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.}}
{{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 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.


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]], 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]]. Chords that require 176/175 and 540/539 tempering are marked [[guanyin chords|guanyin]].  
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]], 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]]. Chords that require 176/175 and 540/539 tempering are marked [[guanyin chords| guanyin]].  


== Triads ==
== Triads ==
{| class="wikitable"
{| class="wikitable"
|+
| +
|-
|-
! #
! #
! Transversal
! Transversal
! Type
! Type
!Complexity
! Complexity
|-
|-
|1
| 1
|1/1-9/8-3/2
| 1-9/8-3/2
|ambitonal
| ambitonal
|2
| 2
|-
|-
|2
| 2
|1/1-3/2-12/7
| 1-3/2-12/7
|utonal
| utonal
|3
| 3
|-
|-
|3
| 3
|1/1-8/7-12/7
| 1-8/7-12/7
|otonal
| otonal
|3
| 3
|-
|-
|4
| 4
|1/1-9/7-3/2
| 1-9/7-3/2
|utonal
| utonal
|4
| 4
|-
|-
|5
| 5
|1/1-8/7-9/7
| 1-8/7-9/7
|ambitonal
| ambitonal
|4
| 4
|-
|-
|6
| 6
|1/1-9/7-12/7
| 1-9/7-12/7
|otonal
| otonal
|4
| 4
|-
|-
|7
| 7
|1/1-10/9-12/7
| 1-10/9-12/7
|sensamagic
| sensamagic
|7
| 7
|-
|-
|8
| 8
|1/1-10/9-9/7
| 1-10/9-9/7
|sensamagic
| sensamagic
|7
| 7
|-
|-
|9
| 9
|1/1-3/2-5/3
| 1-3/2-5/3
|otonal
| otonal
|8
| 8
|-
|-
|10
| 10
|1/1-9/7-5/3
| 1-9/7-5/3
|sensamagic
| sensamagic
|8
| 8
|-
|-
|11
| 11
|1/1-10/9-5/3
| 1-10/9-5/3
|utonal
| utonal
|8
| 8
|-
|-
|12
| 12
|1/1-5/4-3/2
| 1-5/4-3/2
|otonal
| otonal
|9
| 9
|-
|-
|13
| 13
|1/1-9/8-5/4
| 1-9/8-5/4
|otonal
| otonal
|9
| 9
|-
|-
|14
| 14
|1/1-10/9-5/4
| 1-10/9-5/4
|utonal
| utonal
|9
| 9
|-
|-
|15
| 15
|1/1-5/4-5/3
| 1-5/4-5/3
|utonal
| utonal
|9
| 9
|-
|-
|16
| 16
|1/1-8/7-10/7
| 1-8/7-10/7
|
|  
|
|  
|-
|-
|17
| 17
|1/1-12/7-10/7
| 1-12/7-10/7
|
|  
|
|  
|-
|-
|18
| 18
|1/1-9/7-10/7
| 1-9/7-10/7
|
|  
|
|  
|-
|-
|19
| 19
|1/1-10/9-10/7
| 1-10/9-10/7
|
|  
|
|  
|-
|-
|20
| 20
|1/1-5/3-10/7
| 1-5/3-10/7
|
|  
|
|  
|-
|-
|21
| 21
|1/1-5/4-10/7
| 1-5/4-10/7
|
|  
|
|  
|-
|-
|22
| 22
|1/1-12/7-11/9
| 1-12/7-11/9
|
|  
|
|  
|-
|-
|23
| 23
|1/1-10/9-11/9
| 1-10/9-11/9
|
|  
|
|  
|-
|-
|24
| 24
|1/1-10/7-11/9
| 1-10/7-11/9
|
|  
|
|  
|-
|-
|25
| 25
|1/1-3/2-11/6
| 1-3/2-11/6
|
|  
|
|  
|-
|-
|26
| 26
|1/1-9/7-11/6
| 1-9/7-11/6
|
|  
|
|  
|-
|-
|27
| 27
|1/1-10/9-11/6
| 1-10/9-11/6
|
|  
|
|  
|-
|-
|28
| 28
|1/1-5/3-11/6
| 1-5/3-11/6
|
|  
|
|  
|-
|-
|29
| 29
|1/1-10/7-11/6
| 1-10/7-11/6
|
|  
|
|  
|-
|-
|30
| 30
|1/1-11/9-11/6
| 1-11/9-11/6
|
|  
|
|  
|-
|-
|31
| 31
|1/1-3/2-11/8
| 1-3/2-11/8
|otonal
| otonal
|
|  
|-
|-
|32
| 32
|1/1-9/8-11/8
| 1-9/8-11/8
|otonal
| otonal
|
|  
|-
|-
|33
| 33
|1/1-11/10-11/8
| 1-110-11/8
|utonal
| utonal
|
|  
|-
|-
|34
| 34
|1/1-5/3-11/8
| 1-5/3-11/8
|ptolemismic
| ptolemismic
|
|  
|-
|-
|35
| 35
|1/1-5/4-11/8
| 1-5/4-11/8
|otonal
| otonal
|
|  
|-
|-
|36
| 36
|1/1-11/9-11/8
| 1-11/9-11/8
|utonal
| utonal
|
|  
|-
|-
|37
| 37
|1/1-11/6-11/8
| 1-11/6-11/8
|utonal
| utonal
|
|  
|-
|-
|38
| 38
|1/1-8/7-11/7
| 1-8/7-11/7
|
|  
|
|  
|-
|-
|39
| 39
|1/1-12/7-11/7
| 1-12/7-11/7
|
|  
|
|  
|-
|-
|40
| 40
|1/1-9/7-11/7
| 1-9/7-11/7
|
|  
|
|  
|-
|-
|41
| 41
|1/1-10/9-11/7
| 1-10/9-11/7
|
|  
|
|  
|-
|-
|42
| 42
|1/1-5/4-11/7
| 1-5/4-11/7
|
|  
|
|  
|-
|-
|43
| 43
|1/1-10/7-11/7
| 1-10/7-11/7
|
|  
|
|  
|-
|-
|44
| 44
|1/1-11/9-11/7
| 1-11/9-11/7
|
|  
|
|  
|-
|-
|45
| 45
|1/1-11/6-11/7
| 1-11/6-11/7
|
|  
|
|  
|-
|-
|46
| 46
|1/1-11/8-11/7
| 1-11/8-11/7
|
|  
|
|  
|}
| }


