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 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 perfect fifth [[generator]]s above the root.

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 [[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.

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]].

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 [[comma]]s 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.

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 or 10/9 above the root.

Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.09[[{{c}}]]) and [[27edo|16\27]] (711.11{{c}}), and generates [[~~MOS~~]] scales of the patterns [[2L 3s]] (~~pentatonic~~), [[5L 2s]] (diatonic), [[5L 7s]] (p-chromatic), [[5L 12s]], [[5L 17s]], and [[22L 5s]]. The ~~highest complexity of any chord on this list is 18 generators, and would thus require the 22-note 5L 17s MOS, though there are many chords of much lower complexity. Even the pentatonic~~ and diatonic ~~MOSes~~ contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12~~- and 17~~-note ~~MOSes are~~ needed to properly utilize ~~full 7~~- and 11-~~limit harmonies~~. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth ~~hasn't~~ been explored much either, so these ~~MOS~~ scales would be a great place to start such explorations.

Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.{{Overline|09}}[[{{c}}]]) and [[27edo|16\27]] (711.{{Overline|11}}{{c}}), and generates [[mos]] scales of the patterns [[2L 3s]] (pentic), [[5L 2s]] (diatonic), [[5L 7s]] (p-chromatic), [[5L 12s]], [[5L 17s]], and [[22L 5s]]. The pentic and diatonic scales contain some chords in the [[2.3.7 subgroup|2.3.7]] [[subgroup]], though the 12-note chromatic scale is needed to properly utilize intervals of [[5/1|5]], and intervals of [[11/1|11]] don't become common until the 17- and 22-note scales. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth has not been explored much either, so these mos scales would be a great place to start such explorations.

== Triads ==

{| class="wikitable sortable"

{| class="wikitable sortable center-1"

|-

! #

Line 45:

| 1–8/7–9/7

| Otonal/utonal

|

| 7:8:9~1/(9:8:7)

|-

| 6

Line 141:

| 1–5/4–10/7

| Utonal

| [[~~20:~~28:35|1/(7:5:4)]]

| [[28:35:40|1/(10:8:7)]]

|-

| 22

Line 153:

| 1–10/9–11/9

| Otonal/utonal

|

| 9:10:11~1/(11:10:9)

|-

| 24

Line 295:

== Tetrads ==

{| class="wikitable sortable"

{| class="wikitable sortable center-1"

|-

! #

Line 319:

| 1–9/7–3/2–12/7

| Ambitonal

| [[12:14:18:21]], [[14:18:21:24]]<br> 9-odd-limit [[ASS]]

| [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]]

|-

| 4

Line 534:

| 0–7–9–16

| 1–10/9–5/4–11/8

| Ptolemismic

| Ptolemismic/valinorsmic

|

|-

Line 719:

== Pentads ==

{| class="wikitable sortable"

{| class="wikitable sortable center-1"

|-

! #

Line 803:

| 1–9/8–5/4–11/8–3/2

| Otonal

|

| [[4:5:6:9:11]]

|-

| 14

Line 833:

| 1–11/10–11/9–11/8–11/6

| Utonal

|

| [[330:396:495:720:880|1/(24:20:16:11:9)]]

|-

| 19

Line 839:

| 1–8/7–9/7–11/7–12/7

| Otonal

|

| [[4:6:7:9:11]]

|-

| 20

Line 851:

| 1–8/7–10/7–11/7–12/7

| Otonal

|

| [[4:5:6:7:11]]

|-

| 22

Line 857:

| 1–8/7–9/7–10/7–11/7

| Otonal

|

| [[4:5:7:9:11]]

|-

| 23

Line 863:

| 1–9/7–10/7–11/7–12/7

| Otonal

|

| [[5:6:7:9:11]]

|-

| 24

Line 929:

| 1–11/10–11/9–11/7–11/6

| Utonal

|

| [[1155:1386:1980:2520:3080|1/(24:20:14:11:9)]]

|-

| 35

Line 953:

| 1–11/10–11/9–11/8–11/7

| Utonal

|

| [[924:1155:1320:2016:2464|1/(20:16:14:11:9)]]

|-

| 39

Line 959:

| 1–11/10–11/8–11/7–11/6

| Utonal

|

| [[770:924:1155:1320:1680|1/(24:20:16:14:11)]]

|-

| 40

Line 965:

| 1–11/9–11/8–11/7–11/6

| Utonal

|

| [[462:693:792:1008:1232|1/(24:16:14:11:9)]]

|}

== Hexads ==

{| class="wikitable sortable"

