Chords of superpyth - Revision history

Overthink: more specific

2026-02-01T01:22:43Z

more specific

← Older revision		Revision as of 01:22, 1 February 2026
Line 6:		Line 6:
	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.		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.{{Overline\|09}}[[{{c}}]]) and [[27edo\|16\27]] (711.{{Overline\|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 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.		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 ==		== Triads ==

FloraC at 21:11, 29 January 2026

2026-01-29T21:11:45Z

← Older revision		Revision as of 21:11, 29 January 2026
Line 319:		Line 319:
	\| 1–9/7–3/2–12/7		\| 1–9/7–3/2–12/7
	\| Ambitonal		\| 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		\| 4
Line 534:		Line 534:
	\| 0–7–9–16		\| 0–7–9–16
	\| 1–10/9–5/4–11/8		\| 1–10/9–5/4–11/8
	\| Ptolemismic		\| Ptolemismic/valinorsmic
	\|		\|
	\|-		\|-

FloraC: /* Triads */

2026-01-24T08:34:21Z

Triads

← Older revision		Revision as of 08:34, 24 January 2026
Line 141:		Line 141:
	\| 1–5/4–10/7		\| 1–5/4–10/7
	\| Utonal		\| Utonal
	\| [[~~20:~~28:35\|1/(7:5:4)]]		\| [[28:35:40\|1/(10:8:7)]]
	\|-		\|-
	\| 22		\| 22

FloraC: Use internal link

2026-01-23T11:15:32Z

Use internal link

← Older revision		Revision as of 11:15, 23 January 2026
Line 1:		Line 1:
	{{Breadcrumb\|Superpyth}}		{{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 nonnegative 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 [[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]].		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]].

FloraC: Don't see a reason to right-align

2026-01-23T10:46:39Z

Don't see a reason to right-align

← Older revision		Revision as of 10:46, 23 January 2026
Line 9:		Line 9:

	== Triads ==		== Triads ==
	{\| class="wikitable sortable ~~right~~-1 ~~right-4 right-5~~"		{\| class="wikitable sortable center-1"
	\|-		\|-
	! #		! #
Line 295:		Line 295:

	== Tetrads ==		== Tetrads ==
	{\| class="wikitable sortable ~~right~~-1 ~~right-4 right-5~~"		{\| class="wikitable sortable center-1"
	\|-		\|-
	! #		! #
Line 719:		Line 719:

	== Pentads ==		== Pentads ==
	{\| class="wikitable sortable ~~right~~-1 ~~right-4 right-5~~"		{\| class="wikitable sortable center-1"
	\|-		\|-
	! #		! #
Line 969:		Line 969:

	== Hexads ==		== Hexads ==
	{\| class="wikitable sortable ~~right~~-1 ~~right-4 right-5~~"		{\| class="wikitable sortable center-1"
	\|-		\|-
	! #		! #

Overthink: more correct

2026-01-22T22:45:41Z

more correct

← Older revision		Revision as of 22:45, 22 January 2026
Line 1:		Line 1:
	{{Breadcrumb\|Superpyth}}		{{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 [[Wikipedia: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 [[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]].		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]].

Overthink: table formatting

2026-01-22T22:33:06Z

table formatting

← Older revision		Revision as of 22:33, 22 January 2026
Line 9:		Line 9:

	== Triads ==		== Triads ==
	{\| class="wikitable sortable"		{\| class="wikitable sortable right-1 right-4 right-5"
	\|-		\|-
	! #		! #
Line 295:		Line 295:

	== Tetrads ==		== Tetrads ==
	{\| class="wikitable sortable"		{\| class="wikitable sortable right-1 right-4 right-5"
	\|-		\|-
	! #		! #
Line 719:		Line 719:

	== Pentads ==		== Pentads ==
	{\| class="wikitable sortable"		{\| class="wikitable sortable right-1 right-4 right-5"
	\|-		\|-
	! #		! #
Line 969:		Line 969:

	== Hexads ==		== Hexads ==
	{\| class="wikitable sortable"		{\| class="wikitable sortable right-1 right-4 right-5"
	\|-		\|-
	! #		! #

FloraC: I think the old logic is clearer

2026-01-20T15:52:17Z

I think the old logic is clearer

← Older revision		Revision as of 15:52, 20 January 2026
Line 2:		Line 2:
	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 [[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.

