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Below are listed the [[dyadic chord]]s of 11-limit [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.  
Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[octacot]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[540/539]] are [[swetismic chords|swetismic]], by [[441/440]] [[werckismic chords|werckismic]], by [[243/242]] [[rastmic chords|rastmic]], by [[245/243]] [[sensamagic chords|sensamagic]], by [[245/242]] [[frostmic chords|frostmic]], and by [[100/99]] [[ptolemismic chords|ptolemismic]]. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled [[jove chords|jove]], those requiring any two of 441/440, 245/242 or 100/99 [[nakika chords|nakika]], those requiring any two of 540/539, 245/243 or 100/99 [[octarod chords|octarod]]. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.  


Octacot has MOS of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.
Octacot has [[mos]] of size 13, 14, 27, 41, and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that 88-[[cent]] equal temperament ([[88cET]]) is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88cET. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4, and 11/8 to 9/4, 5/2, and 11/4.


= Triads =
== Triads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! Number
! #
! Chord
! Chord
! Transversal
! Transversal
! Type
! Type
! Hash
|-
|-
| 1
| 1
Line 110: Line 109:
| 0–2–11
| 0–2–11
| 1–10/9–7/4
| 1–10/9–7/4
| werkismic
| werckismic
|-
|-
| 21
| 21
Line 120: Line 119:
| 0–4–11
| 0–4–11
| 1–11/9–7/4
| 1–11/9–7/4
| werkismic
| werckismic
|-
|-
| 23
| 23
| 0–7–11
| 0–7–11
| 1–10/7–7/4
| 1–10/7–7/4
| werkismic
| werckismic
|-
|-
| 24
| 24
Line 135: Line 134:
| 0–9–11
| 0–9–11
| 1–11/7–7/4
| 1–11/7–7/4
| werkismic
| werckismic
|-
|-
| 26
| 26
Line 190: Line 189:
| 0–7–16
| 0–7–16
| 1–10/7–9/8
| 1–10/7–9/8
| werkismic
| werckismic
|-
|-
| 37
| 37
Line 200: Line 199:
| 0–9–16
| 0–9–16
| 1–11/7–9/8
| 1–11/7–9/8
| werkismic
| werckismic
|-
|-
| 39
| 39
Line 230: Line 229:
| 0–9–18
| 0–9–18
| 1–11/7–5/4
| 1–11/7–5/4
| cassacot
| frostmic
|-
|-
| 45
| 45
Line 293: Line 292:
|}
|}