== Tetrads ==
== Tetrads ==


{| class="wikitable"
{| class="wikitable"
|+
| +
|-
|-
! #
! #
Line 254: Line 254:
!Complexity
!Complexity
|-
|-
|1
| 1
|1/1-3/2-8/7-12/7
| 1-3/2-8/7-12/7
|
|  
|
|  
|-
|-
|2
| 2
|1/1-3/2-8/7-9/7
| 1-3/2-8/7-9/7
|
|  
|
|  
|-
|-
|3
| 3
|1/1-3/2-12/7-9/7
| 1-3/2-12/7-9/7
|
|  
|
|  
|-
|-
|4
| 4
|1/1-8/7-12/7-9/7
| 1-8/7-12/7-9/7
|
|  
|
|  
|-
|-
|5
| 5
|1/1-12/7-9/7-10/9
| 1-12/7-9/7-10/9
|
|  
|
|  
|-
|-
|6
| 6
|1/1-3/2-9/7-5/3
| 1-3/2-9/7-5/3
|
|  
|
|  
|-
|-
|7
| 7
|1/1-9/7-10/9-5/3
| 1-9/7-10/9-5/3
|
|  
|
|  
|-
|-
|8
| 8
|1/1-3/2-8/7-5/4
| 1-3/2-8/7-5/4
|
|  
|
|  
|-
|-
|9
| 9
|1/1-3/2-5/3-5/4
| 1-3/2-5/3-5/4
|
|  
|
|  
|-
|-
|10
| 10
|1/1-10/9-5/3-5/4
| 1-10/9-5/3-5/4
|
|  
|
|  
|-
|-
|11
| 11
|1/1-8/7-12/7-10/7
| 1-8/7-12/7-10/7
|
|  
|
|  
|-
|-
|12
| 12
|1/1-8/7-9/7-10/7
| 1-8/7-9/7-10/7
|
|  
|
|  
|-
|-
|13
| 13
|1/1-12/7-9/7-10/7
| 1-12/7-9/7-10/7
|
|  
|
|  
|-
|-
|14
| 14
|1/1-12/7-10/9-10/7
| 1-12/7-10/9-10/7
|
|  
|
|  
|-
|-
|15
| 15
|1/1-9/7-10/9-10/7
| 1-9/7-10/9-10/7
|
|  
|
|  
|-
|-
|16
| 16
|1/1-9/7-5/3-10/7
| 1-9/7-5/3-10/7
|
|  
|
|  
|-
|-
|17
| 17
|1/1-10/9-5/3-10/7
| 1-10/9-5/3-10/7
|
|  
|
|  
|-
|-
|18
| 18
|1/1-8/7-5/4-10/7
| 1-8/7-5/4-10/7
|
|  
|
|  
|-
|-
|19
| 19
|1/1-10/9-5/4-10/7
| 1-10/9-5/4-10/7
|
|  
|
|  
|-
|-
|20
| 20
|1/1-5/3-5/4-10/7
| 1-5/3-5/4-10/7
|
|  
|
|  
|-
|-
|21
| 21
|1/1-12/7-10/9-11/9
| 1-12/7-10/9-11/9
|
|  
|
|  
|-
|-
|22
| 22
|1/1-12/7-10/7-11/9
| 1-12/7-10/7-11/9
|
|  
|
|  
|-
|-
|23
| 23
|1/1-10/9-10/7-11/9
| 1-10/9-10/7-11/9
|
|  
|
|  
|-
|-
|24
| 24
|1/1-3/2-9/7-11/6
| 1-3/2-9/7-11/6
|
|  
|
|  
|-
|-
|25
| 25
|1/1-9/7-10/9-11/6
| 1-9/7-10/9-11/6
|
|  
|
|  
|-
|-
|26
| 26
|1/1-3/2-5/3-11/6
| 1-3/2-5/3-11/6
|
|  
|
|  
|-
|-
|27
| 27
|1/1-9/7-5/3-11/6
| 1-9/7-5/3-11/6
|
|  
|
|  
|-
|-
|28
| 28
|1/1-10/9-5/3-11/6
| 1-10/9-5/3-11/6
|
|  
|
|  
|-
|-
|29
| 29
|1/1-9/7-10/7-11/6
| 1-9/7-10/7-11/6
|
|  
|
|  
|-
|-
|30
| 30
|1/1-10/9-10/7-11/6
| 1-10/9-10/7-11/6
|
|  
|
|  
|-
|-
|31
| 31
|1/1-5/3-10/7-11/6
| 1-5/3-10/7-11/6
|
|  
|
|  
|-
|-
|32
| 32
|1/1-10/9-11/9-11/6
| 1-10/9-11/9-11/6
|
|  
|
|  
|-
|-
|33
| 33
|1/1-10/7-11/9-11/6
| 1-10/7-11/9-11/6
|
|  
|
|  
|-
|-
|34
| 34
|1/1-3/2-8/7-11/8
| 1-3/2-8/7-11/8
|
|  
|
|  