	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. ~~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~~.		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]].

	~~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 or 10/9 above the root.

	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]] (pentatonic), [[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.		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]] (pentatonic), [[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.

FloraC: /* Pentads */ label subchords of 4:5:6:7:9:11 (+1)

2026-01-20T15:38:05Z

Pentads: label subchords of 4:5:6:7:9:11 (+1)

← Older revision		Revision as of 15:38, 20 January 2026
Line 953:		Line 953:
	\| 1–11/10–11/9–11/8–11/7		\| 1–11/10–11/9–11/8–11/7
	\| Utonal		\| Utonal
	\|		\| [[924:1155:1320:2016:2464\|1/(20:16:14:11:9)]]
	\|-		\|-
	\| 39		\| 39

FloraC: /* Pentads */ label subchords of 4:5:6:7:9:11

2026-01-20T15:15:20Z

Pentads: label subchords of 4:5:6:7:9:11

← Older revision		Revision as of 15:15, 20 January 2026
Line 803:		Line 803:
	\| 1–9/8–5/4–11/8–3/2		\| 1–9/8–5/4–11/8–3/2
	\| Otonal		\| Otonal
	\|		\| [[4:5:6:9:11]]
	\|-		\|-
	\| 14		\| 14
Line 833:		Line 833:
	\| 1–11/10–11/9–11/8–11/6		\| 1–11/10–11/9–11/8–11/6
	\| Utonal		\| Utonal
	\|		\| [[330:396:495:720:880\|1/(24:20:16:11:9)]]
	\|-		\|-
	\| 19		\| 19
Line 839:		Line 839:
	\| 1–8/7–9/7–11/7–12/7		\| 1–8/7–9/7–11/7–12/7
	\| Otonal		\| Otonal
	\|		\| [[4:6:7:9:11]]
	\|-		\|-
	\| 20		\| 20
Line 851:		Line 851:
	\| 1–8/7–10/7–11/7–12/7		\| 1–8/7–10/7–11/7–12/7
	\| Otonal		\| Otonal
	\|		\| [[4:5:6:7:11]]
	\|-		\|-
	\| 22		\| 22
Line 857:		Line 857:
	\| 1–8/7–9/7–10/7–11/7		\| 1–8/7–9/7–10/7–11/7
	\| Otonal		\| Otonal
	\|		\| [[4:5:7:9:11]]
	\|-		\|-
	\| 23		\| 23
Line 863:		Line 863:
	\| 1–9/7–10/7–11/7–12/7		\| 1–9/7–10/7–11/7–12/7
	\| Otonal		\| Otonal
	\|		\| [[5:6:7:9:11]]
	\|-		\|-
	\| 24		\| 24
Line 929:		Line 929:
	\| 1–11/10–11/9–11/7–11/6		\| 1–11/10–11/9–11/7–11/6
	\| Utonal		\| Utonal
	\|		\| [[1155:1386:1980:2520:3080\|1/(24:20:14:11:9)]]
	\|-		\|-
	\| 35		\| 35
Line 959:		Line 959:
	\| 1–11/10–11/8–11/7–11/6		\| 1–11/10–11/8–11/7–11/6
	\| Utonal		\| Utonal
	\|		\| [[770:924:1155:1320:1680\|1/(24:20:16:14:11)]]
	\|-		\|-
	\| 40		\| 40
Line 965:		Line 965:
	\| 1–11/9–11/8–11/7–11/6		\| 1–11/9–11/8–11/7–11/6
	\| Utonal		\| Utonal
	\|		\| [[462:693:792:1008:1232\|1/(24:16:14:11:9)]]
	\|}		\|}

← Older revision		Revision as of 11:15, 23 January 2026
Line 1:		Line 1:
	{{Breadcrumb\|Superpyth}}		{{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 nonnegative 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 [[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]].		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]].

← Older revision		Revision as of 22:45, 22 January 2026
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	{{Breadcrumb\|Superpyth}}		{{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 [[Wikipedia: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 [[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]].		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]].

← Older revision		Revision as of 15:52, 20 January 2026
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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 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 [[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.

	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. ~~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~~.		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]].

	~~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 or 10/9 above the root.

	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]] (pentatonic), [[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.		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]] (pentatonic), [[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.