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User:Moremajorthanmajor/8L 3s (perfect twelfth-equivalent): Difference between revisions

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Line 152: Line 152:
|7L+4s
|7L+4s
|-
|-
| colspan="8" style="text-align:center" |The chromatic 19-note MOS (either [[8L 11s (tritave equivalent)|8L 11s]], [[11L 8s (tritave equivalent)|11L 8s]], or [[19edt]]) also has the following intervals (from some root):
| colspan="8" style="text-align:center" |The chromatic 19-note MOS (either [[8L 11s (perfect twelfth equivalent)|8L 11s]], [[11L 8s (perfect twelfth equivalent)|11L 8s]], or [[19edt]]) also has the following intervals (from some root):
|-
|-
|12
|12
Line 238: Line 238:
|minor 2nd
|minor 2nd
|1\19, 100.00
|1\19, 100.00
|1\27, 70.59 (70.37)
|1\27, 70.59
|2\30, 126.32 (126.67)
|2\30, 126.32  
|Hf
|Hf
| -8
| -8
Line 245: Line 245:
|major 2nd
|major 2nd
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765
|3\30, 189.47 (190.00)
|3\30, 189.47
|H
|H
|3
|3
Line 252: Line 252:
|minor 3rd
|minor 3rd
|3\19, 300.00
|3\19, 300.00
|4\27, 282.35 (281.48)
|4\27, 282.35
|5\30, 315.79 (316.67)
|5\30, 315.79
|Jf
|Jf
| -5
| -5
Line 259: Line 259:
|major 3rd
|major 3rd
|4\19, 400.00
|4\19, 400.00
|6\27, 423.53 (422.22)
|6\27, 423.53
|6\30, 378.95 (380.00)
|6\30, 378.95
|J
|J
|6
|6
Line 266: Line 266:
|natural 4th
|natural 4th
|5\19, 500.00
|5\19, 500.00
|7\27, 494.12 (493.59)
|7\27, 494.12
|8\30, 505,26 (506.67)
|8\30, 505,26
|K
|K
| -2
| -2
Line 273: Line 273:
|augmented 4th
|augmented 4th
| rowspan="2" |6\19, 600.00
| rowspan="2" |6\19, 600.00
|9\27, 635.29 (633.33)
|9\27, 635.29
|9\30, 568.42 (570.00)
|9\30, 568.42
|K#
|K#
|9
|9
|-
|-
|diminished 5th
|diminished 5th
|8\27, 564.71 (562.96)
|8\27, 564.71
|10\30, 631.58 (633.33)
|10\30, 631.58
|Lf
|Lf
| -10
| -10
Line 286: Line 286:
|perfect 5th
|perfect 5th
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88
|11\30, 694.74 (696.67)
|11\30, 694.74
|L
|L
|1
|1
Line 293: Line 293:
|minor 6th
|minor 6th
|8\19, 800.00
|8\19, 800.00
|11\27, 776.47 (774.07)
|11\27, 776.47
|13\30, 821.05 (823.33)
|13\30, 821.05
|Af
|Af
| -7
| -7
Line 300: Line 300:
|major 6th
|major 6th
|9\19, 900.00
|9\19, 900.00
|13\27, 917.65 (914.81)
|13\27, 917.65
|14\30, 884.21 (886.67)
|14\30, 884.21
|A
|A
|4
|4
Line 307: Line 307:
|minor 7th
|minor 7th
|10\19, 1000.00
|10\19, 1000.00
|14\27, 988.235 (985.19)
|14\27, 988.235
|16\30, 1010.53 (1013.33)
|16\30, 1010.53
|Bf
|Bf
| -4
| -4
Line 314: Line 314:
|major 7th
|major 7th
|11\19, 1100.00
|11\19, 1100.00
|16\27, 1129.42 (1125.93)
|16\27, 1129.42
|17\30, 1073.68 (1076.67)
|17\30, 1073.68
|B
|B
|7
|7
Line 321: Line 321:
|perfect octave
|perfect octave
|12\19, 1200.00
|12\19, 1200.00
|17\27, 1200.00 (1196.30)
|17\27, 1200.00
|19\30, 1200.00 (1203.33)
|19\30, 1200.00
|C
|C
| -1
| -1
Line 328: Line 328:
|augmented octave
|augmented octave
| rowspan="2" |13\19, 1300.00
| rowspan="2" |13\19, 1300.00
|19\27, 1341.18 (1337.04)
|19\27, 1341.18
|20\30, 1263.16 (1266.67)
|20\30, 1263.16
|C#
|C#
|10
|10
|-
|-
|minor 9th
|minor 9th
|18\27, 1270.59 (1266.67)
|18\27, 1270.59
|21\30, 1326.32 (1330.00)
|21\30, 1326.32
|Df
|Df
| -9
| -9
Line 341: Line 341:
|major 9th
|major 9th
|14\19, 1400.00
|14\19, 1400.00
|20\27, 1411.765 (1406.07)
|20\27, 1411.765
|22\30, 1389.47 (1393.33)
|22\30, 1389.47
|D
|D
|2
|2