= Tetrads =
== Tetrads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! Number
! #
! Chord
! Chord
! Transversal
! Transversal
! Type
! Type
! Hash
|-
|-
| 1
| 1
Line 385: Line 383:
| 0–2–4–11
| 0–2–4–11
| 1–10/9–11/9–7/4
| 1–10/9–11/9–7/4
| octagari
| nakika
|-
|-
| 18
| 18
| 0–2–7–11
| 0–2–7–11
| 1–10/9–10/7–7/4
| 1–10/9–10/7–7/4
| werkismic
| werckismic
|-
|-
| 19
| 19
Line 415: Line 413:
| 0–2–9–11
| 0–2–9–11
| 1–10/9–11/7–7/4
| 1–10/9–11/7–7/4
| octagari
| nakika
|-
|-
| 24
| 24
| 0–4–9–11
| 0–4–9–11
| 1–11/9–11/7–7/4
| 1–11/9–11/7–7/4
| werkismic
| werckismic
|-
|-
| 25
| 25
| 0–7–9–11
| 0–7–9–11
| 1–10/7–11/7–7/4
| 1–10/7–11/7–7/4
| octagari
| nakika
|-
|-
| 26
| 26
Line 530: Line 528:
| 0–5–7–16
| 0–5–7–16
| 1–9/7–10/7–9/8
| 1–9/7–10/7–9/8
| werkismic
| werckismic
|-
|-
| 47
| 47
Line 550: Line 548:
| 0–5–9–16
| 0–5–9–16
| 1–9/7–11/7–9/8
| 1–9/7–11/7–9/8
| werkismic
| werckismic
|-
|-
| 51
| 51
| 0–7–9–16
| 0–7–9–16
| 1–10/7–11/7–9/8
| 1–10/7–11/7–9/8
| octagari
| nakika
|-
|-
| 52
| 52
Line 565: Line 563:
| 0–7–11–16
| 0–7–11–16
| 1–10/7–7/4–9/8
| 1–10/7–7/4–9/8
| werkismic
| werckismic
|-
|-
| 54
| 54
Line 575: Line 573:
| 0–9–11–16
| 0–9–11–16
| 1–11/7–7/4–9/8
| 1–11/7–7/4–9/8
| werkismic
| werckismic
|-
|-
| 56
| 56
Line 610: Line 608:
| 0–2–9–18
| 0–2–9–18
| 1–10/9–11/7–5/4
| 1–10/9–11/7–5/4
| octagari
| nakika
|-
|-
| 63
| 63
| 0–7–9–18
| 0–7–9–18
| 1–10/7–11/7–5/4
| 1–10/7–11/7–5/4
| octagari
| nakika
|-
|-
| 64
| 64
Line 635: Line 633:
| 0–2–11–18
| 0–2–11–18
| 1–10/9–7/4–5/4
| 1–10/9–7/4–5/4
| werkismic
| werckismic
|-
|-
| 68
| 68
| 0–7–11–18
| 0–7–11–18
| 1–10/7–7/4–5/4
| 1–10/7–7/4–5/4
| werkismic
| werckismic
|-
|-
| 69
| 69
Line 650: Line 648:
| 0–9–11–18
| 0–9–11–18
| 1–11/7–7/4–5/4
| 1–11/7–7/4–5/4
| octagari
| nakika
|-
|-
| 71
| 71
| 0–7–16–18
| 0–7–16–18
| 1–10/7–9/8–5/4
| 1–10/7–9/8–5/4
| werkismic
| werckismic
|-
|-
| 72
| 72
Line 665: Line 663:
| 0–9–16–18
| 0–9–16–18
| 1–11/7–9/8–5/4
| 1–11/7–9/8–5/4
| octagari
| nakika
|-
|-
| 74
| 74
Line 705: Line 703:
| 0–2–11–20
| 0–2–11–20
| 1–10/9–7/4–11/8
| 1–10/9–7/4–11/8
| octagari
| nakika
|-
|-
| 82
| 82
| 0–4–11–20
| 0–4–11–20
| 1–11/9–7/4–11/8
| 1–11/9–7/4–11/8
| werkismic
| werckismic
|-
|-
| 83
| 83
Line 720: Line 718:
| 0–9–11–20
| 0–9–11–20
| 1–11/7–7/4–11/8
| 1–11/7–7/4–11/8
| werkismic
| werckismic
|-
|-
| 85
| 85
Line 760: Line 758:
| 0–9–16–20
| 0–9–16–20
| 1–11/7–9/8–11/8
| 1–11/7–9/8–11/8
| werkismic
| werckismic
|-
|-
| 93
| 93
Line 785: Line 783:
| 0–9–18–20
| 0–9–18–20
| 1–11/7–5/4–11/8
| 1–11/7–5/4–11/8
| octagari
| nakika
|-
|-
| 98
| 98
Line 803: Line 801:
|}
|}


