List of anomalous saturated suspensions: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>FREEZE No edit summary |
m formatting, category |
||
| Line 1: | Line 1: | ||
Below is a complete list of [http://x31eq.com/ass.htm Anomalous Saturated Suspensions] through the 23-limit. Each chord listed is either ambitonal or has a [[Otonality_and_utonality|o/utonal]] inverse that is also an ASS. | Below is a complete list of [http://x31eq.com/ass.htm Anomalous Saturated Suspensions] through the 23-limit. Each chord listed is either [[Otonality_and_utonality|ambitonal]] or has a [[Otonality_and_utonality|o/utonal]] inverse that is also an ASS. | ||
==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. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| | ! | Formal name | ||
| | ! | Odd limit | ||
| | ! | Harmonic series | ||
| | ! | Scale | ||
| | ! | Common name | ||
|- | |- | ||
| | '''A'''<span style="vertical-align: sub;">{9,1a}</span> | | | '''A'''<span style="vertical-align: sub;">{9,1a}</span> | ||
| Line 181: | Line 180: | ||
| | | | | | ||
|} | |} | ||
[[category:todo:add definition]] | |||
[[category:chord]] | |||
[[category:ass]] | |||
Revision as of 22:52, 10 December 2018
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.
| Formal name | Odd limit | Harmonic series | Scale | Common name |
|---|---|---|---|---|
| A{9,1a} | 9 | 3:5:9:15 | 1/1 6/5 3/2 9/5 | Minor 7th Chord |
| A{9,2a} | 9 | 3:7:9:21 | 1/1 7/6 3/2 7/4 | Septimal Minor 7th Chord |
| A{11,1a} | 11 | 3:9:11:33 | 1/1 11/8 3/2 11/6 | |
| A{13,1a} | 13 | 3:9:13:39 | 1/1 13/12 3/2 13/8 | |
| A{15,1o} | 15 | 3:7:9:15:21 | 1/1 7/6 5/4 3/2 7/4 | Hendrix |
| A{15,1u} | 15 | 15:21:35:45:105 | 1/1 7/6 7/5 3/2 7/4 | Inverted Hendrix |
| A{15,2o} | 15 | 3:9:11:15:33 | 1/1 5/4 11/8 3/2 11/6 | 11-Hendrix |
| A{15,2u} | 15 | 15:33:45:55:165 | 1/1 11/10 11/8 3/2 11/6 | Inverted 11-Hendrix |
| A{15,3o} | 15 | 3:9:13:15:39 | 1/1 13/12 5/4 3/2 13/8 | 13-Hendrix |
| A{15,3u} | 15 | 15:39:45:65:195 | 1/1 13/12 13/10 3/2 13/8 | Inverted 13-Hendrix |
| A{17,1o} | 17 | 3:9:15:17:51 | 1/1 17/16 5/4 17/12 3/2 | 17-Hendrix |
| A{17,1u} | 17 | 15:45:51:85:255 | 1/1 17/16 17/12 3/2 17/10 | Inverted 17-Hendrix |
| A{19,1o} | 19 | 3:9:15:19:57 | 1/1 19/16 5/4 3/2 19/12 | 19-Hendrix |
| A{19,1u} | 19 | 15:45:57:95:285 | 1/1 19/16 3/2 19/12 19/10 | Inverted 19-Hendrix |
| A{21,1o} | 21 | 3:5:9:15:21:45 | 1/1 15/14 9/8 9/7 3/2 12/7 | |
| A{21,1u} | 21 | 7:15:21:35:63:105 | 1/1 15/14 9/8 5/4 3/2 15/8 | |
| A{21,2o} | 21 | 3:7:9:15:21:63 | 1/1 21/20 9/8 6/5 3/2 9/5 | |
| A{21,2u} | 21 | 5:15:21:35:45:105 | 1/1 21/20 9/8 21/16 3/2 7/4 | |
| A{21,3o} | 21 | 3:9:11:15:21:33 | 1/1 5/4 11/8 3/2 7/4 11/6 | |
| A{21,3u} | 21 | 105:165:231:315:385:1155 | 1/1 12/11 6/5 3/2 18/11 12/7 | |
| A{21,4o} | 21 | 3:9:13:15:21:39 | 1/1 13/12 5/4 3/2 13/8 7/4 | |
| A{21,4u} | 21 | 105:195:273:315:455:1365 | 1/1 6/5 18/13 3/2 12/7 24/13 | |
| A{21,5o} | 21 | 3:9:15:17:21:51 | 1/1 17/16 5/4 17/12 3/2 7/4 | |
| A{21,5u} | 21 | 105:255:315:357:595:1785 | 1/1 18/17 6/5 24/17 3/2 12/7 | |
| A{21,6o} | 21 | 3:9:15:19:21:57 | 1/1 19/16 5/4 3/2 19/12 7/4 | |
| A{21,6u} | 21 | 105:285:315:399:665:1995 | 1/1 6/5 24/19 3/2 12/7 36/19 | |
| A{23,1o} | 23 | 3:9:15:21:23:69 | 1/1 5/4 23/16 3/2 7/4 23/12 | |
| A{23,1u} | 23 | 105:315:345:483:805:2415 | 1/1 24/23 6/5 3/2 36/23 12/7 |