|-
|-
|35
| 35
|1/1-3/2-5/3-11/8
| 1-3/2-5/3-11/8
|
|  
|
|  
|-
|-
|36
| 36
|1/1-10/9-5/3-11/8
| 1-10/9-5/3-11/8
|
|  
|
|  
|-
|-
|37
| 37
|1/1-3/2-5/4-11/8
| 1-3/2-5/4-11/8
|
|  
|
|  
|-
|-
|38
| 38
|1/1-8/7-5/4-11/8
| 1-8/7-5/4-11/8
|
|  
|
|  
|-
|-
|39
| 39
|1/1-10/9-5/4-11/8
| 1-10/9-5/4-11/8
|
|  
|
|  
|-
|-
|40
| 40
|1/1-5/3-5/4-11/8
| 1-5/3-5/4-11/8
|
|  
|
|  
|-
|-
|41
| 41
|1/1-10/9-11/9-11/8
| 1-10/9-11/9-11/8
|
|  
|
|  
|-
|-
|42
| 42
|1/1-3/2-11/6-11/8
| 1-3/2-11/6-11/8
|
|  
|
|  
|-
|-
|43
| 43
|1/1-10/9-11/6-11/8
| 1-10/9-11/6-11/8
|
|  
|
|  
|-
|-
|44
| 44
|1/1-5/3-11/6-11/8
| 1-5/3-11/6-11/8
|
|  
|
|  
|-
|-
|45
| 45
|1/1-11/9-11/6-11/8
| 1-11/9-11/6-11/8
|
|  
|
|  
|-
|-
|46
| 46
|1/1-8/7-12/7-11/7
| 1-8/7-12/7-11/7
|
|  
|
|  
|-
|-
|47
| 47
|1/1-8/7-9/7-11/7
| 1-8/7-9/7-11/7
|
|  
|
|  
|-
|-
|48
| 48
|1/1-12/7-9/7-11/7
| 1-12/7-9/7-11/7
|
|  
|
|  
|-
|-
|49
| 49
|1/1-12/7-10/9-11/7
| 1-12/7-10/9-11/7
|
|  
|
|  
|-
|-
|50
| 50
|1/1-9/7-10/9-11/7
| 1-9/7-10/9-11/7
|
|  
|
|  
|-
|-
|51
| 51
|1/1-8/7-5/4-11/7
| 1-8/7-5/4-11/7
|
|  
|
|  
|-
|-
|52
| 52
|1/1-10/9-5/4-11/7
| 1-10/9-5/4-11/7
|
|  
|
|  
|-
|-
|53
| 53
|1/1-8/7-10/7-11/7
| 1-8/7-10/7-11/7
|
|  
|
|  
|-
|-
|54
| 54
|1/1-12/7-10/7-11/7
| 1-12/7-10/7-11/7
|
|  
|
|  
|-
|-
|55
| 55
|1/1-9/7-10/7-11/7
| 1-9/7-10/7-11/7
|
|  
|
|  
|-
|-
|56
| 56
|1/1-10/9-10/7-11/7
| 1-10/9-10/7-11/7
|
|  
|
|  
|-
|-
|57
| 57
|1/1-5/4-10/7-11/7
| 1-5/4-10/7-11/7
|
|  
|
|  
|-
|-
|58
| 58
|1/1-12/7-11/9-11/7
| 1-12/7-11/9-11/7
|
|  
|
|  
|-
|-
|59
| 59
|1/1-10/9-11/9-11/7
| 1-10/9-11/9-11/7
|
|  
|
|  
|-
|-
|60
| 60
|1/1-10/7-11/9-11/7
| 1-10/7-11/9-11/7
|
|  
|
|  
|-
|-
|61
| 61
|1/1-9/7-11/6-11/7
| 1-9/7-11/6-11/7
|
|  
|
|  
|-
|-
|62
| 62
|1/1-10/9-11/6-11/7
| 1-10/9-11/6-11/7
|
|  
|
|  
|-
|-
|63
| 63
|1/1-10/7-11/6-11/7
| 1-10/7-11/6-11/7
|
|  
|
|  
|-
|-
|64
| 64
|1/1-11/9-11/6-11/7
| 1-11/9-11/6-11/7
|
|  
|
|  
|-
|-
|65
| 65
|1/1-8/7-11/8-11/7
| 1-8/7-11/8-11/7
|
|  
|
|  
|-
|-
|66
| 66
|1/1-10/9-11/8-11/7
| 1-10/9-11/8-11/7
|
|  
|
|  
|-
|-
|67
| 67
|1/1-5/4-11/8-11/7
| 1-5/4-11/8-11/7
|
|  
|
|  
|-
|-
|68
| 68
|1/1-11/9-11/8-11/7
| 1-11/9-11/8-11/7
|
|  
|
|  
|-
|-
|69
| 69
|1/1-11/6-11/8-11/7
| 1-11/6-11/8-11/7
|
|  
|
|  
|}
| }


