Dyadic chord - Revision history

Xenllium: Merged list of innate chords to the list of essentially tempered dyadic chords

2026-06-07T08:07:02Z

Merged list of innate chords to the list of essentially tempered dyadic chords

← Older revision		Revision as of 08:07, 7 June 2026
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	== List of essentially tempered dyadic chords ==		== List of essentially tempered dyadic chords ==
	Here are some pages on certain essentially tempered dyadic chords, sorted by the lowest odd limit in which they are available. See [[Dyadic chord/Pattern of essentially tempered chords]] for some notable abstract chord patterns.		Here are some pages on certain essentially tempered dyadic chords, sorted by the lowest odd limit in which they are available (<span style="background-color:#D4D4D4">shaded rows</span> mark [[octave-splitting comma]] chords, which are induced by octave-splitting commas). See [[Dyadic chord/Pattern of essentially tempered chords]] for some notable abstract chord patterns.

			=== 5-odd-limit ===
			{\| class="wikitable"
			\|-
			! Chords !! Associated Temperament !! Associated Commas
			\|-
			\| bgcolor="#D4D4D4" \| [[Augmented triad]] \|\| bgcolor="#D4D4D4" \| [[Augmented (temperament)\|Augmented]] \|\| bgcolor="#D4D4D4" \| [[128/125]]
			\|}

	=== 7-odd-limit ===		=== 7-odd-limit ===
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	! Chords !! Associated temperament !! Associated commas		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]		\| bgcolor="#D4D4D4" \| [[Jubilismic chords]] \|\| bgcolor="#D4D4D4" \| [[Jubilismic]] \|\| bgcolor="#D4D4D4" \| [[50/49]]
	\|-		\|-
	\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]		\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]
	\|-		\|-
	\| [[Starling chords]] \|\| [[Starling]] \|\| [[126/125]]		\| [[Starling chords]] \|\| [[Starling]] \|\| [[126/125]]
			\|-
			\| bgcolor="#D4D4D4" \| [[5edo\|Blackwood pentad]] \|\| bgcolor="#D4D4D4" \| [[Blackwood]] \|\| bgcolor="#D4D4D4" \| [[28/27]], [[49/48]]
			\|-
			\| bgcolor="#D4D4D4" \| [[Diminished seventh chord]] \|\| bgcolor="#D4D4D4" \| [[Diminished (temperament)\|Diminished]] \|\| bgcolor="#D4D4D4" \| [[36/35]], [[50/49]]
	\|}		\|}

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	\|-		\|-
	\| [[Pentacircle chords]] \|\| [[Pentacircle]] \|\| [[896/891]]		\| [[Pentacircle chords]] \|\| [[Pentacircle]] \|\| [[896/891]]
			\|-
			\| bgcolor="#D4D4D4" \| [[Jubilismic chords\|Undecimal jubilismic chords]] \|\| bgcolor="#D4D4D4" \| [[Jubilismic family\|Undecimal jubilismic]] \|\| bgcolor="#D4D4D4" \| [[50/49]], [[99/98]]
	\|-		\|-
	\| [[Undecimal marvel chords]] \|\| [[Marvel]] \|\| 225/224, 385/384		\| [[Undecimal marvel chords]] \|\| [[Marvel]] \|\| 225/224, 385/384
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	\|-		\|-
	\| [[Jacobin chords]] \|\| [[The Jacobins\|Jacobin]] \|\| [[6656/6655]]		\| [[Jacobin chords]] \|\| [[The Jacobins\|Jacobin]] \|\| [[6656/6655]]
	\|}

	~~== List of innate comma chords ==~~
	~~{\| class="wikitable"~~
	\|-
	~~! Chords !! Associated Temperament !! Associated Commas~~
	\|-
	~~\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]~~
	\|-
	~~\| [[Augmented triad]] \|\| [[Augmented (temperament)\|Augmented]] \|\| [[128/125]]~~
	\|}		\|}

FloraC: Undo. See talk

2026-05-09T10:52:00Z

Undo. See talk

← Older revision		Revision as of 10:52, 9 May 2026
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	== Innate comma chord ==		== Innate comma chord ==
	An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[#~~Essentially_tempered_dyadic_chord~~\|essentially tempered chord]], an innate comma chord describes only the general chord shape: the [[mapped interval]] representations or the [[interval span\|sizes]] of its constituent intervals.		An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[#Essentially tempered dyadic chord\|essentially tempered chord]], an innate comma chord describes only the general chord shape: the [[mapped interval]] representations or the [[interval span\|sizes]] of its constituent intervals.

