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Chords of pajara: Difference between revisions

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If a chord is [[dyadic chord #Essentially tempered dyadic chord|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 [[dyadic chord #Essentially tempered dyadic chord|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.
== Triads ==
{| class="wikitable sortable right-1 right-4 right-5"
|-
! #
! class="unsortable" | Generators
! class="unsortable" | Transversal
! Type
! class="unsortable" | 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 ==
{| class="wikitable sortable right-1 right-4 right-5"
|-
! #
! class="unsortable" | Generators
! class="unsortable" | Transversal
! Type
! class="unsortable" | 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 ==
{| class="wikitable sortable right-1 right-4 right-5"
|-
! #
! class="unsortable" | Generators
! class="unsortable" | Transversal
! Type
! class="unsortable" | 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 ==
{| class="wikitable sortable right-1 right-4 right-5"
|-
! #
! class="unsortable" | Generators
! class="unsortable" | Transversal
! Type
! class="unsortable" | 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
|
|
|}
Retrieved from "https://en.xen.wiki/w/Chords_of_pajara"