Line 348: Line 348:
|minor 10th
|minor 10th
|15\19, 1500.00
|15\19, 1500.00
|21\27, 1482.35 (1477.78)
|21\27, 1482.35
|24\30, 1515.79 (1520.00)
|24\30, 1515.79
|Ef
|Ef
| -6
| -6
Line 355: Line 355:
|major 10th
|major 10th
|16\19, 1600.00
|16\19, 1600.00
|23\27, 1623.53 (1618.52)
|23\27, 1623.53
|25\30, 1578.95 (1583.33)
|25\30, 1578.95
|E
|E
|5
|5
Line 362: Line 362:
|natural 11th
|natural 11th
|17\19, 1700.00
|17\19, 1700.00
|24\27, 1694.12 (1688.89)
|24\27, 1694.12
|27\30, 1705.26 (1710.00)
|27\30, 1705.26
|Ff
|Ff
| -3
| -3
Line 369: Line 369:
|augmented 11th
|augmented 11th
|18\19, 1800.00
|18\19, 1800.00
|26\27, 1835.29 (1829.63)
|26\27, 1835.29  
|28\30, 1768.42 (1773.33)
|28\30, 1768.42
|F
|F
|8
|8
Line 392: Line 392:
|generator (g)
|generator (g)
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88
|17\46, 703.45 (702.17)
|17\46, 703.45
|-
|-
|L (3g - ~tritave)
|L (3g - ~tritave)
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765
|5\46, 206.90 (206.52)
|5\46, 206.90
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
|1\19, 100.00
|1\19, 100.00
|1\27, 70.59 (70.37)
|1\27, 70.59
|2\46, 82.76 (82.61)
|2\46, 82.76
|}
|}
====Intervals====
====Intervals====
Line 425: Line 425:
|minor 2nd
|minor 2nd
|1\19, 100.00
|1\19, 100.00
|1\27, 70.59 (70.37)
|1\27, 70.59
|2\46, 82.76 (82.61)
|2\46, 82.76
|Hf
|Hf
| -8
| -8
Line 432: Line 432:
|major 2nd
|major 2nd
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765
|5\46, 206.90 (206.52)
|5\46, 206.90
|H
|H
|3
|3
Line 439: Line 439:
|minor 3rd
|minor 3rd
|3\19, 300.00
|3\19, 300.00
|4\27, 282.35 (281.48)
|4\27, 282.35
|7\46, 289.655 (289.13)
|7\46, 289.655
|Jf
|Jf
| -5
| -5
Line 446: Line 446:
|major 3rd
|major 3rd
|4\19, 400.00
|4\19, 400.00
|6\27, 423.53 (422.22)
|6\27, 423.53
|10\46, 413.79 (413.04)
|10\46, 413.79
|J
|J
|6
|6
Line 453: Line 453:
|natural 4th
|natural 4th
|5\19, 500.00
|5\19, 500.00
|7\27, 494.12 (493.59)
|7\27, 494.12
|12\46, 496.55 (495.65)
|12\46, 496.55
|K
|K
| -2
| -2
Line 460: Line 460:
|augmented 4th
|augmented 4th
| rowspan="2" |6\19, 600.00
| rowspan="2" |6\19, 600.00
|9\27, 635.29 (633.33)
|9\27, 635.29
|15\46, 620.69 (619.565)
|15\46, 620.69
|K#
|K#
|9
|9
|-
|-
|diminished 5th
|diminished 5th
|8\27, 564.71 (562.96)
|8\27, 564.71
|14\46, 579.31 (578.26)
|14\46, 579.31
|Lf
|Lf
| -10
| -10
Line 473: Line 473:
|perfect 5th
|perfect 5th
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88
|17\46, 703.45 (702.17)
|17\46, 703.45
|L
|L
|1
|1
Line 480: Line 480:
|minor 6th
|minor 6th
|8\19, 800.00
|8\19, 800.00
|11\27, 776.47 (774.07)
|11\27, 776.47
|19\46, 786.21 (784.78)
|19\46, 786.21
|Af
|Af
| -7
| -7
Line 487: Line 487:
|major 6th
|major 6th
|9\19, 900.00
|9\19, 900.00
|13\27, 917.65 (914.81)
|13\27, 917.65
|22\46, 910.345 (908.70)
|22\46, 910.345
|A
|A
|4
|4
Line 494: Line 494:
|minor 7th
|minor 7th
|10\19, 1000.00
|10\19, 1000.00
|14\27, 988.235 (985.19)
|14\27, 988.235
|24\46, 993.10 (991.30)
|24\46, 993.10
|Bf
|Bf
| -4
| -4
Line 501: Line 501:
|major 7th
|major 7th
|11\19, 1100.00
|11\19, 1100.00
|16\27, 1129.42 (1125.93)
|16\27, 1129.42
|27\46, 1117.24 (1115.22)
|27\46, 1117.24
|B
|B
|7
|7
Line 508: Line 508:
|perfect octave
|perfect octave
|12\19, 1200.00
|12\19, 1200.00
|17\27, 1200.00 (1196.30)
|17\27, 1200.00
|29\46, 1200.00 (1197.83)
|29\46, 1200.00
|C
|C
| -1
| -1
Line 515: Line 515:
|augmented octave
