2563.{{Overline|63}}
|-
|-
|Df, Sf
|3b, 3d
|1f
|1f
|Df
|Df
|54\11
|54\11, 2492.308
2492; 3.25
|63\13, 2438.710
|63\13
|24\5, 2400
2438; 1.1{{Overline|36}}
|57\12, 2358.621
|24\5
|33\7, 2329.412
2400
|42\9, 2390.{{Overline|90}}
|57\12
2358; 1.61̄
|33\7
2329; 2, 2.{{Overline|3}}
|42\9
2390.{{Overline|90}}
|-
|-
!D, S
! 1
!3
!1
!D
!D
!55\11
!55\11, 2538.462
2538; 2.1{{Overline|6}}
!40\8, 2526.316
!40\8
! 65\13, 2516.129
2526; 3.1{{Overline|6}}
!25\5, 2500
!65\13
!60\12, 2482.759
2516; 7.75
!35\7, 2470.588
!25\5
!45\9, 2454.{{Overline|54}}
2500
!60\12
2482; '''1.3{{Overline|18}}'''
!35\7
2470; 1.7
!45\9
2454.{{Overline|54}}
|-
|-
|D#, S#
|3#
|1#
|1#
|D#
|D#
|56\11
|56\11, 2584.615
2584; 1.625
|41\8, 2589.474
|41\8
|67\13, 2593.548
2589; 2.1̄
| rowspan="2" |26\5, 2600
|67\13
|63\12, 2606.897
2593; 1, 1, 4.{{Overline|6}}
|37\7, 2611.765
| rowspan="2" |26\5
|48\9, 2618.{{Overline|18}}
2600
|63\12
2606; 1, 8.{{Overline|6}}
|37\7
2611; 1, 3.25
|48\9
2618.{{Overline|18}}
|-
|-
|Ef
|4b, 4d
|2f
|2f
|Ef
|Ef
|58\11
|58\11, 2676.923
2676; 1.08{{Overline|3}}
| 42\8, 2652.632
|42\8
|69\13, 2670.968
2652; 1.58{{Overline|3}}
|62\12, 2565.517
|69\13
|36\7, 2541.176
2670; 1.0{{Overline|3}}
|46\9, 2509.{{Overline|09}}
|62\12
2565; 1.9{{Overline|3}}
|36\7
2541; 5.{{Overline|6}}
|46\9
2509.{{Overline|09}}
|-
|-
|'''E'''
|'''4'''
|'''2'''
|'''2'''
|'''E'''
|'''E'''
|'''59\11'''
|'''59\11,''' '''2723.077'''
'''2723; 13'''
|'''43\8,''' '''2715.789'''
|'''43\8'''
|'''70\13,''' '''2709.677'''
'''2715; 1.2{{Overline|6}}'''
|'''27\5,''' '''2700'''
|'''70\13'''
|'''65\12,''' '''2689.655'''
'''2709; 1, 2.1'''
|'''38\7,''' '''2682.353'''
|'''27\5'''
|'''49\9,''' '''2672.{{Overline|72}}'''
'''2700'''
|'''65\12'''
'''2689; 1, 1.9'''
|'''38\7'''
'''2682; 2.8{{Overline|3}}'''
|'''49\9'''
'''2672.{{Overline|72}}'''
|-
|-
|E#
|4#
|2#
|2#
|E#
|E#
|60\11
|60\11, 2769.231
 
|44\8, 2778.947
2769; 4.{{Overline|3}}
|72\13, 2787.097
|44\8
| rowspan="2" |'''28\5,''' '''2800'''
2778; 1.05̄
|68\12, 2813.793
|72\13
|40\7, 2823.529
2787; 10.{{Overline|3}}
|52\9, 2836.{{Overline|36}}
| rowspan="2" |'''28\5'''
'''2800'''
|68\12
2813; 1, 3.8{{Overline|3}}
|40\7
2823; 1.{{Overline|8}}
|52\9
2836.{{Overline|36}}
|-
|-
|'''Ff'''
|'''5b, 5d'''
|'''3f'''
|'''3f'''
|'''Ff'''
|'''Ff'''
|'''62\11'''
|'''62\11,''' '''2861.538'''
'''2861; 1, 1.1{{Overline|6}}'''
|'''45\8,''' '''2842.105'''
|'''45\8'''
|'''73\13,''' '''2825.806'''
'''2842; 9.5'''
|'''67\12,''' '''2772.034'''
|'''73\13'''