== Pentads ==
== Pentads ==


{| class="wikitable"
{| class="wikitable"
|+
| +
|-
|-
! #
! #
Line 610: Line 610:
!Complexity
!Complexity
|-
|-
|1
| 1
|1/1-3/2-8/7-12/7-9/7
| 1-3/2-8/7-12/7-9/7
|
|  
|
|  
|-
|-
|2
| 2
|1/1-8/7-12/7-9/7-10/7
| 1-8/7-12/7-9/7-10/7
|
|  
|
|  
|-
|-
|3
| 3
|1/1-12/7-9/7-10/9-10/7
| 1-12/7-9/7-10/9-10/7
|
|  
|
|  
|-
|-
|4
| 4
|1/1-9/7-10/9-5/3-10/7
| 1-9/7-10/9-5/3-10/7
|
|  
|
|  
|-
|-
|5
| 5
|1/1-10/9-5/3-5/4-10/7
| 1-10/9-5/3-5/4-10/7
|
|  
|
|  
|-
|-
|6
| 6
|1/1-12/7-10/9-10/7-11/9
| 1-12/7-10/9-10/7-11/9
|
|  
|
|  
|-
|-
|7
| 7
|1/1-3/2-9/7-5/3-11/6
| 1-3/2-9/7-5/3-11/6
|
|  
|
|  
|-
|-
|8
| 8
|1/1-9/7-10/9-5/3-11/6
| 1-9/7-10/9-5/3-11/6
|
|  
|
|  
|-
|-
|9
| 9
|1/1-9/7-10/9-10/7-11/6
| 1-9/7-10/9-10/7-11/6
|
|  
|
|  
|-
|-
|10
| 10
|1/1-9/7-5/3-10/7-11/6
| 1-9/7-5/3-10/7-11/6
|
|  
|
|  
|-
|-
|11
| 11
|1/1-10/9-5/3-10/7-11/6
| 1-10/9-5/3-10/7-11/6
|
|  
|
|  
|-
|-
|12
| 12
|1/1-10/9-10/7-11/9-11/6
| 1-10/9-10/7-11/9-11/6
|
|  
|
|  
|-
|-
|13
| 13
|1/1-3/2-8/7-5/4-11/8
| 1-3/2-8/7-5/4-11/8
|
|  
|
|  
|-
|-
|14
| 14
|1/1-3/2-5/3-5/4-11/8
| 1-3/2-5/3-5/4-11/8
|
|  
|
|  
|-
|-
|15
| 15
|1/1-10/9-5/3-5/4-11/8
| 1-10/9-5/3-5/4-11/8
|
|  
|
|  
|-
|-
|16
| 16
|1/1-3/2-5/3-11/6-11/8
| 1-3/2-5/3-11/6-11/8
|
|  
|
|  
|-
|-
|17
| 17
|1/1-10/9-5/3-11/6-11/8
| 1-10/9-5/3-11/6-11/8
|
|  
|
|  
|-
|-
|18
| 18
|1/1-10/9-11/9-11/6-11/8
| 1-10/9-11/9-11/6-11/8
|
|  
|
|  
|-
|-
|19
| 19
|1/1-8/7-12/7-9/7-11/7
| 1-8/7-12/7-9/7-11/7
|
|  
|
|  
|-
|-
|20
| 20
|1/1-12/7-9/7-10/9-11/7
