User:Hkm/Interval categories: Difference between revisions

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The internal logic should be apparent. 9\72 or 1(6) + 3 \72, or any just interval which is reasonably mapped to that interval, could be called a neutral 2nd.
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!#
!
!/6
!
!%6
!
!Cents
!Approximate ratios
!name
!other names
|-
|-
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|0
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|0
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|0
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|0.0
|-
|1/1
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|unison
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|-
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|-
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|-
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|-
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|-
|-
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|1
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|0
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|1
|16.7
|81/80, 91/90, 99/98, 100/99, 105/104
|comma
|
|
|-
|-
|
|2
|
|0
|
|2
|33.3
|45/44, 49/48, 50/49, 55/54, 64/63
|sixth-tone
|
|
|-
|-
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|3
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|0
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|3
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|50.0
|-
|33/32, 36/35, 40/39
|
|quarter-tone
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|
|
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|-
|-
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|4
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|0
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|4
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|66.7
|25/24, 26/25, 27/26, 28/27
|subminor 2nd
|third-tone
|-
|-
|
|5
|
|0
|
|5
|83.3
|20/19, 21/20, 22/21
|neominor 2nd
|
|
|-
|-
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|6
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|1
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|0
|100.0
|17/16, 18/17, 19/18
|novaminor 2nd
|
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|-
|-
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|7
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|1
|
|1
|116.7
|15/14, 16/15
|pentaminor 2nd
|
|
|-
|-
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|8
|
|1
|
|2
|133.3
|13/12, 14/13, 27/25
|supraminor 2nd
|
|
|-
|-
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|9
|
|1
|
|3
|150.0
|12/11
|neutral 2nd
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|-
|-
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|10
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|1
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|4
|166.7
|11/10
|submajor 2nd
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|-
|-
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|11
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|1
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|5
|183.3
|10/9
|pentamajor 2nd
|
|
|-
|-
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|12
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|2
|
|0
|200.0
|9/8
|novamajor 2nd
|
|
|-
|-
|
|13
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|2
|
|1
|216.7
|17/15, 25/22
|neomajor 2nd
|
|
|-
|-
|
|14
|
|2
|
|2
|233.3
|8/7
|supermajor 2nd
|
|
|-
|-
|
|15
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|2
|
|3
|
|250.0
|15/13, 22/19
|2nd-3rd
|inframajor 2nd, inframinor 3rd
|-
|-
|
|16
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|2
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|4
|266.7
|7/6
|subminor 3nd
|
|
|-
|-
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|17
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|3
|
|5
|283.3
|13/11, 20/17
|neominor 3nd
|
|
|-
|-
|
|18
|
|3
|
|0
|300.0
|19/16, 25/21, 32/27
|novaminor 3nd
|
|
|-
|-
|
|19
|
|3
|
|1
|316.7
|6/5
|pentaminor 3nd
|
|
|-
|-
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|20
|
|3
|
|2
|333.3
|17/14, 39/32, 40/33
|supraminor 3nd
|
|
|-
|-
|
|21
|
|3
|
|3
|350.0
|11/9, 27/22
|neutral 3nd
|
|
|-
|-
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|22
|
|3
|
|4
|366.7
|16/13, 21/17, 26/21
|submajor 3nd
|
|
|-
|-
|
|23
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|3
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|5
|383.3
|5/4
|pentamajor 3nd
|
|
|-
|-
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|24
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|4
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|0
|400.0
|24/19
|novamajor 3nd
|
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|-
|-
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|25
|
|4
|
|1
|416.7
|14/11
|neomajor 3nd
|
|
|-
|-
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|26
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|4
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|2