|augmented octave
| rowspan="2" |13\19, 1300.00
| rowspan="2" |13\19, 1300.00
|19\27, 1341.18 (1337.04)
|19\27, 1341.18
|32\46, 1324.14 (1321.74)
|32\46, 1324.14
|C#
|C#
|10
|10
|-
|-
|minor 9th
|minor 9th
|18\27, 1270.59 (1266.67)
|18\27, 1270.59
|31\46, 1282.76 (1280.435)
|31\46, 1282.76
|Df
|Df
| -9
| -9
Line 528: Line 528:
|major 9th
|major 9th
|14\19, 1400.00
|14\19, 1400.00
|20\27, 1411.765 (1406.07)
|20\27, 1411.765
|34\46, 1406.90 (1404.35)
|34\46, 1406.90
|D
|D
|2
|2
Line 535: Line 535:
|minor 10th
|minor 10th
|15\19, 1500.00
|15\19, 1500.00
|21\27, 1482.35 (1477.78)
|21\27, 1482.35
|36\46, 1489.655 (1486.96)
|36\46, 1489.655
|Ef
|Ef
| -6
| -6
Line 542: Line 542:
|major 10th
|major 10th
|16\19, 1600.00
|16\19, 1600.00
|23\27, 1623.53 (1618.52)
|23\27, 1623.53
|39\46, 1613.79 (1610.87)
|39\46, 1613.79
|E
|E
|5
|5
Line 549: Line 549:
|natural 11th
|natural 11th
|17\19, 1700.00
|17\19, 1700.00
|24\27, 1694.12 (1688.89)
|24\27, 1694.12
|41\46, 1696.55 (1693.48)
|41\46, 1696.55
|Ff
|Ff
| -3
| -3
Line 556: Line 556:
|augmented 11th
|augmented 11th
|18\19, 1800.00
|18\19, 1800.00
|26\27, 1835.29 (1829.63)
|26\27, 1835.29  
|44\46, 1820.69 (1817.39)
|44\46, 1820.69
|F
|F
|8
|8
Line 573: Line 573:
|-
|-
|generator (g)
|generator (g)
|11\30, 694.74 (696.67)
|11\30, 694.74
|18\49, 696.77 (697.96)
|18\49, 696.77
|-
|-
|L (3g - ~tritave)
|L (3g - ~tritave)
|3\30, 189.47 (190.00)
|3\30, 189.47
|5\49, 193.55 (193.87)
|5\49, 193.55  
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
|2\30, 126.32 (126.67)
|2\30, 126.32  
|3\49, 116.13 (116.33)
|3\49, 116.13
|}
|}
====Intervals====
====Intervals====
Line 603: Line 603:
|-
|-
|minor 2nd
|minor 2nd
|2\30, 126.32 (126.67)
|2\30, 126.32  
|3\49, 116.13 (116.33)
|3\49, 116.13
|Hf
|Hf
|16/15
|16/15
Line 610: Line 610:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
|major 2nd
|3\30, 189.47 (190.00)
|3\30, 189.47
|5\49, 193.55 (193.87)
|5\49, 193.55  
|H
|H
|10/9, 9/8
|10/9, 9/8
Line 617: Line 617:
|-
|-
|minor 3rd
|minor 3rd
|5\30, 315.79 (316.67)
|5\30, 315.79
|8\49, 309.68 (310.20)
|8\49, 309.68
|Jf
|Jf
|6/5
|6/5
Line 624: Line 624:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|6\30, 378.95 (380.00)
|6\30, 378.95
|10\49, 387.10 (387.755)
|10\49, 387.10
|J
|J
|5/4
|5/4
Line 631: Line 631:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
|natural 4th
|8\30, 505,26 (506.67)
|8\30, 505,26
|13\49, 503.23 (504.08)
|13\49, 503.23
|K
|K
|4/3
|4/3
Line 638: Line 638:
|-
|-
|augmented 4th
|augmented 4th
|9\30, 568.42 (570.00)
|9\30, 568.42
|15\49, 580.645 (581.63)
|15\49, 580.645
|K#
|K#
|7/5
|7/5
Line 645: Line 645:
|-
|-
|diminished 5th
|diminished 5th
|10\30, 631.58 (633.33)
|10\30, 631.58
|16\49, 619.355 (620.41)
|16\49, 619.355
|Lf
|Lf
|10/7
|10/7
Line 652: Line 652:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|11\30, 694.74 (696.67)
|11\30, 694.74
|18\49, 696.77 (697.96)
|18\49, 696.77
|L
|L
|3/2
|3/2
Line 659: Line 659:
|-
|-
|minor 6th
|minor 6th
|13\30, 821.05 (823.33)
|13\30, 821.05
|21\49, 812.90 (814.29)
|21\49, 812.90
|Af
|Af
|8/5
|8/5
Line 666: Line 666:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|14\30, 884.21 (886.67)
|14\30, 884.21
|23\49, 890.32 (891.84)
|23\49, 890.32
|A
|A
|5/3
|5/3
Line 673: Line 673:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|16\30, 1010.53 (1013.33)
|16\30, 1010.53
|26\49, 1006.45 (1008.16)
