List of anomalous saturated suspensions: Difference between revisions
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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. | Every chord has a plausible homonym. The alternate root is bolded in the scale. The Color Names column names the homonym for some of the chords. For example, the first chord Cg7 has as a homonym gEby6. | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 10:23, 24 February 2019
Below is a complete list of Anomalous Saturated Suspensions through the 23-limit. Each chord listed is either ambitonal or has a o/utonal inverse that is also an ASS.
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.
Every chord has a plausible homonym. The alternate root is bolded in the scale. The Color Names column names the homonym for some of the chords. For example, the first chord Cg7 has as a homonym gEby6.
| Formal name | Odd limit | Harmonic series | Scale | Color Name | Common name |
|---|---|---|---|---|---|
| A{9,1a} | 9 | 3:5:9:15 | 1/1 6/5 3/2 9/5 | g7 = y6 | Minor 7th Chord |
| A{9,2a} | 9 | 3:7:9:21 | 1/1 7/6 3/2 7/4 | z7 = r6 | Septimal Minor 7th Chord |
| A{11,1a} | 11 | 3:9:11:33 | 1/1 11/8 3/2 11/6 | 1o7(1o4) = 1u6(1u2) | |
| A{13,1a} | 13 | 3:9:13:39 | 1/1 13/12 3/2 13/8 | 3o6(3o2) = 3u7(3u4) | |
| A{15,1o} | 15 | 3:7:9:15:21 | 1/1 7/6 5/4 3/2 7/4 | h7,z10 = r6,ry9 | Hendrix |
| A{15,1u} | 15 | 15:21:35:45:105 | 1/1 7/6 7/5 3/2 7/4 | z7,zg5 = r6,g3 | Inverted Hendrix |
| A{15,2o} | 15 | 3:9:11:15:33 | 1/1 5/4 11/8 3/2 11/6 | y,1o7,1o11 = 1u6,1u9(1uy4) | 11-Hendrix |
| A{15,2u} | 15 | 15:33:45:55:165 | 1/1 11/10 11/8 3/2 11/6 | 1o7(1o4)1og9 = g,1u6,1u9 | Inverted 11-Hendrix |
| A{15,3o} | 15 | 3:9:13:15:39 | 1/1 13/12 5/4 3/2 13/8 | y,3o6,3o9 = 3u7(3u4)3uy9 | 13-Hendrix |
| A{15,3u} | 15 | 15:39:45:65:195 | 1/1 13/12 13/10 3/2 13/8 | 3o6,3o9(3og4) = g,3u7,3u11 | Inverted 13-Hendrix |
| A{17,1o} | 17 | 3:9:15:17:51 | 1/1 17/16 5/4 17/12 3/2 | y,17o9,17o12 | 17-Hendrix |
| A{17,1u} | 17 | 15:45:51:85:255 | 1/1 17/16 17/12 3/2 17/10 | 17og7(17o2)17o12 | Inverted 17-Hendrix |
| A{19,1o} | 19 | 3:9:15:19:57 | 1/1 19/16 5/4 3/2 19/12 | 19o6,y3 = 19u7,19uy5 | 19-Hendrix |
| A{19,1u} | 19 | 15:45:57:95:285 | 1/1 19/16 3/2 19/12 19/10 | 19o6,19og8 = 19u7,g3 | Inverted 19-Hendrix |
| A{21,1o} | 21 | 3:5:9:15:21:45 | 1/1 5/4 3/2 5/3 7/4 15/8 | y6,z7,y7 = g9,zg9 | |
| A{21,1u} | 21 | 7:15:21:35:63:105 | 1/1 15/14 9/8 5/4 3/2 15/8 | y9,ry8 = g7,g6,r6 | |
| A{21,2o} | 21 | 3:7:9:15:21:63 | 1/1 7/6 5/4 21/16 3/2 7/4 | h7,z10,z11 = r6,ry8,9 | Hendrix add11? |
| A{21,2u} | 21 | 5:15:21:35:45:105 | 1/1 21/20 9/8 21/16 3/2 7/4 | z9(z4)zg9 = r6,g3,r9 | |
| A{21,3o} | 21 | 3:9:11:15:21:33 | 1/1 5/4 11/8 3/2 7/4 11/6 | h7,1o7,1o11 | |
| A{21,3u} | 21 | 105:165:231:315:385:1155 | 1/1 12/11 6/5 3/2 18/11 12/7 | s6,1u6,1u9 | |
| A{21,4o} | 21 | 3:9:13:15:21:39 | 1/1 13/12 5/4 3/2 13/8 7/4 | h7,3o6,3o9 | |
| A{21,4u} | 21 | 105:195:273:315:455:1365 | 1/1 6/5 18/13 3/2 12/7 24/13 | s6,3u4,3u7 | |
| A{21,5o} | 21 | 3:9:15:17:21:51 | 1/1 17/16 5/4 17/12 3/2 7/4 | h7,17o9,17o12 | dom7b9#11 |
| A{21,5u} | 21 | 105:255:315:357:595:1785 | 1/1 18/17 6/5 24/17 3/2 12/7 | s6,17u8,17u11 | min6b9#11 |
| A{21,6o} | 21 | 3:9:15:19:21:57 | 1/1 19/16 5/4 3/2 19/12 7/4 | 19o6,y3,z7 | dom7#9b13 |
| A{21,6u} | 21 | 105:285:315:399:665:1995 | 1/1 6/5 24/19 3/2 12/7 36/19 | 19u7,g3,r6 | maj7#9,13 |
| A{23,1o} | 23 | 3:9:15:21:23:69 | 1/1 5/4 23/16 3/2 7/4 23/12 | h7,23o5,23o8 | |
| A{23,1u} | 23 | 105:315:345:483:805:2415 | 1/1 24/23 6/5 3/2 36/23 12/7 | s6,23u5,23u8 |