Chords of superpyth: Difference between revisions

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Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[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 are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[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.


Chords essentially tempered by [[64/63]] are labeled archytas, by [[100/99]] ptolemismic, by [[176/175]] by [[245/243]] sensamagic, etc., (Todo: Complete essential tempering types
Chords essentially tempered by [[64/63]] are labeled archytas, by [[100/99]] ptolemismic, by [[176/175]] by [[245/243]] sensamagic, etc., (Todo: Complete essential tempering types)
 
== Triads ==
== Triads ==
{| class="wikitable"
|+
|-
! #
! Transversal
! Type
|-
|1
|1/1-3/2-9/8
|ambitonal
|-
|2
|1/1-3/2-12/7
|utonal
|-
|3
|1/1-8/7-12/7
|otonal
|-
|
|1/1-3/2-9/7
|
|-
|
|1/1-8/7-9/7
|
|-
|
|1/1-12/7-9/7
|
|-
|
|1/1-12/7-10/9
|
|-
|
|1/1-9/7-10/9
|
|-
|
|1/1-3/2-5/3
|
|-
|
|1/1-9/7-5/3
|
|-
|
|1/1-10/9-5/3
|
|-
|
|1/1-3/2-5/4
|
|-
|
|1/1-8/7-5/4
|
|-
|
|1/1-10/9-5/4
|
|-
|
|1/1-5/3-5/4
|
|-
|
|1/1-8/7-10/7
|
|-
|
|1/1-12/7-10/7
|
|-
|
|1/1-9/7-10/7
|
|-
|
|1/1-10/9-10/7
|
|-
|
|1/1-5/3-10/7
|
|-
|
|1/1-5/4-10/7
|
|-
|
|1/1-12/7-11/9
|
|-
|
|1/1-10/9-11/9
|
|-
|
|1/1-10/7-11/9
|
|-
|
|1/1-3/2-11/6
|
|-
|
|1/1-9/7-11/6
|
|-
|
|1/1-10/9-11/6
|
|-
|
|1/1-5/3-11/6
|
|-
|
|1/1-10/7-11/6
|
|-
|
|1/1-11/9-11/6
|
|-
|
|1/1-3/2-11/8
|
|-
|
|1/1-8/7-11/8
|
|-
|
|1/1-10/9-11/8
|
|-
|
|1/1-5/3-11/8
|
|-
|
|1/1-5/4-11/8
|
|-
|
|1/1-11/9-11/8
|
|-
|
|1/1-11/6-11/8
|
|-
|
|1/1-8/7-11/7
|
|-
|
|1/1-12/7-11/7
|
|-
|
|1/1-9/7-11/7
|
|-
|
|1/1-10/9-11/7
|
|-
|
|1/1-5/4-11/7
|
|-
|
|1/1-10/7-11/7
|
|-
|
|1/1-11/9-11/7
|
|-
|
|1/1-11/6-11/7
|
|-
|
|1/1-11/8-11/7
|
|}
== Tetrads ==
{| class="wikitable"
|+
|-
! #
! Transversal
! Type
|-
|
|1/1-3/2-8/7-12/7
|
|-
|
|1/1-3/2-8/7-9/7
|
|-
|
|1/1-3/2-12/7-9/7
|
|-
|
|1/1-8/7-12/7-9/7
|
|-
|
|1/1-12/7-9/7-10/9
|
|-
|
|1/1-3/2-9/7-5/3
|
|-
|
|1/1-9/7-10/9-5/3
|
|-
|
|1/1-3/2-8/7-5/4
|
|-
|
|1/1-3/2-5/3-5/4
|
|-
|
|1/1-10/9-5/3-5/4
|
|-
|
|1/1-8/7-12/7-10/7
|
|-
|
|1/1-8/7-9/7-10/7
|
|-
|
|1/1-12/7-9/7-10/7
|
|-
|
|1/1-12/7-10/9-10/7
|
|-
|
|1/1-9/7-10/9-10/7
|
|-
|
|1/1-9/7-5/3-10/7
|
|-
|
|1/1-10/9-5/3-10/7
|
|-
|
|1/1-8/7-5/4-10/7
|
|-
|
|1/1-10/9-5/4-10/7
|
|-
|
|1/1-5/3-5/4-10/7
|
|-
|
|1/1-12/7-10/9-11/9
|
|-
|
|1/1-12/7-10/7-11/9
|
|-
|
|1/1-10/9-10/7-11/9
|
|-
|
|1/1-3/2-9/7-11/6
|
|-
|
|1/1-9/7-10/9-11/6
|
|-
|
|1/1-3/2-5/3-11/6
|
|-
|
|1/1-9/7-5/3-11/6
|
|-
|
|1/1-10/9-5/3-11/6
|
|-
|
|1/1-9/7-10/7-11/6
|
|-
|
|1/1-10/9-10/7-11/6
|
|-
|
|1/1-5/3-10/7-11/6