{| class="wikitable sortable center-1"

|-

! #

Line 1,020:

|}

~~~~

[[Category:Superpyth]]

[[Category:Lists of chords]]

[[Category:Dyadic chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Hexads]]

@@ Line 1: / Line 1: @@
-{{Editable user page| Please complete the description and tables. This page is planned to be moved to main space once completed.}}
+{{Breadcrumb|Superpyth}}
-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 perfect fifth [[generator]]s above the root.
+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 [[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.
-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]].
+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 [[comma]]s 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.
+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 or 10/9 above the root.
-Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.09[[{{c}}]]) and [[27edo|16\27]] (711.11{{c}}), and generates [[MOS]] scales of the patterns [[2L&nbsp;3s]] (pentatonic), [[5L&nbsp;2s]] (diatonic), [[5L&nbsp;7s]] (p-chromatic), [[5L&nbsp;12s]], [[5L&nbsp;17s]], and [[22L&nbsp;5s]]. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note 5L&nbsp;17s MOS, though there are many chords of much lower complexity. Even the pentatonic and diatonic MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to properly utilize full 7- and 11-limit harmonies. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth hasn't been explored much either, so these MOS scales would be a great place to start such explorations.
+Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.{{Overline|09}}[[{{c}}]]) and [[27edo|16\27]] (711.{{Overline|11}}{{c}}), and generates [[mos]] scales of the patterns [[2L&nbsp;3s]] (pentic), [[5L&nbsp;2s]] (diatonic), [[5L&nbsp;7s]] (p-chromatic), [[5L&nbsp;12s]], [[5L&nbsp;17s]], and [[22L&nbsp;5s]]. The pentic and diatonic scales contain some chords in the [[2.3.7 subgroup|2.3.7]] [[subgroup]], though the 12-note chromatic scale is needed to properly utilize intervals of [[5/1|5]], and intervals of [[11/1|11]] don't become common until the 17- and 22-note scales. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth has not been explored much either, so these mos scales would be a great place to start such explorations.
 == Triads ==
-{| class="wikitable sortable"
+{| class="wikitable sortable center-1"
 |-
 ! #
@@ Line 45: / Line 45: @@
 | 1–8/7–9/7
 | Otonal/utonal
-|
+| 7:8:9~1/(9:8:7)
 |-
 | 6
@@ Line 141: / Line 141: @@
 | 1–5/4–10/7
 | Utonal
-| [[20:28:35|1/(7:5:4)]]
+| [[28:35:40|1/(10:8:7)]]
 |-
 | 22
@@ Line 153: / Line 153: @@
 | 1–10/9–11/9
 | Otonal/utonal
-|
+| 9:10:11~1/(11:10:9)
 |-
 | 24
@@ Line 295: / Line 295: @@
 == Tetrads ==
-{| class="wikitable sortable"
+{| class="wikitable sortable center-1"
 |-
 ! #
@@ Line 319: / Line 319: @@
 | 1–9/7–3/2–12/7
 | Ambitonal
-| [[12:14:18:21]], [[14:18:21:24]]<br> 9-odd-limit [[ASS]]
+| [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]]
 |-
 | 4
@@ Line 534: / Line 534: @@
 | 0–7–9–16
 | 1–10/9–5/4–11/8
-| Ptolemismic
+| Ptolemismic/valinorsmic
 |
 |-
@@ Line 719: / Line 719: @@
 == Pentads ==
-{| class="wikitable sortable"
+{| class="wikitable sortable center-1"
 |-
 ! #
@@ Line 803: / Line 803: @@
 | 1–9/8–5/4–11/8–3/2
 | Otonal
-|
+| [[4:5:6:9:11]]
 |-
 | 14
@@ Line 833: / Line 833: @@
 | 1–11/10–11/9–11/8–11/6
 | Utonal
-|
+| [[330:396:495:720:880|1/(24:20:16:11:9)]]
 |-
 | 19
@@ Line 839: / Line 839: @@
 | 1–8/7–9/7–11/7–12/7
 | Otonal
-|
+| [[4:6:7:9:11]]
 |-
 | 20
@@ Line 851: / Line 851: @@
 | 1–8/7–10/7–11/7–12/7
 | Otonal
-|
+| [[4:5:6:7:11]]
 |-
 | 22
@@ Line 857: / Line 857: @@
 | 1–8/7–9/7–10/7–11/7
 | Otonal
-|
+| [[4:5:7:9:11]]
 |-
 | 23
@@ Line 863: / Line 863: @@
 | 1–9/7–10/7–11/7–12/7
 | Otonal
-|
+| [[5:6:7:9:11]]
 |-
 | 24
@@ Line 929: / Line 929: @@
 | 1–11/10–11/9–11/7–11/6
 | Utonal
-|
+| [[1155:1386:1980:2520:3080|1/(24:20:14:11:9)]]
 |-
 | 35
@@ Line 953: / Line 953: @@
 | 1–11/10–11/9–11/8–11/7
 | Utonal
-|
+| [[924:1155:1320:2016:2464|1/(20:16:14:11:9)]]
 |-
 | 39
@@ Line 959: / Line 959: @@
 | 1–11/10–11/8–11/7–11/6
 | Utonal
-|
+| [[770:924:1155:1320:1680|1/(24:20:16:14:11)]]
 |-
 | 40
@@ Line 965: / Line 965: @@
 | 1–11/9–11/8–11/7–11/6
 | Utonal
-|
+| [[462:693:792:1008:1232|1/(24:16:14:11:9)]]
 |}
 == Hexads ==
-{| class="wikitable sortable"
+{| class="wikitable sortable center-1"
 |-
 ! #
@@ Line 1,020: / Line 1,020: @@
 |}
-<!-- Add categories after moving to main space -->
+[[Category:Superpyth]]
+[[Category:Lists of chords]]
+[[Category:Dyadic chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
+[[Category:Hexads]]