|'''39\7,''' '''2752.941'''
'''2825; 1.24'''
|'''50\9,''' '''2727.{{Overline|27}}'''
|'''67\12'''
'''2772; 29'''
|'''39\7'''
'''2752; 1.0625'''
|'''50\9'''
'''2727.{{Overline|27}}'''
|-
|-
| 3
|F
|F
|5
|63\11, 2907.692
|3
|46\8, 2905.263
|F
|75\13, 2903.226
|63\11
|29\5, 2900
2907; 1.{{Overline|4}}
|70\12, 2896.552
|46\8
|41\7, 2894.118
2905; 3.8
|53\9, 2890.{{Overline|90}}
|75\13
2903; 4, 2.3̄
|29\5
2900
|70\12
2896; 1.8125
|41\7
2894; 8.5
|53\9
2890.{{Overline|90}}
|-
|-
|F#
|5#
|3#
|3#
|F#
|F#
|64\11
|64\11, 2953.846
2953; 1.{{Overline|18}}
| rowspan="2" |47\8, 2968.421
| rowspan="2" |47\8
|77\13, 2980.645
2968; 2.375
|30\5, 3000
|77\13
|73\12, 3020.690
2980; 1.55
|43\7, 3035.294
|30\5
|55\9, 3000
3000
|73\12
3020; 1.45
|43\7
3035; 3,4
|55\9
3000
|-
|-
|Gf
|6b, 6d
|4f
|4f
|0f
|0f
|65\11
|65\11, 3000
3000
|76\13, 2941.935
|76\13
|29\5, 2900
2941; 1, 14.5
|69\29, 2855.172
|29\5
|40\7, 2823.529
2900
|52\9, 2836.{{Overline|36}}
|69\29
2855; 5.8
|40\7
2823; 1.{{Overline|8}}
|52\9
2836.{{Overline|36}}
|-
|-
!G
!6
!4
!4
!0
!0
!66\11
!66\11, 3046.154
3046; 6.5
!48\8, 30'''31.579'''
!48\8
!78\13, 30'''19.355'''
30'''31; 1.{{Overline|72}}'''
!30\5, 3000
!78\13
!72\12, 29'''79.310'''
30'''19; 2.{{Overline|81}}'''
!42\7, 2964.706
!30\5
!54\9, 2945.{{Overline|45}}
3000
!72\12
29'''79; 3.{{Overline|2}}'''
!42\7
2964; 1, 3.25
!54\9
2945.{{Overline|45}}
|}
|}
==Intervals==
==Intervals==
Line 1,256: Line 1,131:
|perfect fourth
|perfect fourth
|-
|-
|1
| 1
|Mib, Sib
|Mib, Sib
|diminished third
|diminished third
Line 1,274: Line 1,149:
|3
|3
|Dob, Solb
|Dob, Solb
|diminished fourth
| diminished fourth
| -3
| -3
|Do#, Sol#
|Do#, Sol#
Line 1,332: Line 1,207:
!pattern
!pattern
!notation
!notation
!2nd
! 2nd
!3rd
!3rd
|-
|-
Line 1,375: Line 1,250:


[[Optimal ET sequence]]: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)
[[Optimal ET sequence]]: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)
====Scale tree====
====Scale tree ====
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Generator
! colspan="3" |Generator
(bright)
(bright)
!Cents<ref name=":05" />
!Cents
!L
!L
!s
!s
Line 1,389: Line 1,264:
|
|
|
|
|171; 2.{{Overline|3}}
|171.429
|1
| 1
|1
|1
|1.000
|1.000
Line 1,398: Line 1,273:
|
|
|
|
|180
|180.000
|6
|6
|5
|5
|1.200
|1.200
|
|-
|
|11\31
|
|180; 1.21{{Overline|6}}
|11
|9
|1.222
|
|
|-
|-
Line 1,425: Line 1,291:
|14\39
|14\39
|
|
|182; 1, 1.5
|182.609
|14
|14
|11
|11
Line 1,434: Line 1,300:
|9\25
|9\25
|
|
|183; 19.{{Overline|6}}
|183.051
|9
|9