| 1-12/7-9/7-10/9-11/7
|
|  
|
|  
|-
|-
|21
| 21
|1/1-8/7-12/7-10/7-11/7
| 1-8/7-12/7-10/7-11/7
|
|  
|
|  
|-
|-
|22
| 22
|1/1-8/7-9/7-10/7-11/7
| 1-8/7-9/7-10/7-11/7
|
|  
|
|  
|-
|-
|23
| 23
|1/1-12/7-9/7-10/7-11/7
| 1-12/7-9/7-10/7-11/7
|
|  
|
|  
|-
|-
|24
| 24
|1/1-12/7-10/9-10/7-11/7
| 1-12/7-10/9-10/7-11/7
|
|  
|
|  
|-
|-
|25
| 25
|1/1-9/7-10/9-10/7-11/7
| 1-9/7-10/9-10/7-11/7
|
|  
|
|  
|-
|-
|26
| 26
|1/1-8/7-5/4-10/7-11/7
| 1-8/7-5/4-10/7-11/7
|
|  
|
|  
|-
|-
|27
| 27
|1/1-10/9-5/4-10/7-11/7
| 1-10/9-5/4-10/7-11/7
|
|  
|
|  
|-
|-
|28
| 28
|1/1-12/7-10/9-11/9-11/7
| 1-12/7-10/9-11/9-11/7
|
|  
|
|  
|-
|-
|29
| 29
|1/1-12/7-10/7-11/9-11/7
| 1-12/7-10/7-11/9-11/7
|
|  
|
|  
|-
|-
|30
| 30
|1/1-10/9-10/7-11/9-11/7
| 1-10/9-10/7-11/9-11/7
|
|  
|
|  
|-
|-
|31
| 31
|1/1-9/7-10/9-11/6-11/7
| 1-9/7-10/9-11/6-11/7
|
|  
|
|  
|-
|-
|32
| 32
|1/1-9/7-10/7-11/6-11/7
| 1-9/7-10/7-11/6-11/7
|
|  
|
|  
|-
|-
|33
| 33
|1/1-10/9-10/7-11/6-11/7
| 1-10/9-10/7-11/6-11/7
|
|  
|
|  
|-
|-
|34
| 34
|1/1-10/9-11/9-11/6-11/7
| 1-10/9-11/9-11/6-11/7
|
|  
|
|  
|-
|-
|35
| 35
|1/1-10/7-11/9-11/6-11/7
| 1-10/7-11/9-11/6-11/7
|
|  
|
|  
|-
|-
|36
| 36
|1/1-8/7-5/4-11/8-11/7
| 1-8/7-5/4-11/8-11/7
|
|  
|
|  
|-
|-
|37
| 37
|1/1-10/9-5/4-11/8-11/7
| 1-10/9-5/4-11/8-11/7
|
|  
|
|  
|-
|-
|38
| 38
|1/1-10/9-11/9-11/8-11/7
| 1-10/9-11/9-11/8-11/7
|
|  
|
|  
|-
|-
|39
| 39
|1/1-10/9-11/6-11/8-11/7
| 1-10/9-11/6-11/8-11/7
|
|  
|
|  
|-
|-
|40
| 40
|1/1-11/9-11/6-11/8-11/7
| 1-11/9-11/6-11/8-11/7
|
|  
|
|  
|}
| }