|26\49, 1006.45
|Bf
|Bf
|16/9, 9/5
|16/9, 9/5
Line 680: Line 680:
|-
|-
|major 7th
|major 7th
|17\30, 1073.68 (1076.67)
|17\30, 1073.68
|28\49, 1083.87 (1085.71)
|28\49, 1083.87
|B
|B
|15/8
|15/8
Line 687: Line 687:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|19\30, 1200.00 (1203.33)
|19\30, 1200.00
|31\49, 1200.00 (1202.04)
|31\49, 1200.00
|C
|C
|2/1
|2/1
Line 694: Line 694:
|-
|-
|augmented octave
|augmented octave
|20\30, 1263.16 (1266.67)
|20\30, 1263.16
|33\49, 1277.42 (1279.59)
|33\49, 1277.42
|C#
|C#
|25/24
|25/24
Line 701: Line 701:
|-
|-
|minor 9th
|minor 9th
|21\30, 1326.32 (1330.00)
|21\30, 1326.32
|34\49, 1316.13 (1318.37)
|34\49, 1316.13
|Df
|Df
|15/7
|15/7
Line 708: Line 708:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|22\30, 1389.47 (1393.33)
|22\30, 1389.47
|36\49, 1393.55 (1395.92)
|36\49, 1393.55
|D
|D
|20/9, 9/4
|20/9, 9/4
Line 715: Line 715:
|-
|-
|minor 10th
|minor 10th
|24\30, 1515.79 (1520.00)
|24\30, 1515.79
|39\49, 1508.68 (1512.245)
|39\49, 1508.68
|Ef
|Ef
|12/5
|12/5
Line 722: Line 722:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|25\30, 1578.95 (1583.33)
|25\30, 1578.95
|41\49, 1587.10 (1590.80)
|41\49, 1587.10
|E
|E
|5/2
|5/2
Line 729: Line 729:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 11th
|natural 11th
|27\30, 1705.26 (1710.00)
|27\30, 1705.26
|44\49, 1703.23 (1706.13j
|44\49, 1703.23
|Ff
|Ff
|8/3
|8/3
Line 736: Line 736:
|-
|-
|augmented 11th
|augmented 11th
|28\30, 1768.42 (1773.33)
|28\30, 1768.42
|46\49, 1780.645 (1783.67)
|46\49, 1780.645
|F
|F
|14/5
|14/5
Line 753: Line 753:
|-
|-
|generator (g)
|generator (g)
|15\41, 692.31 (695.12)
|15\41, 692.31
|19\52, 690.91 (694.23)
|19\52, 690.91
|-
|-
|L (3g - ~tritave)
|L (3g - ~tritave)
|4\41, 184.615 (185.37)
|4\41, 184.615
|5\52, 181.81 (182.69)
|5\52, 181.81
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
|3\41, 138.46 (139.02)
|3\41, 138.46  
|4\52, 145.455 (146.15)
|4\52, 145.455
|}
|}
====Intervals====
====Intervals====
Line 781: Line 781:
|-
|-
|chroma
|chroma
|1\41, 46.15 (46.34)
|1\41, 46.15
|G#
|G#
|[[33/32]], [[49/48]], [[36/35]], [[25/24]]
|[[33/32]], [[49/48]], [[36/35]], [[25/24]]
Line 787: Line 787:
|-
|-
|diminished 2nd
|diminished 2nd
|2\41, 92.31 (92.68)
|2\41, 92.31
|Hff
|Hff
|[[21/20]], [[22/21]], [[26/25]]
|[[21/20]], [[22/21]], [[26/25]]
Line 793: Line 793:
|-
|-
|minor 2nd
|minor 2nd
|3\41, 138.46 (139.02)
|3\41, 138.46
|Hf
|Hf
|[[12/11]], [[13/12]], [[14/13]], [[16/15]]
|[[12/11]], [[13/12]], [[14/13]], [[16/15]]
Line 799: Line 799:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
|major 2nd
|4\41, 184.615 (185.37)
|4\41, 184.615
|H
|H
|[[9/8]], [[10/9]], [[11/10]]
|[[9/8]], [[10/9]], [[11/10]]
Line 805: Line 805:
|-
|-
|augmented 2nd
|augmented 2nd
|5\41, 230.77 (231.71)
|5\41, 230.77
|H#
|H#
|[[8/7]], [[15/13]]
|[[8/7]], [[15/13]]
Line 811: Line 811:
|-
|-
|diminished 3rd
|diminished 3rd
|6\41, 276.92 (278.05)
|6\41, 276.92
|Jff
|Jff
|[[7/6]], [[13/11]], [[33/28]]
|[[7/6]], [[13/11]], [[33/28]]
Line 817: Line 817:
|-
|-
|minor 3rd
|minor 3rd
|7\41, 323.08 (324.39)
|7\41, 323.08
|Jf
|Jf
|[[135/112]], [[6/5]]
|[[135/112]], [[6/5]]
Line 823: Line 823:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|8\41, 369.23 (370.73)
|8\41, 369.23
|J
|J
|[[5/4]], [[11/9]], [[16/13]]
|[[5/4]], [[11/9]], [[16/13]]
Line 829: Line 829:
|-
|-
|augmented 3rd
