|
This user page is editable by any wiki editor.
As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages.
However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits).
|
This page lists all 11-odd-limit dyadic chords of 11-limit pajara temperament. Each chord listed has multiple inversions; only one is listed, that being the inversion where all notes are a nonnegative number of perfect fifth generators above the root or semioctave, which may not be the optimal voicing of the chord. Note that there are many common chords, such as the classical major seventh chord with ratios 8:10:12:15, which are not listed; in this case because 15/8 is not a ratio of the 11-odd-limit.
If a chord is essentially just, then it is classified as otonal if it is best analyzed in terms of the harmonic series, utonal if best analyzed in terms of the subharmonic series, and ambitonal if it is equally well analyzed with either. If a chord is essentially tempered, it is classified based on which commas are needed to define the chord. Chords essentially tempered by 50/49 are labeled jubilismic, by 64/63 archytas, by 99/98 mothwellsmic, by 100/99 ptolemismic, by 176/175 valinorsmic, by 225/224 marvel, and by 896/891 pentacircle. Chords that require any two of 50/49, 64/63, and 225/224 to vanish are labeled (placeholder), and chords that require any two of 50/49, 99/98, and 100/99 to vanish are labeled jubilee. Chords that require any two of 64/63, 99/98, and 896/891 to vanish are labeled supra (placeholder), and chords that require any two of 64/63, 100/99, and 176/175 to vanish are labeled ares. Chords that require any two of 99/98, 176/175, and 225/224 to vanish are labeled minerva, and chords that require any two of 100/99, 225/224, and 896/891 to vanish are labeled apollo. Finally, chords that require any three independent commas listed above to vanish are labeled pajara.
- Please review essential tempering types
Triads
| #
|
Generators
|
Transversal
|
Type
|
Comments
|
| 1
|
0–0'–2
|
1–8/7–7/5
|
|
|
| 2
|
0–1–2
|
1–8/7–3/2
|
|
|
| 3
|
0–0'–2'
|
1–7/5–8/5
|
|
|
| 4
|
0–2–2'
|
1–8/7–8/5
|
|
|
| 5
|
0–0'–3
|
1–7/5–12/7
|
|
|
| 6
|
0–1–3
|
1–3/2–12/7
|
|
|
| 7
|
0–2–3
|
1–8/7–12/7
|
|
|
| 8
|
0–0'–3'
|
1–6/5–7/5
|
|
|
| 9
|
0–1–3'
|
1–6/5–3/2
|
|
|
| 10
|
0–2'–3'
|
1–6/5–8/5
|
|
|
| 11
|
0–3–3'
|
1–6/5–12/7
|
|
|
| 12
|
0–0'–4
|
1–9/7–7/5
|
|
|
| 13
|
0–1–4
|
1–9/7–3/2
|
|
|
| 14
|
0–2–4
|
1–8/7–9/7
|
|
|
| 15
|
0–2'–4
|
1–9/7–8/5
|
|
|
| 16
|
0–3–4
|
1–9/7–12/7
|
|
|
| 17
|
0–0'–4'
|
1–7/5–9/5
|
|
|
| 18
|
0–1–4'
|
1–3/2–9/5
|
|
|
| 19
|
0–2–4'
|
1–8/7–9/5
|
|
|
| 20
|