== Hexads ==
== Hexads ==


{| class="wikitable"
{| class="wikitable"
|+
| +
|-
|-
! #
! #
Line 821: Line 821:
!Complexity
!Complexity
|-
|-
|1
| 1
|1/1-9/7-10/9-5/3-10/7-11/6
| 1-9/7-10/9-5/3-10/7-11/6
|
|  
|15
| 15
|-
|-
|2
| 2
|1/1-8/7-9/7-10/7-11/7-12/7
| 1-8/7-9/7-10/7-11/7-12/7
|otonal
| otonal
|18
| 18
|-
|-
|3
| 3
|1/1-12/7-9/7-10/9-10/7-11/7
| 1-12/7-9/7-10/9-10/7-11/7
|
|  
|18
| 18
|-
|-
|4
| 4
|1/1-12/7-10/9-10/7-11/9-11/7
| 1-12/7-10/9-10/7-11/9-11/7
|
|  
|18
| 18
|-
|-
|5
| 5
|1/1-9/7-10/9-10/7-11/6-11/7
| 1-9/7-10/9-10/7-11/6-11/7
|
|  
|18
| 18
|-
|-
|6
| 6
|1/1-10/9-10/7-11/9-11/6-11/7
| 1-10/9-10/7-11/9-11/6-11/7
|
|  
|18
| 18
|-
|-
|7
| 7
|1/1-11/10-11/9-11/8-11/7-11/6
| 1-110-11/9-11/8-11/7-11/6
|utonal
| utonal
|18
| 18
|}
| }


