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This page lists all [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[pajara]] temperament. Each chord listed has multiple {{W|Chord inversion|inversions}}; only one is listed, that being the inversion where all notes are a nonnegative number of perfect fifth [[generator]]s above the root or semioctave, which may not be the optimal {{W|Voicing (music)|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.
This page lists all [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[pajara]] temperament. Each chord listed has multiple {{W|Chord inversion|inversions}}; only one is listed, that being the inversion where all notes are a nonnegative number of perfect fifth [[generator]]s above the root or semioctave, which may not be the optimal {{W|Voicing (music)|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 [[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 tempered]], it is classified based on which [[comma]]s are needed to define the chord. Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[99/98]] [[mothwellsmic chords|mothwellsmic]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[225/224]] [[marvel chords|marvel]], and by [[896/891]] [[pentacircle chords|pentacircle]]. Chords that require any two of 50/49, 64/63, and 225/224 to vanish are labeled [[pajara chords|pajara]] [not known to exist], and chords that require any two of 50/49, 99/98, and 100/99 to vanish are labeled [[jubilee chords|jubilee]] [not known to exist]. Chords that require any two of 64/63, 99/98, and 896/891 to vanish are labeled [[supra chords|supra]] [placeholder name, not known to exist], and chords that require any two of 64/63, 100/99, and 176/175 to vanish are labeled [[ares chords|ares]]. Chords that require any two of 99/98, 176/175, and 225/224 to vanish are labeled [[minerva chords|minerva]], and chords that require any two of 100/99, 225/224, and 896/891 to vanish are labeled [[apollo chords|apollo]]. Finally, chords that require any three independent commas listed above to vanish are labeled [[undecimal pajara chords|pajara11]] [not known to exist].
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 tempered]], it is classified based on which [[comma]]s are needed to define the chord. Chords essentially tempered by [[50/49]] are labeled [[jubilismic chords|jubilismic]], by [[64/63]] [[archytas chords|archytas]], by [[99/98]] [[mothwellsmic chords|mothwellsmic]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[225/224]] [[marvel chords|marvel]], and by [[896/891]] [[pentacircle chords|pentacircle]]. Chords that require any two of 50/49, 64/63, and 225/224 to vanish are labeled [[pajara chords|pajara]] [not known to exist], and chords that require any two of 50/49, 99/98, and 100/99 to vanish are labeled [[jubilee chords|jubilee]]. Chords that require any two of 64/63, 99/98, and 896/891 to vanish are labeled [[supra chords|supra]] [placeholder name, not known to exist], and chords that require any two of 64/63, 100/99, and 176/175 to vanish are labeled [[ares chords|ares]]. Chords that require any two of 99/98, 176/175, and 225/224 to vanish are labeled [[minerva chords|minerva]], and chords that require any two of 100/99, 225/224, and 896/891 to vanish are labeled [[apollo chords|apollo]]. Finally, chords that require any three independent commas listed above to vanish are labeled [[undecimal pajara chords|pajara11]] [not known to exist].


