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List of anomalous saturated suspensions: Difference between revisions

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==Formal names==
==Formal names==
For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal.
For each odd limit we can list ambitonal chords in lexicographic order by harmonic series representation, along with o/utonal chord pairs according to the harmonic series representation of the otonal chord in the pair. Each chord is then designated by a capital "A" whose subscript is a tuple, where the first value is its odd limit and the second value is its index in the list for that odd limit. This is followed by an "a," "o," or "u" depending on whether the chord is ambitonal, otonal, or utonal.
Every chord has a plausible homonym. The alternate root is bolded in the scale. The Color Names column names the homonym for some chords.


{| class="wikitable"
{| class="wikitable"
Line 10: Line 12:
! | Harmonic series
! | Harmonic series
! | Scale
! | Scale
![[Color notation|Color Name]]
! | Common name
! | Common name
|-
|-
Line 15: Line 18:
| | 9
| | 9
| | 3:5:9:15
| | 3:5:9:15
| | 1/1 6/5 3/2 9/5
| | 1/1 '''6/5''' 3/2 9/5
|g7 = y6
| | Minor 7th Chord
| | Minor 7th Chord
|-
|-
Line 21: Line 25:
| | 9
| | 9
| | 3:7:9:21
| | 3:7:9:21
| | 1/1 7/6 3/2 7/4
| | 1/1 '''7/6''' 3/2 7/4
|z7 = r6
| | Septimal Minor 7th Chord
| | Septimal Minor 7th Chord
|-
|-
Line 27: Line 32:
| | 11
| | 11
| | 3:9:11:33
| | 3:9:11:33
| | 1/1 11/8 3/2 11/6
| | 1/1 11/8 3/2 '''11/6'''
|1o7(1o4) = 1u6(1u2)
| |  
| |  
|-
|-
Line 33: Line 39:
| | 13
| | 13
| | 3:9:13:39
| | 3:9:13:39
| | 1/1 13/12 3/2 13/8
| | 1/1 '''13/12''' 3/2 13/8
|3o6(3o2) = 3u7(3u4)
| |  
| |  
|-
|-
Line 39: Line 46:
| | 15
| | 15
| | 3:7:9:15:21
| | 3:7:9:15:21
| | 1/1 7/6 5/4 3/2 7/4
| | 1/1 '''7/6''' 5/4 3/2 7/4
|h7,z10 = r6,ry9
| | Hendrix
| | Hendrix
|-
|-
Line 45: Line 53:
| | 15
| | 15
| | 15:21:35:45:105
| | 15:21:35:45:105
| | 1/1 7/6 7/5 3/2 7/4
| | 1/1 '''7/6''' 7/5 3/2 7/4
|z7,zg5 = r6,g3
| | Inverted Hendrix
| | Inverted Hendrix
|-
|-
Line 51: Line 60:
| | 15
| | 15
| | 3:9:11:15:33
| | 3:9:11:15:33
| | 1/1 5/4 11/8 3/2 11/6
| | 1/1 5/4 11/8 3/2 '''11/6'''
|y,1o7,1o11 = 1u6,1u9(1uy4)
| | 11-Hendrix
| | 11-Hendrix
|-
|-
Line 57: Line 67:
| | 15
| | 15
| | 15:33:45:55:165
| | 15:33:45:55:165
| | 1/1 11/10 11/8 3/2 11/6
| | 1/1 11/10 11/8 3/2 '''11/6'''
|1o7(1o4)1og9 = g,1u6,1u9
| | Inverted 11-Hendrix
| | Inverted 11-Hendrix
|-
|-
Line 63: Line 74:
| | 15
| | 15
| | 3:9:13:15:39
| | 3:9:13:15:39
| | 1/1 13/12 5/4 3/2 13/8
| | 1/1 '''13/12''' 5/4 3/2 13/8
|y,3o6,3o9 = 3u7(3u4)3uy9
| | 13-Hendrix
| | 13-Hendrix
|-
|-
Line 69: Line 81:
| | 15
| | 15
| | 15:39:45:65:195
| | 15:39:45:65:195
| | 1/1 13/12 13/10 3/2 13/8
| | 1/1 '''13/12''' 13/10 3/2 13/8
|3o6,3o9(3og4) = g,3u7,3u11
| | Inverted 13-Hendrix
| | Inverted 13-Hendrix
|-
|-
Line 75: Line 88:
| | 17
| | 17
| | 3:9:15:17:51
| | 3:9:15:17:51
| | 1/1 17/16 5/4 17/12 3/2
| | 1/1 17/16 5/4 '''17/12''' 3/2
|y,17o9,17o12
| | 17-Hendrix
| | 17-Hendrix
|-
|-
Line 81: Line 95:
| | 17
| | 17
| | 15:45:51:85:255
| | 15:45:51:85:255
| | 1/1 17/16 17/12 3/2 17/10
| | 1/1 17/16 '''17/12''' 3/2 17/10
|17og7(17o2)17o12
| | Inverted 17-Hendrix
| | Inverted 17-Hendrix
|-
|-
Line 87: Line 102:
| | 19
| | 19
| | 3:9:15:19:57
| | 3:9:15:19:57
| | 1/1 19/16 5/4 3/2 19/12
| | 1/1 19/16 5/4 3/2 '''19/12'''
|19o6,y3 = 19u7,19uy5
| | 19-Hendrix
| | 19-Hendrix
|-
|-
Line 93: Line 109:
| | 19
| | 19
| | 15:45:57:95:285
| | 15:45:57:95:285
| | 1/1 19/16 3/2 19/12 19/10
| | 1/1 19/16 3/2 '''19/12''' 19/10
|19o6,19og8 = 19u7,g3
| | Inverted 19-Hendrix
| | Inverted 19-Hendrix
|-
|-
Line 99: Line 116:
| | 21
| | 21
| | 3:5:9:15:21:45
| | 3:5:9:15:21:45
| | 1/1 15/14 9/8 9/7 3/2 12/7
| |1/1 5/4 3/2 '''5/3''' 7/4 15/8
| |  
|y6,z7,y7 = g9,zg9
| |
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,1u}</span>
| | '''A'''<span style="vertical-align: sub;">{21,1u}</span>
| | 21
| | 21
| | 7:15:21:35:63:105
| | 7:15:21:35:63:105
| | 1/1 15/14 9/8 5/4 3/2 15/8
| | 1/1 15/14 9/8 '''5/4''' 3/2 15/8
| |  
|y9,ry8 = g7,g6,r6
| |
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,2o}</span>
| | '''A'''<span style="vertical-align: sub;">{21,2o}</span>
| | 21
| | 21
| | 3:7:9:15:21:63
| | 3:7:9:15:21:63
| | 1/1 21/20 9/8 6/5 3/2 9/5
| |1/1 '''7/6''' 5/4 21/16 3/2 7/4
| |  
|h7,z10,z11 = r6,ry8,9
| |Hendrix add11?