|
|-
|
|1/1-10/9-11/9-11/6
|
|-
|
|1/1-10/7-11/9-11/6
|
|-
|
|1/1-3/2-8/7-11/8
|
|-
|
|1/1-3/2-5/3-11/8
|
|-
|
|1/1-10/9-5/3-11/8
|
|-
|
|1/1-3/2-5/4-11/8
|
|-
|
|1/1-8/7-5/4-11/8
|
|-
|
|1/1-10/9-5/4-11/8
|
|-
|
|1/1-5/3-5/4-11/8
|
|-
|
|1/1-10/9-11/9-11/8
|
|-
|
|1/1-3/2-11/6-11/8
|
|-
|
|1/1-10/9-11/6-11/8
|
|-
|
|1/1-5/3-11/6-11/8
|
|-
|
|1/1-11/9-11/6-11/8
|
|-
|
|1/1-8/7-12/7-11/7
|
|-
|
|1/1-8/7-9/7-11/7
|
|-
|
|1/1-12/7-9/7-11/7
|
|-
|
|1/1-12/7-10/9-11/7
|
|-
|
|1/1-9/7-10/9-11/7
|
|-
|
|1/1-8/7-5/4-11/7
|
|-
|
|1/1-10/9-5/4-11/7
|
|-
|
|1/1-8/7-10/7-11/7
|
|-
|
|1/1-12/7-10/7-11/7
|
|-
|
|1/1-9/7-10/7-11/7
|
|-
|
|1/1-10/9-10/7-11/7
|
|-
|
|1/1-5/4-10/7-11/7
|
|-
|
|1/1-12/7-11/9-11/7
|
|-
|
|1/1-10/9-11/9-11/7
|
|-
|
|1/1-10/7-11/9-11/7
|
|-
|
|1/1-9/7-11/6-11/7
|
|-
|
|1/1-10/9-11/6-11/7
|
|-
|
|1/1-10/7-11/6-11/7
|
|-
|
|1/1-11/9-11/6-11/7
|
|-
|
|1/1-8/7-11/8-11/7
|
|-
|
|1/1-10/9-11/8-11/7
|
|-
|
|1/1-5/4-11/8-11/7
|
|-
|
|1/1-11/9-11/8-11/7
|
|-
|
|1/1-11/6-11/8-11/7
|
|}
== Pentads ==
{| class="wikitable"
|+
|-
! #
! Transversal
! Type
|-
|
|1/1-3/2-8/7-12/7-9/7
|
|-
|
|1/1-8/7-12/7-9/7-10/7
|
|-
|
|1/1-12/7-9/7-10/9-10/7
|
|-
|
|1/1-9/7-10/9-5/3-10/7
|
|-
|
|1/1-10/9-5/3-5/4-10/7
|
|-
|
|1/1-12/7-10/9-10/7-11/9
|
|-
|
|1/1-3/2-9/7-5/3-11/6
|
|-
|
|1/1-9/7-10/9-5/3-11/6
|
|-
|
|1/1-9/7-10/9-10/7-11/6
|
|-
|
|1/1-9/7-5/3-10/7-11/6
|
|-
|
|1/1-10/9-5/3-10/7-11/6
|
|-
|
|1/1-10/9-10/7-11/9-11/6
|
|-
|
|1/1-3/2-8/7-5/4-11/8
|
|-
|
|1/1-3/2-5/3-5/4-11/8
|
|-
|
|1/1-10/9-5/3-5/4-11/8
|
|-
|
|1/1-3/2-5/3-11/6-11/8
|
|-
|
|1/1-10/9-5/3-11/6-11/8
|
|-
|
|1/1-10/9-11/9-11/6-11/8
|
|-
|
|1/1-8/7-12/7-9/7-11/7
|
|-
|
|1/1-12/7-9/7-10/9-11/7
|
|-
|
|1/1-8/7-12/7-10/7-11/7
|
|-
|
|1/1-8/7-9/7-10/7-11/7
|
|-
|
|1/1-12/7-9/7-10/7-11/7
|
|-
|
|1/1-12/7-10/9-10/7-11/7
|
|-
|
|1/1-9/7-10/9-10/7-11/7
|
|-
|
|1/1-8/7-5/4-10/7-11/7
|
|-
|
|1/1-10/9-5/4-10/7-11/7
|
|-
|
|1/1-12/7-10/9-11/9-11/7
|
|-
|
|1/1-12/7-10/7-11/9-11/7
|
|-
|
|1/1-10/9-10/7-11/9-11/7
|
|-
|
|1/1-9/7-10/9-11/6-11/7
|
|-
|
|1/1-9/7-10/7-11/6-11/7
|
|-
|
|1/1-10/9-10/7-11/6-11/7
|
|-
|
|1/1-10/9-11/9-11/6-11/7
|
|-
|
|1/1-10/7-11/9-11/6-11/7
|
|-
|
|1/1-8/7-5/4-11/8-11/7
|
|-
|
|1/1-10/9-5/4-11/8-11/7
|
|-
|
|1/1-10/9-11/9-11/8-11/7
|
|-
|
|1/1-10/9-11/6-11/8-11/7
|
|-
|
|1/1-11/9-11/6-11/8-11/7
|
|}
== Hexads ==
{| class="wikitable"
|+
|-
! #
! Transversal
! Type
|-
|
|1/1-9/7-10/9-5/3-10/7-11/6
|
|-
|
|1/1-8/7-12/7-9/7-10/7-11/7
|
|-
|
|1/1-12/7-9/7-10/9-10/7-11/7
|
|-
|
|1/1-12/7-10/9-10/7-11/9-11/7
|
|-
|
|1/1-9/7-10/9-10/7-11/6-11/7
|
|-
|
|1/1-10/9-10/7-11/9-11/6-11/7
|
|-
|
|1/1-10/9-11/9-11/6-11/8-11/7
|
|}