0–2'–4'
|
1–8/5–9/5
|
|
|
| 21
|
0–3'–4'
|
1–6/5–9/5
|
|
|
| 22
|
0–4–4'
|
1–9/7–9/5
|
|
|
| 23
|
0–2–6
|
1–8/7–16/11
|
|
|
| 24
|
0–2'–6
|
1–16/11–8/5
|
|
|
| 25
|
0–3–6
|
1–16/11–12/7
|
|
|
| 26
|
0–3'–6
|
1–6/5–16/11
|
|
|
| 27
|
0–4–6
|
1–9/7–16/11
|
|
|
| 28
|
0–4'–6
|
1–16/11–9/5
|
|
|
| 29
|
0–1–7
|
1–12/11–3/2
|
|
|
| 30
|
0–3–7
|
1–12/11–12/7
|
|
|
| 31
|
0–3'–7
|
1–12/11–6/5
|
|
|
| 32
|
0–4–7
|
1–12/11–9/7
|
|
|
| 33
|
0–4'–7
|
1–12/11–9/5
|
|
|
| 34
|
0–6–7
|
1–12/11–16/11
|
|
|
| 35
|
0–1–8
|
1–3/2–18/11
|
|
|
| 36
|
0–2–8
|
1–8/7–18/11
|
|
|
| 37
|
0–4–8
|
1–9/7–18/11
|
|
|
| 38
|
0–4'–8
|
1–18/11–9/5
|
|
|
| 39
|
0–6–8
|
1–16/11–18/11
|
|
|
| 40
|
0–7–8
|
1–12/11–18/11
|
|
|
Tetrads
| #
|
Generators
|
Transversal
|
Type
|
Comments
|
| 1
|
0–0'–2–2'
|
1–8/7–7/5–8/5
|
|
|
| 2
|
0–0'–2–3
|
1–8/7–7/5–12/7
|
|
|
| 3
|
0–1–2–3
|
1–8/7–3/2–12/7
|
|
|
| 4
|
0–0'–2'–3'
|
1–6/5–7/5–8/5
|
|
|
| 5
|
0–0'–3–3'
|
1–6/5–7/5–12/7
|
|
|
| 6
|
0–1–3–3'
|
1–6/5–3/2–12/7
|
|
|
| 7
|
0–0'–2–4
|
1–8/7–9/7–7/5
|
|
|
| 8
|
0–1–2–4
|
1–8/7–9/7–3/2
|
|
|
| 9
|
0–0'–2'–4
|
1–9/7–7/5–8/5
|
|
|
| 10
|
0–2–2'–4
|
1–8/7–9/7–8/5
|
|
|
| 11
|
0–0'–3–4
|
1–9/7–7/5–12/7
|
|
|
| 12
|
0–1–3–4
|
1–9/7–3/2–12/7
|
|
|
| 13
|
0–2–3–4
|
1–8/7–9/7–12/7
|
|
|
| 14
|
0–0'–2–4'
|
1–8/7–7/5–9/5
|
|
|
| 15
|
0–1–2–4'
|
1–8/7–3/2–9/5
|
|
|
| 16
|
0–0'–2'–4'
|
1–7/5–8/5–9/5
|
|
|
| 17
|
0–2–2'–4'
|
1–8/7–8/5–9/5
|
|
|
| 18
|
0–0'–3'–4'
|
1–6/5–7/5–9/5
|
|
|
| 19
|
0–1–3'–4'
|
1–6/5–3/2–9/5
|
|
|
| 20
|
0–2'–3'–4'
|
1–6/5–8/5–9/5
|
|
|
| 21
|
0–0'–4–4'
|
1–9/7–7/5–9/5
|
|
|
| 22
|
0–1–4–4'
|
1–9/7–3/2–9/5
|
|
|
| 23
|
0–2–4–4'
|
1–8/7–9/7–9/5
|
|
|
| 24
|
0–2'–4–4'
|
1–9/7–8/5–9/5
|
|
|
| 25
|
0–2–2'–6
|
1–8/7–16/11–8/5
|
|
|
| 26
|
0–2–3–6
|
1–8/7–16/11–12/7
|
|
|
| 27
|
0–2'–3'–6
|
1–6/5–16/11–8/5
|
|
|
| 28
|
0–3–3'–6
|
1–6/5–16/11–12/7
|
|
|
| 29
|
0–2–4–6
|
1–8/7–9/7–16/11
|
|
|
| 30
|
0–2'–4–6
|
1–9/7–16/11–8/5
|
|
|
| 31
|
0–3–4–6
|
1–9/7–16/11–12/7
|
|
|
| 32
|
0–2–4'–6
|
1–8/7–16/11–9/5
|
|
|
| 33
|
0–2'–4'–6
|
1–16/11–8/5–9/5
|
|
|
| 34
|
0–3'–4'–6
|
1–6/5–16/11–9/5
|
|
|
| 35
|
0–4–4'–6
|
1–9/7–16/11–9/5
|
|
|
| 36
|
0–1–3–7
|
1–12/11–3/2–12/7
|
|
|
| 37
|
0–1–3'–7
|
1–12/11–6/5–3/2
|
|
|
| 38
|
0–3–3'–7
|
1–12/11–6/5–12/7
|
|
|
| 39
|
0–1–4–7
|
1–12/11–9/7–3/2
|
|
|
| 40
|
0–3–4–7
|
1–12/11–9/7–12/7
|
|
|
| 41
|
0–1–4'–7
|
1–12/11–3/2–9/5
|
|
|
| 42
|
0–3'–4'–7
|
1–12/11–6/5–9/5
|
|
|
| 43
|
0–4–4'–7
|
1–12/11–9/7–9/5
|
|
|
| 44
|
0–3–6–7
|
1–12/11–16/11–12/7
|
|
|
| 45
|
0–3'–6–7
|
1–12/11–6/5–16/11
|
|
|
| 46
|
0–4–6–7
|
1–12/11–9/7–16/11
|
|
|
| 47
|
0–4'–6–7
|
1–12/11–16/11–9/5