|augmented 3rd
|9\41, 415.385 (417.07)
|9\41, 415.385
|J#
|J#
|[[9/7]], [[14/11]], [[33/26]]
|[[9/7]], [[14/11]], [[33/26]]
Line 835: Line 835:
|-
|-
|diminished 4th
|diminished 4th
|10\41, 461.54 (463.415)
|10\41, 461.54
|Kff
|Kff
|[[21/16]], [[13/10]]
|[[21/16]], [[13/10]]
Line 841: Line 841:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
|natural 4th
|11\41, 507.69 (509.76)
|11\41, 507.69
|Kf
|Kf
|[[75/56]], [[4/3]]
|[[75/56]], [[4/3]]
Line 847: Line 847:
|-
|-
|augmented 4th
|augmented 4th
|12\41, 553.85 (556.10)
|12\41, 553.85
|K
|K
|[[11/8]], [[18/13]]
|[[11/8]], [[18/13]]
Line 853: Line 853:
|-
|-
|doubly augmented 4th, doubly diminished 5th
|doubly augmented 4th, doubly diminished 5th
|13\41, 600.00 (602.44)
|13\41, 600.00
|K#, Lff
|K#, Lff
|[[7/5]], [[10/7]]
|[[7/5]], [[10/7]]
Line 859: Line 859:
|-
|-
|diminished 5th
|diminished 5th
|14\41, 646.15 (648.78)
|14\41, 646.15
|Lf
|Lf
|[[16/11]], [[13/9]]
|[[16/11]], [[13/9]]
Line 865: Line 865:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|15\41, 692.31 (695.12)
|15\41, 692.31
|L
|L
|[[112/75]], [[3/2]]
|[[112/75]], [[3/2]]
Line 871: Line 871:
|-
|-
|augmented 5th
|augmented 5th
|16\41, 738.46 (741.46)
|16\41, 738.46
|L#
|L#
|[[32/21]], [[20/13]]
|[[32/21]], [[20/13]]
Line 877: Line 877:
|-
|-
|diminished 6th
|diminished 6th
|17\41, 784.615 (787.805)
|17\41, 784.615
|Aff
|Aff
|[[11/7]], [[14/9]]
|[[11/7]], [[14/9]]
Line 883: Line 883:
|-
|-
|minor 6th
|minor 6th
|18\41, 830.77 (834.15)
|18\41, 830.77
|Af
|Af
|[[13/8]], [[8/5]]
|[[13/8]], [[8/5]]
Line 889: Line 889:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|19\41, 876.92 (880.49)
|19\41, 876.92
|A
|A
|[[5/3]], [[224/135]]
|[[5/3]], [[224/135]]
Line 895: Line 895:
|-
|-
|augmented 6th
|augmented 6th
|20\41, 923.08 (926.83)
|20\41, 923.08
|A#
|A#
|[[12/7]], [[22/13]]
|[[12/7]], [[22/13]]
Line 901: Line 901:
|-
|-
|diminished 7th
|diminished 7th
|21\41, 969.23 (973.17)
|21\41, 969.23
|Bff
|Bff
|[[7/4]], [[26/15]]
|[[7/4]], [[26/15]]
Line 907: Line 907:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|minor 7th
|minor 7th
|22\41, 1015.385 (1019.51)
|22\41, 1015.385
|Bf
|Bf
|[[9/5]], [[16/9]], [[20/11]]
|[[9/5]], [[16/9]], [[20/11]]
Line 913: Line 913:
|-
|-
|major 7th
|major 7th
|23\41, 1061.54 (1065.85)
|23\41, 1061.54
|B
|B
|[[11/6]], [[13/7]], [[15/8]], [[24/13]]
|[[11/6]], [[13/7]], [[15/8]], [[24/13]]
Line 919: Line 919:
|-
|-
|augmented 7th
|augmented 7th
|24\41, 1107.69 (1112.195)
|24\41, 1107.69
|B#
|B#
|[[21/11]], [[25/13]], [[40/21]]
|[[21/11]], [[25/13]], [[40/21]]
Line 925: Line 925:
|-
|-
|diminished octave
|diminished octave
|25\41, 1153.85 (1158.54)
|25\41, 1153.85
|Cf
|Cf
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
Line 931: Line 931:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|26\41, 1200.00 (1204.88)
|26\41, 1200.00
|C
|C
|2/1
|2/1
Line 937: Line 937:
|-
|-
|augmented octave
|augmented octave
|27\41, 1246.15 (1251.22)
|27\41, 1246.15
|C#
|C#
|33/16, 49/24, 72/35, 25/12
|33/16, 49/24, 72/35, 25/12
Line 943: Line 943:
|-
|-
|doubly augmented octave, diminished 9th
|doubly augmented octave, diminished 9th
|28\41, 1292.31 (1297.56)
|28\41, 1292.31
|Cx, Dff
|Cx, Dff
|21/10, 44/21, 52/25
|21/10, 44/21, 52/25
Line 949: Line 949:
|-
|-
|minor 9th
|minor 9th
|29\41, 1338.46 (1343.90)
|29\41, 1338.46
|Df
|Df
|24/11, 13/6, 28/13, 32/15