= Pentads =
== Pentads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! Number
! #
! Chord
! Chord
! Transversal
! Transversal
! Type
! Type
! Hash
|-
|-
| 1
| 1
Line 845: Line 842:
| 0–2–4–9–11
| 0–2–4–9–11
| 1–10/9–11/9–11/7–7/4
| 1–10/9–11/9–11/7–7/4
| octagari
| nakika
|-
|-
| 8
| 8
| 0–2–7–9–11
| 0–2–7–9–11
| 1–10/9–10/7–11/7–7/4
| 1–10/9–10/7–11/7–7/4
| octagari
| nakika
|-
|-
| 9
| 9
Line 945: Line 942:
| 0–5–7–9–16
| 0–5–7–9–16
| 1–9/7–10/7–11/7–9/8
| 1–9/7–10/7–11/7–9/8
| octagari
| nakika
|-
|-
| 28
| 28
Line 965: Line 962:
| 0–7–9–11–16
| 0–7–9–11–16
| 1–10/7–11/7–7/4–9/8
| 1–10/7–11/7–7/4–9/8
| octagari
| nakika
|-
|-
| 32
| 32
Line 1,005: Line 1,002:
| 0–2–7–9–18
| 0–2–7–9–18
| 1–10/9–10/7–11/7–5/4
| 1–10/9–10/7–11/7–5/4
| octagari
| nakika
|-
|-
| 40
| 40
Line 1,015: Line 1,012:
| 0–2–7–11–18
| 0–2–7–11–18
| 1–10/9–10/7–7/4–5/4
| 1–10/9–10/7–7/4–5/4
| werkismic
| werckismic
|-
|-
| 42
| 42
| 0–2–9–11–18
| 0–2–9–11–18
| 1–10/9–11/7–7/4–5/4
| 1–10/9–11/7–7/4–5/4
| octagari
| nakika
|-
|-
| 43
| 43
| 0–7–9–11–18
| 0–7–9–11–18
| 1–10/7–11/7–7/4–5/4
| 1–10/7–11/7–7/4–5/4
| octagari
| nakika
|-
|-
| 44
| 44
| 0–7–9–16–18
| 0–7–9–16–18
| 1–10/7–11/7–9/8–5/4
| 1–10/7–11/7–9/8–5/4
| octagari
| nakika
|-
|-
| 45
| 45
| 0–7–11–16–18
| 0–7–11–16–18
| 1–10/7–7/4–9/8–5/4
| 1–10/7–7/4–9/8–5/4
| werkismic
| werckismic
|-
|-
| 46
| 46
Line 1,045: Line 1,042:
| 0–9–11–16–18
| 0–9–11–16–18
| 1–11/7–7/4–9/8–5/4
| 1–11/7–7/4–9/8–5/4
| octagari
| nakika
|-
|-
| 48
| 48
Line 1,055: Line 1,052:
| 0–2–4–11–20
| 0–2–4–11–20
| 1–10/9–11/9–7/4–11/8
| 1–10/9–11/9–7/4–11/8
| octagari
| nakika
|-
|-
| 50
| 50
Line 1,065: Line 1,062:
| 0–2–9–11–20
| 0–2–9–11–20
| 1–10/9–11/7–7/4–11/8
| 1–10/9–11/7–7/4–11/8
| octagari
| nakika
|-
|-
| 52
| 52
| 0–4–9–11–20
| 0–4–9–11–20
| 1–11/9–11/7–7/4–11/8
| 1–11/9–11/7–7/4–11/8
| werkismic
| werckismic
|-
|-
| 53
| 53
Line 1,125: Line 1,122:
| 0–9–11–16–20
| 0–9–11–16–20
| 1–11/7–7/4–9/8–11/8
| 1–11/7–7/4–9/8–11/8
| werkismic
| werckismic
|-
|-
| 64
| 64
Line 1,145: Line 1,142:
| 0–2–9–18–20
| 0–2–9–18–20
| 1–10/9–11/7–5/4–11/8
| 1–10/9–11/7–5/4–11/8
| octagari
| nakika
|-
|-
| 68
| 68
Line 1,160: Line 1,157:
| 0–2–11–18–20
| 0–2–11–18–20
| 1–10/9–7/4–5/4–11/8
| 1–10/9–7/4–5/4–11/8
| octagari
| nakika
|-
|-
| 71
| 71
Line 1,170: Line 1,167:
| 0–9–11–18–20
| 0–9–11–18–20
| 1–11/7–7/4–5/4–11/8
| 1–11/7–7/4–5/4–11/8
| octagari
| nakika
|-
|-
| 73
| 73
Line 1,180: Line 1,177:
| 0–9–16–18–20
| 0–9–16–18–20
| 1–11/7–9/8–5/4–11/8
| 1–11/7–9/8–5/4–11/8
| octagari
| nakika
|-
|-
| 75
| 75
Line 1,188: Line 1,185:
|}
|}


= Hexads =
== Hexads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! Number
! #
! Chord
! Chord
! Transversal
! Transversal
! Type
! Type
! Hash
|-
|-
| 1
| 1
Line 1,245: Line 1,241:
| 0–2–7–9–11–18
| 0–2–7–9–11–18
| 1–10/9–10/7–11/7–7/4–5/4
| 1–10/9–10/7–11/7–7/4–5/4
| octagari
| nakika
|-
|-
| 11
| 11
| 0–7–9–11–16–18
| 0–7–9–11–16–18
| 1–10/7–11/7–7/4–9/8–5/4
| 1–10/7–11/7–7/4–9/8–5/4
| octagari
| nakika
|-
|-
| 12
| 12
| 0–2–4–9–11–20
| 0–2–4–9–11–20
| 1–10/9–11/9–11/7–7/4–11/8
| 1–10/9–11/9–11/7–7/4–11/8
| octagari
| nakika
|-
|-
| 13
| 13
Line 1,285: Line 1,281:
| 0–2–9–11–18–20
| 0–2–9–11–18–20
| 1–10/9–11/7–7/4–5/4–11/8
| 1–10/9–11/7–7/4–5/4–11/8
| octagari
| nakika
|-
|-
| 19
| 19
Line 1,295: Line 1,291:
| 0–9–11–16–18–20
| 0–9–11–16–18–20
| 1–11/7–7/4–9/8–5/4–11/8
| 1–11/7–7/4–9/8–5/4–11/8
| octagari
| nakika
|}
|}


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