Chords of superpyth: Difference between revisions

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Below is a complete list of all [[11-odd-limit]] [[dyadic chord]]s in [[11-limit]] [[superpyth|superpyth temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[Wikipedia:Chord inversion|inversions]]; only one is listed, that being the inversion where all notes are a positive number of [[generator]]s above the root.

If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially just]], 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 equally well analyzed by either. If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially tempered]], it is classified based on which [[Essential tempering comma|commas]] are needed to define the chord. Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[245/243]] [[sensamagic chords|sensamagic]], and by [[540/539]] [[swetismic chords|swetismic]]. Chords that require any two of 64/63, 100/99 and 176/175 to vanish are ~~marked~~ [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 to vanish are ~~marked~~ [[octarod chords|octarod]].

If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially just]], 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 equally well analyzed by either. If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially tempered]], it is classified based on which [[Essential tempering comma|commas]] are needed to define the chord. Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[245/243]] [[sensamagic chords|sensamagic]], and by [[540/539]] [[swetismic chords|swetismic]]. Chords that require any two of 64/63, 100/99 and 176/175 to vanish are labeled [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 to vanish are labeled [[octarod chords|octarod]].

Typing the chords requires consideration of the fact that superpyth conflates [[9/8]] with [[8/7]], and [[11/10]] with [[10/9]]. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. However, sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 8/7 and 10/9 above the root.

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 Below is a complete list of all [[11-odd-limit]] [[dyadic chord]]s in [[11-limit]] [[superpyth|superpyth temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[Wikipedia:Chord inversion|inversions]]; only one is listed, that being the inversion where all notes are a positive number of [[generator]]s above the root.
-If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially just]], 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 equally well analyzed by either. If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially tempered]], it is classified based on which [[Essential tempering comma|commas]] are needed to define the chord. Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[245/243]] [[sensamagic chords|sensamagic]], and by [[540/539]] [[swetismic chords|swetismic]]. Chords that require any two of 64/63, 100/99 and 176/175 to vanish are marked [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 to vanish are marked [[octarod chords|octarod]].
+If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially just]], 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 equally well analyzed by either. If a chord is [[Dyadic chord#Essentially tempered dyadic chord|essentially tempered]], it is classified based on which [[Essential tempering comma|commas]] are needed to define the chord. Chords essentially tempered by [[64/63]] are labeled [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[245/243]] [[sensamagic chords|sensamagic]], and by [[540/539]] [[swetismic chords|swetismic]]. Chords that require any two of 64/63, 100/99 and 176/175 to vanish are labeled [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 to vanish are labeled [[octarod chords|octarod]].
 Typing the chords requires consideration of the fact that superpyth conflates [[9/8]] with [[8/7]], and [[11/10]] with [[10/9]]. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. However, sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 8/7 and 10/9 above the root.