	For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.)		For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.)

	Another example is a [[Jubilismic chords\|jubilismic tetrad]], 1–5/4–7/5–7/4–2 (with steps of 5/4, 8/7, 5/4, 8/7), tempered by [[50/49]], which is an innate comma chord in the 7-odd-limit, with impossibility to tune all two ~5/4s and two ~8/7s (or equate ~7/5 with ~10/7) justly with pure octaves. Other jubilismic tetrads are also innate comma chords: 1–6/5–7/5–12/7–2 (with steps of 6/5, 7/6, 6/5, 7/6) and 1–9/7–7/5–9/5–2 (9-odd-limit, with steps of 9/7, 10/9, 9/7, 10/9).

	== Anomalous saturated suspension ==		== Anomalous saturated suspension ==
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	\|-		\|-
	! Chords !! Associated temperament !! Associated commas		! Chords !! Associated temperament !! Associated commas
			\|-
			\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]
	\|-		\|-
	\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]		\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]
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	\|-		\|-
	\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]		\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]
	\|-
	~~\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]~~
	\|-		\|-
	\| [[Augmented triad]] \|\| [[Augmented (temperament)\|Augmented]] \|\| [[128/125]]		\| [[Augmented triad]] \|\| [[Augmented (temperament)\|Augmented]] \|\| [[128/125]]

Xenllium: Jubilismic chords are innate because they cannot be mapped justly with pure octaves

2026-05-09T10:07:47Z

Jubilismic chords are innate because they cannot be mapped justly with pure octaves

← Older revision		Revision as of 10:07, 9 May 2026
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	== Innate comma chord ==		== Innate comma chord ==
	An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[#Essentially_tempered_dyadic_chord\|essentially tempered chord]], an innate comma chord describes only the general chord shape: the [[mapped interval]] representations or the [[interval span\|sizes]] of its constituent intervals. For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.)		An '''innate comma chord''', proposed by [[Kite Giedraitis]], is the type of chord that cannot be mapped to just intonation in a given prime limit and odd limit. However, instead of specifying the targeted JI ratios as in an [[#Essentially_tempered_dyadic_chord\|essentially tempered chord]], an innate comma chord describes only the general chord shape: the [[mapped interval]] representations or the [[interval span\|sizes]] of its constituent intervals.

			For example, the [[augmented triad]] in 5-limit JI is an innate comma chord below the 25-odd-limit, because it is impossible to tune all three major thirds (in the four-note chord doubling the root up an octave) to [[5/4]] or any other 5-limit interval with odd limit below 25: the innate comma here is 128/125 (41¢). In practice, it might be sung or played justly but with a large odd limit (containing [[wolf interval]]s): for example, 1–5/4–8/5–2, or 1–5/4–25/16–2 (or even 1–5/4–25/16–125/64). Or it might be tempered, e.g. in 12edo as 0¢–400¢–800¢–1200¢. In 7-limit JI, one of the major thirds can be tuned to 9/7, reducing the innate comma to 225/224 (only 8¢). This comma can be distributed among the three thirds, tempering each by only a few cents, which is usually close enough to be acceptable. In 11-limit JI, the augmented chord is not an innate comma chord, because it can be tuned justly as 7:9:11:14, a low enough odd limit to "ring". (However, it is debatable whether this chord qualifies as an augmented triad, because the middle [[11/9]] interval is a neutral third rather than a major third.)

			Another example is a [[Jubilismic chords\|jubilismic tetrad]], 1–5/4–7/5–7/4–2 (with steps of 5/4, 8/7, 5/4, 8/7), tempered by [[50/49]], which is an innate comma chord in the 7-odd-limit, with impossibility to tune all two ~5/4s and two ~8/7s (or equate ~7/5 with ~10/7) justly with pure octaves. Other jubilismic tetrads are also innate comma chords: 1–6/5–7/5–12/7–2 (with steps of 6/5, 7/6, 6/5, 7/6) and 1–9/7–7/5–9/5–2 (9-odd-limit, with steps of 9/7, 10/9, 9/7, 10/9).