|24/11, 13/6, 28/13, 32/15
Line 955: Line 955:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|30\41, 1384.615 (1390.24)
|30\41, 1384.615
|D
|D
|9/4, 20/9, 11/5
|9/4, 20/9, 11/5
Line 961: Line 961:
|-
|-
|augmented 9th
|augmented 9th
|31\41, 1430.77 (1436.595)
|31\41, 1430.77
|D#
|D#
|16/7, 30/13
|16/7, 30/13
Line 967: Line 967:
|-
|-
|diminished 10th
|diminished 10th
|32\41, 1476.92 (1492.93)
|32\41, 1476.92
|Eff
|Eff
|7/3, 26/11, 33/14
|7/3, 26/11, 33/14
Line 973: Line 973:
|-
|-
|minor 10th
|minor 10th
|33\41, 1523.08 (1529.27)
|33\41, 1523.08
|Ef
|Ef
|135/56, 12/5
|135/56, 12/5
Line 979: Line 979:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|34\41, 1569.23 (1575.61)
|34\41, 1569.23
|E
|E
|5/2, 22/9, 32/13
|5/2, 22/9, 32/13
Line 985: Line 985:
|-
|-
|augmented 10th
|augmented 10th
|35\41, 1615.385 (1621.95)
|35\41, 1615.385
|E#
|E#
|18/7, 28/11, 33/13
|18/7, 28/11, 33/13
Line 991: Line 991:
|-
|-
|diminished 11th
|diminished 11th
|36\41, 1661.54 (1668.29)
|36\41, 1661.54
|Ff
|Ff
|21/8, 13/5
|21/8, 13/5
Line 997: Line 997:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 11th
|natural 11th
|37\41, 1709.69 (1714.63)
|37\41, 1709.69
|F
|F
|75/28, 8/3
|75/28, 8/3
Line 1,003: Line 1,003:
|-
|-
|augmented 11th
|augmented 11th
|38\41, 1753.85 (1760.98)
|38\41, 1753.85
|F#
|F#
|11/4, 36/13
|11/4, 36/13
Line 1,009: Line 1,009:
|-
|-
|doubly augmented 11th, doubly diminished 12th
|doubly augmented 11th, doubly diminished 12th
|39\41, 1800.00 (1807.32)
|39\41, 1800.00
|Fx, Gff
|Fx, Gff
|14/5, 20/7
|14/5, 20/7
Line 1,015: Line 1,015:
|-
|-
|diminished 12th
|diminished 12th
|40\41, 1846.15 (1853.66)
|40\41, 1846.15
|Gf
|Gf
|32/11, 26/9
|32/11, 26/9
Line 1,039: Line 1,039:
|-
|-
|chroma
|chroma
|3\35, 163.64 (162.86)
|3\35, 163.64
|G#
|G#
|[[12/11]], [[11/10]], [[10/9]]
|[[12/11]], [[11/10]], [[10/9]]
Line 1,045: Line 1,045:
|-
|-
|minor 2nd
|minor 2nd
|1\35, 54.545 (54.29)
|1\35, 54.545
|Hf
|Hf
|[[36/35]], [[34/33]], [[33/32]], [[32/31]]
|[[36/35]], [[34/33]], [[33/32]], [[32/31]]
Line 1,051: Line 1,051:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
|major 2nd
|4\35, 218.18 (217.14)
|4\35, 218.18
|H
|H
|[[9/8]], [[17/15]], [[8/7]]
|[[9/8]], [[17/15]], [[8/7]]
Line 1,057: Line 1,057:
|-
|-
|augmented 2nd
|augmented 2nd
|7\35, 381.818 (380.00)
|7\35, 381.82
|H#
|H#
|[[5/4]], [[96/77]]
|[[5/4]], [[96/77]]
Line 1,063: Line 1,063:
|-
|-
|diminished 3rd
|diminished 3rd
|2\35, 109.09 (108.57)
|2\35, 109.09
|Jff
|Jff
|[[18/17]], [[17/16]], [[16/15]], [[15/14]]
|[[18/17]], [[17/16]], [[16/15]], [[15/14]]
Line 1,069: Line 1,069:
|-
|-
|minor 3rd
|minor 3rd
|5\35, 272.73 (271.43)
|5\35, 272.73
|Jf
|Jf
|[[20/17]], [[7/6]]
|[[20/17]], [[7/6]]
Line 1,075: Line 1,075:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 3rd
|major 3rd
|8\35, 436.36 (434.29)
|8\35, 436.36
|J
|J
|[[14/11]], [[9/7]], [[22/17]]
|[[14/11]], [[9/7]], [[22/17]]
Line 1,081: Line 1,081:
|-
|-
|augmented 3rd
|augmented 3rd
|11\35, 600.00 (542.86)
|11\35, 600.00
|J#
|J#
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
Line 1,087: Line 1,087:
|-
|-
|diminished 4th
|diminished 4th
|6\35, 327.27 (325.71)
|6\35, 327.27
|Kff
|Kff
|[[6/5]], [[17/14]], [[11/9]]
|[[6/5]], [[17/14]], [[11/9]]
Line 1,093: Line 1,093:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
|natural 4th
|9\35, 490.91 (488.57)
|9\35, 490.91
|Kf
|Kf
|[[4/3]]