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,2u}</span>
| | '''A'''<span style="vertical-align: sub;">{21,2u}</span>
| | 21
| | 21
| | 5:15:21:35:45:105
| | 5:15:21:35:45:105
| | 1/1 21/20 9/8 21/16 3/2 7/4
| | 1/1 21/20 9/8 21/16 3/2 '''7/4'''
|z9(z4)zg9 = r6,g3,r9
| |  
| |  
|-
|-
Line 123: Line 144:
| | 21
| | 21
| | 3:9:11:15:21:33
| | 3:9:11:15:21:33
| | 1/1 5/4 11/8 3/2 7/4 11/6
| | 1/1 5/4 11/8 3/2 7/4 '''11/6'''
|h7,1o7,1o11
| |  
| |  
|-
|-
Line 129: Line 151:
| | 21
| | 21
| | 105:165:231:315:385:1155
| | 105:165:231:315:385:1155
| | 1/1 12/11 6/5 3/2 18/11 12/7
| | 1/1 '''12/11''' 6/5 3/2 18/11 12/7
|s6,1u6,1u9
| |  
| |  
|-
|-
Line 135: Line 158:
| | 21
| | 21
| | 3:9:13:15:21:39
| | 3:9:13:15:21:39
| | 1/1 13/12 5/4 3/2 13/8 7/4
| | 1/1 '''13/12''' 5/4 3/2 13/8 7/4
|h7,3o6,3o9
| |  
| |  
|-
|-
Line 141: Line 165:
| | 21
| | 21
| | 105:195:273:315:455:1365
| | 105:195:273:315:455:1365
| | 1/1 6/5 18/13 3/2 12/7 24/13
| | 1/1 6/5 18/13 3/2 12/7 '''24/13'''
| |  
|s6,3u4,3u7
| |
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,5o}</span>
| | '''A'''<span style="vertical-align: sub;">{21,5o}</span>
| | 21
| | 21
| | 3:9:15:17:21:51
| | 3:9:15:17:21:51
| | 1/1 17/16 5/4 17/12 3/2 7/4
| | 1/1 17/16 5/4 '''17/12''' 3/2 7/4
| |  
|h7,17o9,17o12
| |dom7b9#11
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,5u}</span>
| | '''A'''<span style="vertical-align: sub;">{21,5u}</span>
| | 21
| | 21
| | 105:255:315:357:595:1785
| | 105:255:315:357:595:1785
| | 1/1 18/17 6/5 24/17 3/2 12/7
| | 1/1 18/17 6/5 '''24/17''' 3/2 12/7
| |  
|s6,17u8,17u11
| |min6b9#11
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,6o}</span>
| | '''A'''<span style="vertical-align: sub;">{21,6o}</span>
| | 21
| | 21
| | 3:9:15:19:21:57
| | 3:9:15:19:21:57
| | 1/1 19/16 5/4 3/2 19/12 7/4
| | 1/1 19/16 5/4 3/2 '''19/12''' 7/4
| |  
|19o6,y3,z7
| |dom7#9b13
|-
|-
| | '''A'''<span style="vertical-align: sub;">{21,6u}</span>
| | '''A'''<span style="vertical-align: sub;">{21,6u}</span>
| | 21
| | 21
| | 105:285:315:399:665:1995
| | 105:285:315:399:665:1995
| | 1/1 6/5 24/19 3/2 12/7 36/19
| | 1/1 6/5 '''24/19''' 3/2 12/7 36/19
| |  
|19u7,g3,r6
| |maj7#9,13
|-
|-
| | '''A'''<span style="vertical-align: sub;">{23,1o}</span>
| | '''A'''<span style="vertical-align: sub;">{23,1o}</span>
| | 23
| | 23
| | 3:9:15:21:23:69
| | 3:9:15:21:23:69
| | 1/1 5/4 23/16 3/2 7/4 23/12
| | 1/1 5/4 23/16 3/2 7/4 '''23/12'''
|h7,23o5,23o8
| |  
| |  
|-
|-
Line 177: Line 207:
| | 23
| | 23
| | 105:315:345:483:805:2415
| | 105:315:345:483:805:2415
| | 1/1 24/23 6/5 3/2 36/23 12/7
| | 1/1 '''24/23''' 6/5 3/2 36/23 12/7
|s6,23u5,23u8
| |  
| |  
|}
|}
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