|
|
|
| 48
|
0–1–2–8
|
1–8/7–3/2–18/11
|
|
|
| 49
|
0–1–4–8
|
1–9/7–3/2–18/11
|
|
|
| 50
|
0–2–4–8
|
1–8/7–9/7–18/11
|
|
|
| 51
|
0–1–4'–8
|
1–3/2–18/11–9/5
|
|
|
| 52
|
0–2–4'–8
|
1–8/7–18/11–9/5
|
|
|
| 53
|
0–4–4'–8
|
1–9/7–18/11–9/5
|
|
|
| 54
|
0–2–6–8
|
1–8/7–16/11–18/11
|
|
|
| 55
|
0–4–6–8
|
1–9/7–16/11–18/11
|
|
|
| 56
|
0–4'–6–8
|
1–16/11–18/11–9/5
|
|
|
| 57
|
0–1–7–8
|
1–12/11–3/2–18/11
|
|
|
| 58
|
0–4–7–8
|
1–12/11–9/7–18/11
|
|
|
| 59
|
0–4'–7–8
|
1–12/11–18/11–9/5
|
|
|
| 60
|
0–6–7–8
|
1–12/11–16/11–18/11
|
|
|
Pentads
| #
|
Generators
|
Transversal
|
Type
|
Comments
|
| 1
|
0–0'–2–2'–4
|
1–8/7–9/7–7/5–8/5
|
|
|
| 2
|
0–0'–2–3–4
|
1–8/7–9/7–7/5–12/7
|
|
|
| 3
|
0–1–2–3–4
|
1–8/7–9/7–3/2–12/7
|
|
|
| 4
|
0–0'–2–2'–4'
|
1–8/7–7/5–8/5–9/5
|
|
|
| 5
|
0–0'–2'–3'–4'
|
1–6/5–7/5–8/5–9/5
|
|
|
| 6
|
0–0'–2–4–4'
|
1–8/7–9/7–7/5–9/5
|
|
|
| 7
|
0–1–2–4–4'
|
1–8/7–9/7–3/2–9/5
|
|
|
| 8
|
0–0'–2'–4–4'
|
1–9/7–7/5–8/5–9/5
|
|
|
| 9
|
0–2–2'–4–4'
|
1–8/7–9/7–8/5–9/5
|
|
|
| 10
|
0–2–2'–4–6
|
1–8/7–9/7–16/11–8/5
|
|
|
| 11
|
0–2–3–4–6
|
1–8/7–9/7–16/11–12/7
|
|
|
| 12
|
0–2–2'–4'–6
|
1–8/7–16/11–8/5–9/5
|
|
|
| 13
|
0–2'–3'–4'–6
|
1–6/5–16/11–8/5–9/5
|
|
|
| 14
|
0–2–4–4'–6
|
1–8/7–9/7–16/11–9/5
|
|
|
| 15
|
0–2'–4–4'–6
|
1–9/7–16/11–8/5–9/5
|
|
|
| 16
|
0–1–3–3'–7
|
1–12/11–6/5–3/2–12/7
|
|
|
| 17
|
0–1–3–4–7
|
1–12/11–9/7–3/2–12/7
|
|
|
| 18
|
0–1–3'–4'–7
|
1–12/11–6/5–3/2–9/5
|
|
|
| 19
|
0–1–4–4'–7
|
1–12/11–9/7–3/2–9/5
|
|
|
| 20
|
0–3–3'–6–7
|
1–12/11–6/5–16/11–12/7
|
|
|
| 21
|
0–3–4–6–7
|
1–12/11–9/7–16/11–12/7
|
|
|
| 22
|
0–3'–4'–6–7
|
1–12/11–6/5–16/11–9/5
|
|
|
| 23
|
0–4–4'–6–7
|
1–12/11–9/7–16/11–9/5
|
|
|
| 24
|
0–1–2–4–8
|
1–8/7–9/7–3/2–18/11
|
|
|
| 25
|
0–1–2–4'–8
|
1–8/7–3/2–18/11–9/5
|
|
|
| 26
|
0–1–4–4'–8
|
1–9/7–3/2–18/11–9/5
|
|
|
| 27
|
0–2–4–4'–8
|
1–8/7–9/7–18/11–9/5
|
|
|
| 28
|
0–2–4–6–8
|
1–8/7–9/7–16/11–18/11
|
|
|
| 29
|
0–2–4'–6–8
|
1–8/7–16/11–18/11–9/5
|
|
|
| 30
|
0–4–4'–6–8
|
1–9/7–16/11–18/11–9/5
|
|
|
| 31
|
0–1–4–7–8
|
1–12/11–9/7–3/2–18/11
|
|
|
| 32
|
0–1–4'–7–8
|
1–12/11–3/2–18/11–9/5
|
|
|
| 33
|
0–4–4'–7–8
|
1–12/11–9/7–18/11–9/5
|
|
|
| 34
|
0–4–6–7–8
|
1–12/11–9/7–16/11–18/11
|
|
|
| 35
|
0–4'–6–7–8
|
1–12/11–16/11–18/11–9/5
|
|
|
Hexads
| #
|
Generators
|
Transversal
|
Type
|
Comments
|
| 1
|
0–0'–2–2'–4–4'
|
1–8/7–9/7–7/5–8/5–9/5
|
|
|
| 2
|
0–2–2'–4–4'–6
|
1–8/7–9/7–16/11–8/5–9/5
|
|
|
| 3
|
0–1–2–4–4'–8
|
1–8/7–9/7–3/2–18/11–9/5
|
|
|
| 4
|
0–2–4–4'–6–8
|
1–8/7–9/7–16/11–18/11–9/5
|
|
|
| 5
|
0–1–4–4'–7–8
|
1–12/11–9/7–3/2–18/11–9/5
|
|
|
| 6
|
0–4–4'–6–7–8
|
1–12/11–9/7–16/11–18/11–9/5
|
|
|