|[[4/3]]
Line 1,099: Line 1,099:
|-
|-
|augmented 4th
|augmented 4th
|12\35, 654.545 (651.43)
|12\35, 654.545
|K
|K
|[[16/11]], [[22/15]]
|[[16/11]], [[22/15]]
Line 1,105: Line 1,105:
|-
|-
|diminished 5th
|diminished 5th
|10\35, 545.455 (542.86)
|10\35, 545.455
|Lf
|Lf
|[[15/11]], [[11/8]]
|[[15/11]], [[11/8]]
Line 1,111: Line 1,111:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect 5th
|perfect 5th
|13\35, 709.09 (705.71)
|13\35, 709.09
|L
|L
|[[3/2]]
|[[3/2]]
Line 1,117: Line 1,117:
|-
|-
|augmented 5th
|augmented 5th
|16\35, 872.73 (868.57)
|16\35, 872.73
|L#
|L#
|[[18/11]], [[28/17]], [[5/3]]
|[[18/11]], [[28/17]], [[5/3]]
Line 1,123: Line 1,123:
|-
|-
|diminished 6th
|diminished 6th
|11\35, 600.00 (597.14)
|11\35, 600.00
|Aff
|Aff
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
|[[7/5]], [[24/17]], [[17/12]], [[10/7]]
Line 1,129: Line 1,129:
|-
|-
|minor 6th
|minor 6th
|14\35, 763.64 (760.00)
|14\35, 763.64
|Af
|Af
|[[17/11]], [[14/9]], [[11/7]]
|[[17/11]], [[14/9]], [[11/7]]
Line 1,135: Line 1,135:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 6th
|major 6th
|17\35, 927.27 (822.86)
|17\35, 927.27
|A
|A
|[[17/10]], [[12/7]]
|[[17/10]], [[12/7]]
Line 1,141: Line 1,141:
|-
|-
|augmented 6th
|augmented 6th
|20\35, 1090.909 (1085.71)
|20\35, 1090.91
|A#
|A#
|[[28/15]], [[15/8]], [[32/17]], [[17/9]]
|[[28/15]], [[15/8]], [[32/17]], [[17/9]]
Line 1,147: Line 1,147:
|-
|-
|diminished 7th
|diminished 7th
|15\35, 818.182 (814.29)
|15\35, 818.18
|Bff
|Bff
|[[8/5]], [[77/48]]
|[[8/5]], [[77/48]]
Line 1,153: Line 1,153:
|-
|-
|minor 7th
|minor 7th
|18/35, 981.82 (977.14)
|18/35, 981.82
|Bf
|Bf
|[[7/4]], [[30/17]], [[16/9]]
|[[7/4]], [[30/17]], [[16/9]]
Line 1,159: Line 1,159:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 7th
|major 7th
|21\35, 1145.455 (1140.00)
|21\35, 1145.455
|B
|B
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
Line 1,165: Line 1,165:
|-
|-
|augmented 7th
|augmented 7th
|24\35, 1309.09 (1302.86)
|24\35, 1309.09
|B#
|B#
|36/17, 17/8, 32/15, 15/7
|36/17, 17/8, 32/15, 15/7
Line 1,171: Line 1,171:
|-
|-
|diminished octave
|diminished octave
|19\22, 1036.36 (1031.43)
|19\22, 1036.36
|Cf
|Cf
|[[9/5]], [[11/6]], [[20/11]]
|[[9/5]], [[11/6]], [[20/11]]
Line 1,177: Line 1,177:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|22\35, 1200.00 (1194.29)
|22\35, 1200.00
|C
|C
|[[2/1]]
|[[2/1]]
Line 1,183: Line 1,183:
|-
|-
|augmented octave
|augmented octave
|25\35, 1363.64 (1357.14)
|25\35, 1363.64
|C#
|C#
|24/11, 11/5, 20/9
|24/11, 11/5, 20/9
Line 1,189: Line 1,189:
|-
|-
|minor 9th
|minor 9th
|23\35, 1254.55 (1248.57)
|23\35, 1254.545
|Df
|Df
|72/35, 68/33, 33/16, 64/31
|72/35, 68/33, 33/16, 64/31
Line 1,195: Line 1,195:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|26\35, 1418.18 (1411.43)
|26\35, 1418.18
|D
|D
|9/4, 34/15, 16/7
|9/4, 34/15, 16/7
Line 1,201: Line 1,201:
|-
|-
|augmented 9th
|augmented 9th
|29\35, 1581.81 (1574.29)
|29\35, 1581.81
|D#
|D#
|5/2, 192/77
|5/2, 192/77
Line 1,207: Line 1,207:
|-
|-
|diminished 10th
|diminished 10th
|24\35, 1309.09 (1302.86)
|24\35, 1309.09
|Eff
|Eff
|36/17, 17/8, 32/15, 15/7
|36/17, 17/8, 32/15, 15/7
Line 1,213: Line 1,213:
|-
|-
|minor 10th
|minor 10th
|27\35, 1472.72 (1465.71)
|27\35, 1472.72
|Ef
|Ef
|40/17, 7/3
|40/17, 7/3
Line 1,219: Line 1,219:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|30\35, 1636.36 (1628.57)