== Triads ==
== Triads ==
Line 238: Line 238:
== Tetrads ==
== Tetrads ==


{| class="wikitable sortable right-1 right-4 right-5"
{| class="wikitable sortable center-1"
|-
|-
! #
! #
Line 249: Line 249:
| 0–0'–2–2'
| 0–0'–2–2'
| 1–8/7–7/5–8/5
| 1–8/7–7/5–8/5
|  
| Jubilismic
|  
|  
|-
|-
| 2
| 2
| 0–0'–2–3
| 0–0'–2–3
| 1–8/7–7/5–12/7
| 1–8/7–10/7–12/7
|  
| Otonal
|  
| [[4:5:6:7]]
|-
|-
| 3
| 3
| 0–1–2–3
| 0–1–2–3
| 1–8/7–3/2–12/7
| 1–8/7–3/2–12/7
|  
| Archytas
|  
|  
|-
|-
| 4
| 4
| 0–0'–2'–3'
| 1–6/5–7/5–8/5
|
|
|-
| 5
| 0–0'–3–3'
| 0–0'–3–3'
| 1–6/5–7/5–12/7
| 1–6/5–7/5–12/7
|  
| Jubilismic
|  
|  
|-
|-
| 6
| 5
| 0–1–3–3'
| 0–1–3–3'
| 1–6/5–3/2–12/7
| 1–6/5–3/2–12/7
|  
| Utonal
|  
| [[70:84:105:120|1/(12:10:8:7)]]
|-
|-
| 7
| 6
| 0–0'–2–4
| 0–0'–2–4
| 1–8/7–9/7–7/5
| 1–8/7–9/7–10/7
|  
| Otonal
|  
|  
|-
|-
| 8
| 7
| 0–1–2–4
| 0–1–2–4
| 1–8/7–9/7–3/2
| 1–9/8–9/7–3/2
|  
| Utonal
|  
| [[56:63:72:84|1/(9:8:7:6)]]
|-
|-
| 9
| 8
| 0–0'–2'–4
| 0–0'–2'–4
| 1–9/7–7/5–8/5
| 1–9/7–7/5–8/5
Line 300: Line 294:
|  
|  
|-
|-
| 10
| 9
| 0–2–2'–4
| 0–2–2'–4
| 1–8/7–9/7–8/5
| 1–8/7–9/7–8/5
Line 306: Line 300:
|  
|  
|-
|-
| 11
| 10
| 0–0'–3–4
| 0–0'–3–4
| 1–9/7–7/5–12/7
| 1–9/7–10/7–12/7
|  
| Otonal
|  
| [[6:7:9:10]]
|-
|-
| 12
| 11
| 0–1–3–4
| 0–1–3–4
| 1–9/7–3/2–12/7
| 1–9/7–3/2–12/7
Line 318: Line 312:
|  
|  
|-
|-
| 13
| 12
| 0–2–3–4
| 0–2–3–4
| 1–8/7–9/7–12/7
| 1–8/7–9/7–12/7
Line 324: Line 318:
|  
|  
|-
|-
| 14
| 13
| 0–0'–2–4'
| 1–8/7–7/5–9/5
|
|
|-
| 15
| 0–1–2–4'
| 0–1–2–4'
| 1–8/7–3/2–9/5
| 1–8/7–3/2–9/5
Line 336: Line 324:
|  
|  
|-
|-
| 16
| 14
| 0–0'–2'–4'
| 1–7/5–8/5–9/5
|
|
|-
| 17
| 0–2–2'–4'
| 0–2–2'–4'
| 1–8/7–8/5–9/5
| 1–8/7–8/5–9/5
Line 348: Line 330:
|  
|  
|-
|-
| 18
| 15
| 0–0'–3'–4'
| 1–6/5–7/5–9/5
|
|
|-
| 19
| 0–1–3'–4'
| 0–1–3'–4'
| 1–6/5–3/2–9/5
| 1–6/5–3/2–9/5
Line 360: Line 336:
|  
|  
|-
|-
| 20
| 16
| 0–2'–3'–4'
| 0–2'–3'–4'
| 1–6/5–8/5–9/5
| 1–6/5–8/5–9/5
Line 366: Line 342:
|  
|  
|-
|-
| 21
| 17
| 0–0'–4–4'
| 0–0'–4–4'
| 1–9/7–7/5–9/5
| 1–9/7–7/5–9/5
Line 372: Line 348:
