Chords of superpyth: Difference between revisions

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{{Editable user page| Please complete the description and tables. This page is planned to be moved to main space once completed.}}

Below ~~are listed the~~ [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[superpyth|superpyth temperament]]. ~~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. If ~~the~~ chord is essentially tempered, it is ~~analyzed in terms~~ of the ~~transversal that employs 8/7 and 10/9~~.

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. If a chord is [[Dyadic chord#Types of dyadic chords|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 with either. If a chord is essentially tempered, it is classified based on the minimal amount of tempering required to define the chord.

~~Superpyth has~~ [[~~MOS~~]] ~~scales of 5~~, 7, 12, ~~17, 22~~, and 27. ~~The highest complexity~~ of ~~any chord on this list is 18~~, and ~~would thus require the 22-note mos~~, ~~but even the 5- and 7-note MOSes contain enough~~ chords ~~to be interesting~~, ~~though the 12-~~ and ~~17-note MOSes~~ are ~~needed to properly explore full 7- and 11-limit harmonies~~.

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 tempering are marked [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 tempering are marked [[octarod chords|octarod]].

~~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 tempering are marked~~ [[~~ares chords~~|~~ares~~]]~~. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked~~ [[~~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. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9.

Superpyth [[generate]]s [[MOS]] scales of 5, 7, 12, 17, 22, and 27. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note MOS. That being said, even the 5- and 7-note MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to explore full 7- and 11-limit harmonies.

== Triads ==

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 {{Editable user page| Please complete the description and tables. This page is planned to be moved to main space once completed.}}
-Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[superpyth|superpyth temperament]]. 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. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9.
+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. If a chord is [[Dyadic chord#Types of dyadic chords|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 with either. If a chord is essentially tempered, it is classified based on the minimal amount of tempering required to define the chord.
-Superpyth has [[MOS]] scales of 5, 7, 12, 17, 22, and 27. The highest complexity of any chord on this list is 18, and would thus require the 22-note mos, but even the 5- and 7-note MOSes contain enough chords to be interesting, though the 12- and 17-note MOSes are needed to properly explore full 7- and 11-limit harmonies.
+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 tempering are marked [[ares chords|ares]]. Finally, chords that require any two of 100/99, 245/243 and 540/539 tempering are marked [[octarod chords|octarod]].
-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 tempering are marked [[ares chords|ares]]. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked [[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. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9.
+Superpyth [[generate]]s [[MOS]] scales of 5, 7, 12, 17, 22, and 27. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note MOS. That being said, even the 5- and 7-note MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to explore full 7- and 11-limit harmonies.
 == Triads ==