[[Category:Todo:expand]]
[[Category:Todo:expand]]

Revision as of 06:53, 13 December 2025

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Below are listed the 11-odd-limit 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 valinorsmic, by 245/243 sensamagic, by 540/539 swetismic. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked ares. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked octarod. Chords that require 176/175 and 540/539 tempering are marked guanyin.

Triads

+
# Transversal Type Complexity
1 1-9/8-3/2 ambitonal 2
2 1-3/2-12/7 utonal 3
3 1-8/7-12/7 otonal 3
4 1-9/7-3/2 utonal 4
5 1-8/7-9/7 ambitonal 4
6 1-9/7-12/7 otonal 4
7 1-10/9-12/7 sensamagic 7
8 1-10/9-9/7 sensamagic 7
9 1-3/2-5/3 otonal 8
10 1-9/7-5/3 sensamagic 8
11 1-10/9-5/3 utonal 8
12 1-5/4-3/2 otonal 9
13 1-9/8-5/4 otonal 9
14 1-10/9-5/4 utonal 9
15 1-5/4-5/3 utonal 9
16 1-8/7-10/7
17 1-12/7-10/7
18 1-9/7-10/7
19 1-10/9-10/7
20 1-5/3-10/7
21 1-5/4-10/7
22 1-12/7-11/9
23 1-10/9-11/9
24 1-10/7-11/9
25 1-3/2-11/6
26 1-9/7-11/6
27 1-10/9-11/6
28 1-5/3-11/6
29 1-10/7-11/6
30 1-11/9-11/6
31 1-3/2-11/8 otonal
32 1-9/8-11/8 otonal
33 1-110-11/8 utonal
34 1-5/3-11/8 ptolemismic
35 1-5/4-11/8 otonal
36 1-11/9-11/8 utonal
37 1-11/6-11/8 utonal
38 1-8/7-11/7
39 1-12/7-11/7
40 1-9/7-11/7
41 1-10/9-11/7
42 1-5/4-11/7
43 1-10/7-11/7
44 1-11/9-11/7
45 1-11/6-11/7
46 1-11/8-11/7 }