|  
|  
|-
|-
| 22
| 18
| 0–1–4–4'
| 0–1–4–4'
| 1–9/7–3/2–9/5
| 1–9/7–3/2–9/5
|  
| Utonal
|  
| [[70:90:105:126|1/(9:7:6:5)]]
|-
|-
| 23
| 19
| 0–2–4–4'
| 0–2–4–4'
| 1–8/7–9/7–9/5
| 1–8/7–9/7–9/5
Line 384: Line 360:
|  
|  
|-
|-
| 24
| 20
| 0–2'–4–4'
| 0–2'–4–4'
| 1–9/7–8/5–9/5
| 1–9/7–8/5–9/5
Line 390: Line 366:
|  
|  
|-
|-
| 25
| 21
| 0–2–2'–6
| 0–2–2'–6
| 1–8/7–16/11–8/5
| 1–8/7–16/11–8/5
Line 396: Line 372:
|  
|  
|-
|-
| 26
| 22
| 0–2–3–6
| 0–2–3–6
| 1–8/7–16/11–12/7
| 1–8/7–16/11–12/7
Line 402: Line 378:
|  
|  
|-
|-
| 27
| 23
| 0–2'–3'–6
| 0–2'–3'–6
| 1–6/5–16/11–8/5
| 1–6/5–16/11–8/5
Line 408: Line 384:
|  
|  
|-
|-
| 28
| 24
| 0–3–3'–6
| 0–3–3'–6
| 1–6/5–16/11–12/7
| 1–6/5–16/11–12/7
|  
| Jubilee
|  
|  
|-
|-
| 29
| 25
| 0–2–4–6
| 0–2–4–6
| 1–8/7–9/7–16/11
| 1–8/7–9/7–16/11
Line 420: Line 396:
|  
|  
|-
|-
| 30
| 26
| 0–2'–4–6
| 0–2'–4–6
| 1–9/7–16/11–8/5
| 1–9/7–16/11–8/5
Line 426: Line 402:
|  
|  
|-
|-
| 31
| 27
| 0–3–4–6
| 0–3–4–6
| 1–9/7–16/11–12/7
| 1–9/7–16/11–12/7
Line 432: Line 408:
|  
|  
|-
|-
| 32
| 28
| 0–2–4'–6
| 0–2–4'–6
| 1–8/7–16/11–9/5
| 1–8/7–16/11–9/5
Line 438: Line 414:
|  
|  
|-
|-
| 33
| 29
| 0–2'–4'–6
| 0–2'–4'–6
| 1–16/11–8/5–9/5
| 1–16/11–8/5–9/5
Line 444: Line 420:
|  
|  
|-
|-
| 34
| 30
| 0–3'–4'–6
| 0–3'–4'–6
| 1–6/5–16/11–9/5
| 1–6/5–16/11–9/5
Line 450: Line 426:
|  
|  
|-
|-
| 35
| 31
| 0–4–4'–6
| 0–4–4'–6
| 1–9/7–16/11–9/5
| 1–9/7–16/11–9/5
Line 456: Line 432:
|  
|  
|-
|-
| 36
| 32
| 0–1–3–7
| 0–1–3–7
| 1–12/11–3/2–12/7
| 1–12/11–3/2–12/7
Line 462: Line 438:
|  
|  
|-
|-
| 37
| 33
| 0–1–3'–7
| 0–1–3'–7
| 1–12/11–6/5–3/2
| 1–12/11–6/5–3/2
Line 468: Line 444:
|  
|  
|-
|-
| 38
| 34
| 0–3–3'–7
| 0–3–3'–7
| 1–12/11–6/5–12/7
| 1–12/11–6/5–12/7
Line 474: Line 450:
|  
|  
|-
|-
| 39
| 35
| 0–1–4–7
| 0–1–4–7
| 1–12/11–9/7–3/2
| 1–12/11–9/7–3/2
Line 480: Line 456:
|  
|  
|-
|-
| 40
| 36
| 0–3–4–7
| 0–3–4–7
| 1–12/11–9/7–12/7
| 1–12/11–9/7–12/7
Line 486: Line 462:
|  
|  
|-
|-
| 41
| 37
| 0–1–4'–7
| 0–1–4'–7
| 1–12/11–3/2–9/5
| 1–12/11–3/2–9/5
Line 492: Line 468:
|  
|  
|-
|-
| 42
| 38
| 0–3'–4'–7
| 0–3'–4'–7
| 1–12/11–6/5–9/5
| 1–12/11–6/5–9/5
Line 498: Line 474:
|  
|  
|-
|-
| 43
| 39
| 0–4–4'–7
| 0–4–4'–7
| 1–12/11–9/7–9/5
| 1–12/11–9/7–9/5
Line 504: Line 480:
|  
|  
|-
|-
| 44
| 40
| 0–3–6–7
| 0–3–6–7
| 1–12/11–16/11–12/7
| 1–12/11–16/11–12/7
Line 510: Line 486:
|  
|  
|-
|-
| 45
| 41
| 0–3'–6–7
| 0–3'–6–7
| 1–12/11–6/5–16/11
| 1–12/11–6/5–16/11
Line 516: Line 492:
|  
|  
|-
|-
| 46
| 42
| 0–4–6–7
| 0–4–6–7
| 1–12/11–9/7–16/11
| 1–12/11–9/7–16/11
Line 522: Line 498:
|  
|  
|-
|-
| 47
| 43
| 0–4'–6–7
| 0–4'–6–7
| 1–12/11–16/11–9/5
| 1–12/11–16/11–9/5
Line 528: Line 504:
|  
|  
|-
|-
| 48
| 44
| 0–1–2–8
| 0–1–2–8
| 1–8/7–3/2–18/11
| 1–8/7–3/2–18/11
Line 534: Line 510:
|  
|  
|-
|-
| 49
| 45
| 0–1–4–8
| 0–1–4–8
| 1–9/7–3/2–18/11
| 1–9/7–3/2–18/11
Line 540: Line 516:
|  
|  
|-
|-
| 50
| 46
| 0–2–4–8
| 0–2–4–8
| 1–8/7–9/7–18/11
| 1–8/7–9/7–18/11
Line 546: Line 522:
|  
|  
|-
|-
| 51
| 47
| 0–1–4'–8
| 0–1–4'–8
| 1–3/2–18/11–9/5
| 1–3/2–18/11–9/5
Line 552: Line 528:
|  
|  
|-
|-
| 52
| 48
| 0–2–4'–8
| 0–2–4'–8
| 1–8/7–18/11–9/5
| 1–8/7–18/11–9/5
Line 558: Line 534:
|  
|  
|-
|-
| 53
| 49
| 0–4–4'–8
| 0–4–4'–8
| 1–9/7–18/11–9/5
| 1–9/7–18/11–9/5
|  
| Otonal/utonal
|  
| 7:9:10:11~1/(14:11:10:9)
|-
|-
| 54
| 50
| 0–2–6–8
| 0–2–6–8
| 1–8/7–16/11–18/11
| 1–8/7–16/11–18/11
Line 570: Line 546:
|  
|  
|-
|-
| 55
| 51
| 0–4–6–8
| 0–4–6–8
| 1–9/7–16/11–18/11
| 1–9/7–16/11–18/11
Line 576: Line 552:
|  
|  
|-
|-
| 56
| 52
| 0–4'–6–8
| 0–4'–6–8
| 1–16/11–18/11–9/5
| 1–16/11–18/11–9/5
Line 582: Line 558:
|  
|  
|-
|-
| 57
| 53
| 0–1–7–8
| 0–1–7–8
| 1–12/11–3/2–18/11
| 1–12/11–3/2–18/11
Line 588: Line 564:
|  
|  
|-
|-
| 58
| 54
| 0–4–7–8
| 0–4–7–8
| 1–12/11–9/7–18/11
| 1–12/11–9/7–18/11
Line 594: Line 570:
|  
|  
|-
|-
| 59
| 55
| 0–4'–7–8
| 0–4'–7–8
| 1–12/11–18/11–9/5
| 1–12/11–18/11–20/11
|  
| Otonal
|  
|  
|-
|-
| 60
| 56
| 0–6–7–8
| 0–6–7–8
| 1–12/11–16/11–18/11
| 1–12/11–16/11–18/11
|  
| Otonal
|  
|  
|}
|}
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