|433.3
|9/7
|supermajor 3nd
|
|
|-
|-
|
|27
|
|4
|
|3
|
|450.0
|13/10, 22/17
|ultramajor 3rd
|3rd-4th, inframinor 4th
|-
|-
|
|28
|
|4
|
|4
|466.7
|17/13, 21/16
|sub 4th
|
|
|-
|-
|
|29
|
|4
|
|5
|483.3
|33/25
|neo 4th
|
|
|-
|-
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|30
|
|5
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|0
|500.0
|4/3
|clear 4th
|
|
|-
|-
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|31
|
|5
|
|1
|516.7
|27/20
|penta 4th
|
|
|-
|-
|
|32
|
|5
|
|2
|533.3
|15/11, 19/14, ''26/19''
|supra 4th
|
|
|-
|-
|
|33
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|5
|
|3
|550.0
|11/8
|neutral 4th
|
|
|-
|-
|
|34
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|5
|
|4
|566.7
|18/13, 25/18
|subaugmented 4th
|
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|-
|-
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|35
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|5
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|5
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|583.3
|7/5
|pentaugmented 4th
|small semioctave, neodiminished 5th
|-
|-
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|36
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|6
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|0
|
|600.0
|17/12, 24/17
|medium semioctave
|novaugmented 4th, novadiminished 5th
|-
|-
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|37
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|6
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|1
|
|616.7
|10/7
|pentadiminished 5th
|large semioctave, pentadiminished 5th
|-
|-
|
|38
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|6
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|2
|633.3
|13/9, 36/25
|supradiminished 5th
|
|
|-
|-
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|39
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|6
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|3
|650.0
|16/11
|neutral 5th
|
|
|-
|-
|
|40
|
|6
|
|4
|666.7
|''19/13'', 22/15, 28/19
|sub 5th
|
|
|-
|-
|
|41
|
|6
|
|5
|683.3
|40/27
|penta 5th
|
|
|-
|-
|
|42
|
|7
|
|0
|700.0
|3/2
|clear 5th
|
|
|-
|-
|
|43
|
|7
|
|1
|716.7
|50/33
|neo 5th
|
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|-
|-
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|44
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|7
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|2
|733.3
|26/17, 32/21
|super(major) 5th
|
|
|-
|-
|
|45
|
|7
|
|3
|
|750.0
|17/11, 20/13
|inframinor 6th
|5th-6th, ultramajor 5th
|-
|-
|
|46
|
|7
|
|4
|766.7
|14/9
|subminor 6th
|
|
|-
|-
|
|47
|
|7
|
|5
|783.3
|11/7
|neominor 6th
|
|
|-
|-
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|48
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|8
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|0
|
|800.0
|19/12
|etc.
|etc.
|-
|-
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|49
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|8
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|1
|
|816.7
|8/5
|etc.
|etc.
|-
|-
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|50
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|8
|2
|833.3
|13/8, 21/13, 34/21
|
|
|
|
|-
|-
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|51
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|8
|3
|850.0
|18/11, 44/27
|
|
|
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|-
|-
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|52
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|8
|4
|866.7
|28/17, 33/20, 64/39
|
|
|
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|-
|-
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|53
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|8
|5
|883.3
|5/3
|
|
|
|
|-
|-
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|54
|
|9
|0
|900.0
|27/16, 32/19, 42/25
|
|
|
|
|-
|-
|
|55
|
|9
|1
|916.7
|17/10, 22/13
|
|
|
|
|-
|-
|
|56
|
|9
|2
|933.3
|12/7
|
|
|
|
|-
|-
|
|57
|
|9
|3
|950.0
|19/11, 26/15
|
|
|
|
|-
|-
|
|58
|
|9
|4
|966.7
|7/4
|
|
|
|
|-
|-
|
|59
|
|9
|5
|983.3
|30/17, 44/25
|
|
|
|
|-
|-
|
|60
|
|10
|0
|1000.0
|16/9
|
|
|
|
|-
|-
|
|61
|
|10
|1
|1016.7
|9/5
|
|
|
|
|-
|-
|
|62
|
|10
|2
|1033.3
|20/11
|
|
|
|
|-
|-
|
|63
|
|10
|3
|1050.0
|11/6
|
|
|
|
|-
|-
|
|64
|
|10
|4
|1066.7
|13/7, 24/13, 50/27
|
|
|
|
|-
|-
|
|65
|
|10
|5
|1083.3
|15/8, 28/15
|
|
|
|
|-
|-
|66
|11
|0
|1100.0
|17/9, 32/17, 36/19
|
|
|
|
|
|
|-
|-
|
|67
|
|11
|1
|1116.7
|19/10, 21/11, 40/21
|
|
|
|
|-
|-
|
|68
|
|11
|2
|1133.3
|25/13, 27/14, 48/25, 52/27
|
|
|
|
|-
|-
|
|69
|
|11
|3
|1150.0
|35/18, 39/20, 64/33
|
|
|
|
|-
|-
|
|70
|
|11
|4
|1166.7
|49/25, 55/28, 63/32, 88/45, 96/49
|
|
|
|
|-
|-
|
|71
|
|11
|5
|1183.3
|99/50, 160/81, 180/91, 196/99, 208/105
|
|
|
|
|-
|-
|
|72
|
|12
|0
|1200.0
|2/1
|
|
|
|
|}
|}

Latest revision as of 18:43, 18 April 2025

The internal logic should be apparent. 9\72 or 1(6) + 3 \72, or any just interval which is reasonably mapped to that interval, could be called a neutral 2nd.