Tetrads

+
# Transversal Type Complexity
1 1-3/2-8/7-12/7
2 1-3/2-8/7-9/7
3 1-3/2-12/7-9/7
4 1-8/7-12/7-9/7
5 1-12/7-9/7-10/9
6 1-3/2-9/7-5/3
7 1-9/7-10/9-5/3
8 1-3/2-8/7-5/4
9 1-3/2-5/3-5/4
10 1-10/9-5/3-5/4
11 1-8/7-12/7-10/7
12 1-8/7-9/7-10/7
13 1-12/7-9/7-10/7
14 1-12/7-10/9-10/7
15 1-9/7-10/9-10/7
16 1-9/7-5/3-10/7
17 1-10/9-5/3-10/7
18 1-8/7-5/4-10/7
19 1-10/9-5/4-10/7
20 1-5/3-5/4-10/7
21 1-12/7-10/9-11/9
22 1-12/7-10/7-11/9
23 1-10/9-10/7-11/9
24 1-3/2-9/7-11/6
25 1-9/7-10/9-11/6
26 1-3/2-5/3-11/6
27 1-9/7-5/3-11/6
28 1-10/9-5/3-11/6
29 1-9/7-10/7-11/6
30 1-10/9-10/7-11/6
31 1-5/3-10/7-11/6
32 1-10/9-11/9-11/6
33 1-10/7-11/9-11/6
34 1-3/2-8/7-11/8
35 1-3/2-5/3-11/8
36 1-10/9-5/3-11/8
37 1-3/2-5/4-11/8
38 1-8/7-5/4-11/8
39 1-10/9-5/4-11/8
40 1-5/3-5/4-11/8
41 1-10/9-11/9-11/8
42 1-3/2-11/6-11/8
43 1-10/9-11/6-11/8
44 1-5/3-11/6-11/8
45 1-11/9-11/6-11/8
46 1-8/7-12/7-11/7
47 1-8/7-9/7-11/7
48 1-12/7-9/7-11/7
49 1-12/7-10/9-11/7
50 1-9/7-10/9-11/7
51 1-8/7-5/4-11/7
52 1-10/9-5/4-11/7
53 1-8/7-10/7-11/7
54 1-12/7-10/7-11/7
55 1-9/7-10/7-11/7
56 1-10/9-10/7-11/7
57 1-5/4-10/7-11/7
58 1-12/7-11/9-11/7
59 1-10/9-11/9-11/7
60 1-10/7-11/9-11/7
61 1-9/7-11/6-11/7
62 1-10/9-11/6-11/7
63 1-10/7-11/6-11/7
64 1-11/9-11/6-11/7
65 1-8/7-11/8-11/7
66 1-10/9-11/8-11/7
67 1-5/4-11/8-11/7
68 1-11/9-11/8-11/7
69 1-11/6-11/8-11/7 }

Pentads

+
# Transversal Type Complexity
1 1-3/2-8/7-12/7-9/7
2 1-8/7-12/7-9/7-10/7
3 1-12/7-9/7-10/9-10/7
4 1-9/7-10/9-5/3-10/7
5 1-10/9-5/3-5/4-10/7
6 1-12/7-10/9-10/7-11/9
7 1-3/2-9/7-5/3-11/6
8 1-9/7-10/9-5/3-11/6
9 1-9/7-10/9-10/7-11/6
10 1-9/7-5/3-10/7-11/6
11 1-10/9-5/3-10/7-11/6
12 1-10/9-10/7-11/9-11/6
13 1-3/2-8/7-5/4-11/8
14 1-3/2-5/3-5/4-11/8
15 1-10/9-5/3-5/4-11/8
16 1-3/2-5/3-11/6-11/8
17 1-10/9-5/3-11/6-11/8
18 1-10/9-11/9-11/6-11/8
19 1-8/7-12/7-9/7-11/7
20 1-12/7-9/7-10/9-11/7
21 1-8/7-12/7-10/7-11/7
22 1-8/7-9/7-10/7-11/7
23 1-12/7-9/7-10/7-11/7
24 1-12/7-10/9-10/7-11/7
25 1-9/7-10/9-10/7-11/7
26 1-8/7-5/4-10/7-11/7
27 1-10/9-5/4-10/7-11/7
28 1-12/7-10/9-11/9-11/7
29 1-12/7-10/7-11/9-11/7
30 1-10/9-10/7-11/9-11/7
31 1-9/7-10/9-11/6-11/7
32 1-9/7-10/7-11/6-11/7
33 1-10/9-10/7-11/6-11/7
34 1-10/9-11/9-11/6-11/7
35 1-10/7-11/9-11/6-11/7
36 1-8/7-5/4-11/8-11/7
37 1-10/9-5/4-11/8-11/7
38 1-10/9-11/9-11/8-11/7
39 1-10/9-11/6-11/8-11/7
40 1-11/9-11/6-11/8-11/7 }

Hexads

+
# Transversal Type Complexity
1 1-9/7-10/9-5/3-10/7-11/6 15
2 1-8/7-9/7-10/7-11/7-12/7 otonal 18
3 1-12/7-9/7-10/9-10/7-11/7 18
4 1-12/7-10/9-10/7-11/9-11/7 18
5 1-9/7-10/9-10/7-11/6-11/7 18
6 1-10/9-10/7-11/9-11/6-11/7 18
7 1-110-11/9-11/8-11/7-11/6 utonal 18 }
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