|7
|7
Line 1,443: Line 1,309:
|
|
|
|
|184; 1.625
|184.615
|4
|4
|3
|3
|1.333
|1.333
|
|-
|
|15\41
|
|185; 1.7{{Overline|63}}
|15
|11
|1.364
|
|
|-
|-
Line 1,461: Line 1,318:
|11\30
|11\30
|
|
|185, 1, 10.8{{Overline|3}}
|185.915
|11
|11
|8
| 8
|1.375
|1.375
|
|
Line 1,470: Line 1,327:
|7\19
|7\19
|
|
|186.{{Overline|6}}
| 186.{{Overline|6}}
|7
|7
|5
|5
|1.400
| 1.400
|
|
|-
|-
Line 1,488: Line 1,345:
|13\35
|13\35
|
|
|187; 1, 19.75
|187.952
|13
|13
|9
|9
Line 1,497: Line 1,354:
|16\43
|16\43
|
|
|188; 4.25
|188.253
|16
|16
|11
|11
Line 1,506: Line 1,363:
|
|
|
|
|189; 2.{{Overline|1}}
|189.474
|3
| 3
|2
|2
|1.500
|1.500
|Mahuric-Meantone starts here
| Mahuric-Meantone starts here
|-
|-
|
|
Line 1,516: Line 1,373:
|
|
|190.{{Overline|90}}
|190.{{Overline|90}}
|14
| 14
|9
|9
|1.556
|1.556
Line 1,524: Line 1,381:
|11\29
|11\29
|
|
|191; 3, 2.{{Overline|3}}
|191.304
|11
|11
|7
| 7
|1.571
|1.571
|
|
Line 1,533: Line 1,390:
|8\21
|8\21
|
|
|192
|192.000
|8
|8
|5
|5
Line 1,542: Line 1,399:
|5\13
|5\13
|
|
|193; 1, 1, 4.{{Overline|6}}
| 193.548
|5
|5
|3
|3
Line 1,560: Line 1,417:
|7\18
|7\18
|
|
|195; 2.8{{Overline|6}}
|195.348
|7
|7
|4
|4
Line 1,578: Line 1,435:
|11\28
|11\28
|
|
|197; 67
|197.015
|11
| 11
|6
|6
|1.833
|1.833
Line 1,587: Line 1,444:
|13\33
|13\33
|
|
|197; 2.{{Overline|135}}
|197.468
|13
|13
|7
|7
Line 1,594: Line 1,451:
|-
|-
|
|
|15\38
| 15\38
|
|
|197; 1, 2, 1, 1.{{Overline|54}}
|197.802
|15
| 15
|8
|8
|1.875
|1.875
Line 1,605: Line 1,462:
|17\43
|17\43
|
|
|198; 17.1{{Overline|6}}
|198.058
|17
|17
|9
|9
Line 1,614: Line 1,471:
|19\48
|19\48
|
|
|198: 3, 1, 28
|198.261
|19
|19
|10
|10
Line 1,623: Line 1,480:
|21\53
|21\53
|
|
|198; 2.3{{Overline|518}}
|198.425
|21
|21
|11
|11
Line 1,632: Line 1,489:
|23\58
|23\58
|
|
|198; 1, 3, 1.7
|198.561
|23
|23
|12
|12
Line 1,641: Line 1,498:
|25\63
|25\63
|
|
|198; 1, 2, 12.25
|198.675
|25
|25
|13
|13
Line 1,650: Line 1,507:
|27\68
|27\68
|
|
|198; 1, 3.{{Overline|405}}
|198.773
|27
|27
|14
|14
Line 1,659: Line 1,516:
|29\73
|29\73
|
|
|198; 1, 1.1{{Overline|6}}
|198.857
|29
|29
|15
|15
Line 1,668: Line 1,525:
|31\78
|31\78
|
|
|198; 1, 12, 2.8
|198.930
|31
|31
|16
|16
Line 1,677: Line 1,534:
|33\83
|33\83
|
|
|198; 1.{{Overline|005}}
| 198.995
|33
|33
|17
|17
Line 1,686: Line 1,543:
|35\88
|35\88
|
|
|199; 19.{{Overline|18}}
| 199.009
|35
|35
|18
|18
Line 1,713: Line 1,570:
|15\37
|15\37
|
|
|202; 4.0{{Overline|45}}
|202.247
|15
|15
|7
|7
Line 1,722: Line 1,579:
|13\32
|13\32
|
|