# /6 %6 Cents Approximate ratios name other names
0 0 0 0.0 1/1 unison
1 0 1 16.7 81/80, 91/90, 99/98, 100/99, 105/104 comma
2 0 2 33.3 45/44, 49/48, 50/49, 55/54, 64/63 sixth-tone
3 0 3 50.0 33/32, 36/35, 40/39 quarter-tone
4 0 4 66.7 25/24, 26/25, 27/26, 28/27 subminor 2nd third-tone
5 0 5 83.3 20/19, 21/20, 22/21 neominor 2nd
6 1 0 100.0 17/16, 18/17, 19/18 novaminor 2nd
7 1 1 116.7 15/14, 16/15 pentaminor 2nd
8 1 2 133.3 13/12, 14/13, 27/25 supraminor 2nd
9 1 3 150.0 12/11 neutral 2nd
10 1 4 166.7 11/10 submajor 2nd
11 1 5 183.3 10/9 pentamajor 2nd
12 2 0 200.0 9/8 novamajor 2nd
13 2 1 216.7 17/15, 25/22 neomajor 2nd
14 2 2 233.3 8/7 supermajor 2nd
15 2 3 250.0 15/13, 22/19 2nd-3rd inframajor 2nd, inframinor 3rd
16 2 4 266.7 7/6 subminor 3nd
17 3 5 283.3 13/11, 20/17 neominor 3nd
18 3 0 300.0 19/16, 25/21, 32/27 novaminor 3nd
19 3 1 316.7 6/5 pentaminor 3nd
20 3 2 333.3 17/14, 39/32, 40/33 supraminor 3nd
21 3 3 350.0 11/9, 27/22 neutral 3nd
22 3 4 366.7 16/13, 21/17, 26/21 submajor 3nd
23 3 5 383.3 5/4 pentamajor 3nd
24 4 0 400.0 24/19 novamajor 3nd
25 4 1 416.7 14/11 neomajor 3nd
26 4 2 433.3 9/7 supermajor 3nd
27 4 3 450.0 13/10, 22/17 ultramajor 3rd 3rd-4th, inframinor 4th
28 4 4 466.7 17/13, 21/16 sub 4th
29 4 5 483.3 33/25 neo 4th
30 5 0 500.0 4/3 clear 4th
31 5 1 516.7 27/20 penta 4th
32 5 2 533.3 15/11, 19/14, 26/19 supra 4th
33 5 3 550.0 11/8 neutral 4th
34 5 4 566.7 18/13, 25/18 subaugmented 4th
35 5 5 583.3 7/5 pentaugmented 4th small semioctave, neodiminished 5th
36 6 0 600.0 17/12, 24/17 medium semioctave novaugmented 4th, novadiminished 5th
37 6 1 616.7 10/7 pentadiminished 5th large semioctave, pentadiminished 5th
38 6 2 633.3 13/9, 36/25 supradiminished 5th
39 6 3 650.0 16/11 neutral 5th
40 6 4 666.7 19/13, 22/15, 28/19 sub 5th
41 6 5 683.3 40/27 penta 5th
42 7 0 700.0 3/2 clear 5th
43 7 1 716.7 50/33 neo 5th
44 7 2 733.3 26/17, 32/21 super(major) 5th
45 7 3 750.0 17/11, 20/13 inframinor 6th 5th-6th, ultramajor 5th
46 7 4 766.7 14/9 subminor 6th
47 7 5 783.3 11/7 neominor 6th
48 8 0 800.0 19/12 etc. etc.
49 8 1 816.7 8/5 etc. etc.
50 8 2 833.3 13/8, 21/13, 34/21
51 8 3 850.0 18/11, 44/27
52 8 4 866.7 28/17, 33/20, 64/39
53 8 5 883.3 5/3
54 9 0 900.0 27/16, 32/19, 42/25
55 9 1 916.7 17/10, 22/13
56 9 2 933.3 12/7
57 9 3 950.0 19/11, 26/15
58 9 4 966.7 7/4
59 9 5 983.3 30/17, 44/25
60 10 0 1000.0 16/9
61 10 1 1016.7 9/5
62 10 2 1033.3 20/11
63 10 3 1050.0 11/6
64 10 4 1066.7 13/7, 24/13, 50/27
65 10 5 1083.3 15/8, 28/15
66 11 0 1100.0 17/9, 32/17, 36/19
67 11 1 1116.7 19/10, 21/11, 40/21
68 11 2 1133.3 25/13, 27/14, 48/25, 52/27
69 11 3 1150.0 35/18, 39/20, 64/33
70 11 4 1166.7 49/25, 55/28, 63/32, 88/45, 96/49
71 11 5 1183.3 99/50, 160/81, 180/91, 196/99, 208/105
72 12 0 1200.0 2/1
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