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Chords of pajara: Difference between revisions

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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 [[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 [[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]], and chords that require any two of 50/49, 99/98, and 100/99 to vanish are labeled [[undecimal jubilismic chords|jubilismic11]]. 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]], and chords that require any two of 50/49, 99/98, and 100/99 to vanish are labeled [[undecimal jubilismic chords|jubilismic11]]. 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].
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| 0–1–3–7
| 0–1–3–7
| 1–12/11–3/2–12/7
| 1–12/11–3/2–12/7
|  
| Utonal
|  
|  
|-
|-
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| 0–1–3'–7
| 0–1–3'–7
| 1–12/11–6/5–3/2
| 1–12/11–6/5–3/2
|  
| Utonal
|  
|  
|-
|-
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| 0–3–3'–7
| 0–3–3'–7
| 1–12/11–6/5–12/7
| 1–12/11–6/5–12/7
|  
| Utonal
|  
|  
|-
|-
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| 0–1–4–7
| 0–1–4–7
| 1–12/11–9/7–3/2
| 1–12/11–9/7–3/2
|  
| Mothwellsmic
|  
|  
|-
|-
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| 0–3–4–7
| 0–3–4–7
| 1–12/11–9/7–12/7
| 1–12/11–9/7–12/7
|  
| Mothwellsmic
|  
|  
|-
|-
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| 0–1–4'–7
| 0–1–4'–7
| 1–12/11–3/2–9/5
| 1–12/11–3/2–9/5
|  
| Ptolemismic
|  
|  
|-
|-
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| 0–3'–4'–7
| 0–3'–4'–7
| 1–12/11–6/5–9/5
| 1–12/11–6/5–9/5
|  
| Ptolemismic
|  
|  
|-
|-
| 39
| 39
| 0–4–4'–7
| 0–4–4'–7
| 1–12/11–9/7–9/5
| 1–12/11–14/11–20/11
|  
| Otonal
|  
|  
|-
|-
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| 0–3–6–7
| 0–3–6–7
| 1–12/11–16/11–12/7
| 1–12/11–16/11–12/7
|  
| Mothwellsmic
|  
|  
|-
|-
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| 0–3'–6–7
| 0–3'–6–7
| 1–12/11–6/5–16/11
| 1–12/11–6/5–16/11
|  
| Ptolemismic
|  
|  
|-
|-
| 42
| 42
| 0–4–6–7
| 0–4–6–7
| 1–12/11–9/7–16/11
| 1–12/11–14/11–16/11
|  
| Otonal
|  
|  
|-
|-
| 43
| 43
| 0–4'–6–7
| 0–4'–6–7
| 1–12/11–16/11–9/5
| 1–12/11–16/11–20/11
|  
| Otonal
|  
|  
|-
|-
| 44
| 44
| 0–1–2–8
| 0–1–2–8
| 1–8/7–3/2–18/11
| 1–9/8–3/2–18/11
|  
| Utonal
|  
|  
|-
|-
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| 0–1–4–8
| 0–1–4–8
| 1–9/7–3/2–18/11
| 1–9/7–3/2–18/11
|  
| Utonal
|  
|  
|-
|-
| 46
| 46
| 0–2–4–8
| 0–2–4–8
| 1–8/7–9/7–18/11
| 1–9/8–9/7–18/11
|  
| Utonal
|  
|  
|-
|-
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| 0–1–4'–8
| 0–1–4'–8
| 1–3/2–18/11–9/5
| 1–3/2–18/11–9/5
|  
| Utonal
|  
|  
|-
|-
| 48
| 48
| 0–2–4'–8
| 0–2–4'–8
| 1–8/7–18/11–9/5
| 1–9/8–18/11–9/5
|  
| Utonal
|  
|  
|-
|-
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| 0–2–6–8
| 0–2–6–8
| 1–8/7–16/11–18/11
| 1–8/7–16/11–18/11
|  
| Archytas
|  
|  
|-
|-
| 51
| 51
| 0–4–6–8
| 0–4–6–8
| 1–9/7–16/11–18/11
| 1–14/11–16/11–18/11
|  
| Otonal
|  
|  
|-
|-
| 52
| 52
| 0–4'–6–8
| 0–4'–6–8
| 1–16/11–18/11–9/5
| 1–16/11–18/11–20/11
|  
| Otonal
|  
|  
|-
|-
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| 0–1–7–8
| 0–1–7–8
| 1–12/11–3/2–18/11
| 1–12/11–3/2–18/11
|  
| Ambitonal
|  
| 11-odd-limit ASS
|-
|-
| 54
| 54
| 0–4–7–8
| 0–4–7–8
| 1–12/11–9/7–18/11
| 1–12/11–14/11–18/11
|  
| Otonal
|  
|  
|-
|-
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