|202; 1, 1, 2.0{{Overline|6}}
|202.597
|13
|13
|6
|6
Line 1,731: Line 1,588:
|11\27
|11\27
|
|
|203; 13
|203.077
|11
|11
|5
|5
Line 1,740: Line 1,597:
|9\22
|9\22
|
|
|203; 1, 3.41{{Overline|6}}
|203.774
|9
|9
|4
|4
Line 1,749: Line 1,606:
|7\17
|7\17
|
|
|204; 1. 7.2
|204.878
|7
|7
|3
|3
Line 1,758: Line 1,615:
|
|
|12\29
|12\29
|205; 1.4
|205.714
|12
| 12
|5
|5
|2.400
|2.400
Line 1,767: Line 1,624:
|5\12
|5\12
|
|
|206; 1, 8.{{Overline|6}}
|206.897
|5
|5
|2
|2
Line 1,776: Line 1,633:
|
|
|18\43
|18\43
|207; 1.{{Overline|4}}
|207.693
|18
|18
|7
|7
Line 1,785: Line 1,642:
|
|
|13\31
|13\31
|208
|208.000
|13
|13
|5
|5
Line 1,794: Line 1,651:
|8\19
|8\19
|
|
|208; 1.4375
|208.696
|8
|8
|3
|3
Line 1,803: Line 1,660:
|11\26
|11\26
|
|
|209; 1.{{Overline|90}}
|209.524
|11
|11
|4
|4
Line 1,810: Line 1,667:
|-
|-
|
|
|14\33
| 14\33
|
|
|210
|210.000
|14
|14
|5
|5
Line 1,821: Line 1,678:
|
|
|
|
|211; 1, 3.25
|211.755
|3
|3
|1
|1
Line 1,830: Line 1,687:
|22\51
|22\51
|
|
|212; 1, 9.{{Overline|3}}
|212.903
|22
|22
|7
|7
Line 1,839: Line 1,696:
|19\44
|19\44
|
|
|213; 11.{{Overline|8}}
|213.084
|19
| 19
|6
|6
|3.167
|3.167
Line 1,848: Line 1,705:
|16\37
|16\37
|
|
|213.3̄
|213.{{Overline|3}}
|16
|16
|5
|5
Line 1,857: Line 1,714:
|13\30
|13\30
|
|
|213; 1, 2.3{{Overline|18}}
|213.699
|13
|13
|4
|4
Line 1,866: Line 1,723:
|10\23
|10\23
|
|
|214; 3.5
|214.286
|10
|10
|3
|3
Line 1,875: Line 1,732:
|7\16
|7\16
|
|
|215; 2.6
|215.385
|7
|7
|2
|2
Line 1,884: Line 1,741:
|11\25
|11\25
|
|
|216; 2.541{{Overline|6}}
|216.393
|11
|11
|3
|3
Line 1,893: Line 1,750:
|15\34
|15\34
|
|
|216; 1.152{{Overline|7}}
|216.867
|15
|15
|4
|4
Line 1,902: Line 1,759:
|19\43
|19\43
|
|
|217; 7
|217.143
|19
|19
|5
|5
Line 1,920: Line 1,777:
|13\29
|13\29
|
|
|219; 1, 2.55
|219.718
|13
|13
|3
|3
Line 1,929: Line 1,786:
|9\20
|9\20
|
|
|220; 2.45
|220.408
|9
|9
|2
|2
Line 1,938: Line 1,795:
|14\31
|14\31
|
|
|221; 19
|221.053
|14
|14
|3
|3
Line 1,956: Line 1,813:
|11\24
|11\24
|
|
|223; 1, 2.6875
|223.728
|11
|11
|2
|2
Line 1,965: Line 1,822:
|17\37
|17\37
|
|
|224; 5.7{{Overline|2}}
|224.176
|17
|17
|3
|3
Line 1,974: Line 1,831:
|
|
|
|
|225
|225.000
|6
|6
|1
|1
Line 1,980: Line 1,837:
|
|
|-
|-
|1\3
| 1\3
|
|
|
|
|240
|240.000
|1
|1
|0
|0
Line 1,990: Line 1,847:
|}
|}


== See also ==
==See also==
[[2L 1s (4/3-equivalent)]] - idealized tuning
[[2L 1s (4/3-equivalent)]] - idealized tuning


Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/2L_1s_(perfect_fourth-equivalent)"