|30\35, 1636.36
|E
|E
|28/11, 18/7, 44/17
|28/11, 18/7, 44/17
Line 1,225: Line 1,225:
|-
|-
|augmented 10th
|augmented 10th
|33\35, 1800.00 (1791.43)
|33\35, 1800.00
|E#
|E#
|14/5, 48/17, 17/6, 20/7
|14/5, 48/17, 17/6, 20/7
Line 1,231: Line 1,231:
|-
|-
|diminished 11th
|diminished 11th
|28\35, 1527.27 (1520.00)
|28\35, 1527.27
|Ff
|Ff
|12/5, 17/7, 22/9
|12/5, 17/7, 22/9
Line 1,237: Line 1,237:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 11th
|natural 11th
|31\35, 1690.91 (1682.86)
|31\35, 1690.91
|F
|F
|8/3
|8/3
Line 1,243: Line 1,243:
|-
|-
|augmented 11th
|augmented 11th
|34\35, 1854.545 (1845.71)
|34\35, 1854.545
|F#
|F#
|32/11, 44/15
|32/11, 44/15
Line 1,249: Line 1,249:
|-
|-
|diminished 12th
|diminished 12th
|32\35, 1745.455 (1737.14)
|32\35, 1745.455
|Gf
|Gf
|30/11, 11/4
|30/11, 11/4
Line 1,550: Line 1,550:
! colspan="2" |Generator
! colspan="2" |Generator
!Normalized
!Normalized
!''ed19\12''
|-
|-
|3\8
|3\8
|
|
|<u>720</u>
|<u>720</u>
|''712.5''
|-
|-
|19\51
|19\51
|
|
|<u>712.5</u>
|<u>712.5</u>
|''707.843''
|-
|-
|
|
|35\94
|35\94
|<u>711.864</u>
|<u>711.864</u>
|''707.447''
|-
|-
|16\43
|16\43
|
|
|<u>711.111</u>
|<u>711.111</u>
|''706.977''
|-
|-
|
|
|29\78
|29\78
|<u>710.204</u>
|<u>710.204</u>
|''706.41''
|-
|-
|13\35
|13\35
|
|
|<u>709.091</u>
|<u>709.091</u>
|''705.714''
|-
|-
|
|
|36\97
|36\97
|<u>708.197</u>
|<u>708.197</u>
|705.155
|-
|-
|
|
|23\62
|23\62
|<u>707.692</u>
|<u>707.692</u>
|''704.839''
|-
|-
|
|
|33\89
|33\89
|<u>707.143</u>
|<u>707.143</u>
|''704.494''
|-
|-
|
|
|43\116
|43\116
|<u>706.849</u>
|<u>706.849</u>
|''704.31''
|-
|-
|10\27
|10\27
|
|
|<u>705.882</u>
|<u>705.882</u>
|''703.704''
|-
|-
|
|
|27\73
|27\73
|<u>704.348</u>
|<u>704.348</u>
|''702.738''
|-
|-
|
|
|17\46
|17\46
|<u>703.448</u>
|<u>703.448</u>
|''702.174''
|-
|-
|
|
|24\65
|24\65
|<u>702.439</u>
|<u>702.439</u>
|''701.5385''
|-
|-
|
|
|31\84
|31\84
|<u>701.887</u>
|<u>701.887</u>
|701.1905
|-
|-
|7\19
|7\19
|
|
|<u>700</u>
|<u>700</u>
|''700''
|-
|-
|
|
|60\163
|60\163
|<u>699.029</u>
|<u>699.029</u>
|''699.3865''
|-
|-
|
|
|53\144
|53\144
|<u>698.901</u>
|<u>698.901</u>
|''699.306''
|-
|-
|
|
|46\125
|46\125
|<u>698.734</u>
|<u>698.734</u>
|''699.2''
|-
|-
|
|
|39\106
|39\106
|<u>698.5075</u>
|<u>698.5075</u>
|''699.057''
|-
|-
|
|
|32\87
|32\87
|<u>698.182</u>
|<u>698.182</u>
|698.852
|-
|-
|
|
|25\68
|25\68
|<u>697.674</u>
|<u>697.674</u>
|''698.529''
|-
|-
|
|
|18\49
|18\49
|<u>696.77</u>
|<u>696.77</u>
|''697.959''
|-
|-
|
|
|29\79
|29\79
|<u>696</u>
|<u>696</u>
|''697.468''
|-
|-
|
|
|40\109
|40\109
|<u>695.652</u>
|<u>695.652</u>
|''697.248''
|-
|-
|11\30
|11\30
|
|
|<u>694.737</u>
|<u>694.737</u>
|''696.667''
|-
|-
|
|
|26\71
|26\71
|<u>693.333</u>
|<u>693.333</u>
|''695.775''
|-
|-
|15\41
|15\41
|
|
|<u>692.308</u>
|<u>692.308</u>
|''695.122''
|-
|-
|
|
|34\93
|34\93
|<u>691.525</u>
|<u>691.525</u>
|''694.623''
|-
|-
|19\52
|19\52
|
|
|<u>690.909</u>
|<u>690.909</u>
|''694.231''
|-
|-
|
|
|42\115
|42\115
|<u>690.411</u>
|<u>690.411</u>
|''693.913''
|-
|-
|23\63
|23\63
|
|
|<u>690</u>
|<u>690</u>
|''693.651''
|-
|-
|4\11
|4\11
|
|
|<u>685.714</u>
|<u>685.714</u>
|''690.909''
|}
|}


== See also ==
== See also ==
[[8L 3s (3/1-equivalent)]]
[[8L 3s (3/1-equivalent)]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/8L_3s_(perfect_twelfth-equivalent)"