	== Anomalous saturated suspension ==		== Anomalous saturated suspension ==
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	\|-		\|-
	! Chords !! Associated temperament !! Associated commas		! Chords !! Associated temperament !! Associated commas
	\|-
	~~\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]~~
	\|-		\|-
	\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]		\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]
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	\|-		\|-
	\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]		\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]
			\|-
			\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]
	\|-		\|-
	\| [[Augmented triad]] \|\| [[Augmented (temperament)\|Augmented]] \|\| [[128/125]]		\| [[Augmented triad]] \|\| [[Augmented (temperament)\|Augmented]] \|\| [[128/125]]

FloraC: Jubilismic chords are ordinary det chords. Sooty fox chords exist.

2026-03-05T07:22:31Z

Jubilismic chords are ordinary det chords. Sooty fox chords exist.

← Older revision		Revision as of 07:22, 5 March 2026
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	\|-		\|-
	! Chords !! Associated temperament !! Associated commas		! Chords !! Associated temperament !! Associated commas
			\|-
			\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]
	\|-		\|-
	\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]		\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]
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	\|-		\|-
	\| [[Marveltwin chords]] \|\| [[Marveltwin]] \|\| [[325/324]]		\| [[Marveltwin chords]] \|\| [[Marveltwin]] \|\| [[325/324]]
			\|-
			\| [[Sooty fox chords]] \|\| [[Sooty fox]] \|\| [[343/338]]
	\|-		\|-
	\| [[Ratwolfsmic chords]] \|\| [[Ratwolfsmic]] \|\| [[351/350]]		\| [[Ratwolfsmic chords]] \|\| [[Ratwolfsmic]] \|\| [[351/350]]
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	\|-		\|-
	! Chords !! Associated Temperament !! Associated Commas		! Chords !! Associated Temperament !! Associated Commas
	\|-
	~~\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]~~
	\|-		\|-
	\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]		\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]

Xenllium at 21:57, 4 March 2026

2026-03-04T21:57:46Z

← Older revision		Revision as of 21:57, 4 March 2026
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	\|-		\|-
	! Chords !! Associated temperament !! Associated commas		! Chords !! Associated temperament !! Associated commas
	\|-
	~~\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]~~
	\|-		\|-
	\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]		\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]
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	\|-		\|-
	\| [[Marveltwin chords]] \|\| [[Marveltwin]] \|\| [[325/324]]		\| [[Marveltwin chords]] \|\| [[Marveltwin]] \|\| [[325/324]]
	\|-
	~~\| [[Sooty fox chords]] \|\| [[Sooty fox]] \|\| [[343/338]]~~
	\|-		\|-
	\| [[Ratwolfsmic chords]] \|\| [[Ratwolfsmic]] \|\| [[351/350]]		\| [[Ratwolfsmic chords]] \|\| [[Ratwolfsmic]] \|\| [[351/350]]
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	\| [[Heartlandismic chords]] \|\| [[Heartlandismic]] \|\| [[3971/3969]]		\| [[Heartlandismic chords]] \|\| [[Heartlandismic]] \|\| [[3971/3969]]
	\|-		\|-
	\| [[~~Schisminic~~ chords]] \|\| [[~~Schisminic~~]] \|\| [[4096/4095]]		\| [[Minismic chords]] \|\| [[Minismic]] \|\| [[4096/4095]]
	\|-		\|-
	\| [[Baladismic chords]] \|\| [[Baladismic]] \|\| [[4914/4913]]		\| [[Baladismic chords]] \|\| [[Baladismic]] \|\| [[4914/4913]]
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	\|-		\|-
	! Chords !! Associated Temperament !! Associated Commas		! Chords !! Associated Temperament !! Associated Commas
			\|-
			\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]
	\|-		\|-
	\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]		\| [[Diminished seventh chord]] \|\| [[Diminished (temperament)\|Diminished]] \|\| [[36/35]], [[50/49]]

FloraC: /* List of essentially tempered dyadic chords */ + jubilismic

2026-02-04T12:57:22Z

List of essentially tempered dyadic chords: + jubilismic

← Older revision		Revision as of 12:57, 4 February 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[~~Archytas~~ chords]] \|\| [[Archytas ~~clan~~\|Archytas]] \|\| [[64/63]]		\| [[Jubilismic chords]] \|\| [[Jubilismic]] \|\| [[50/49]]
			\|-
			\| [[Archytas chords]] \|\| [[Archytas]] \|\| [[64/63]]
	\|-		\|-
	\| [[Starling chords]] \|\| [[Starling]] \|\| [[126/125]]		\| [[Starling chords]] \|\| [[Starling]] \|\| [[126/125]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Didymic chords]] \|\| [[Meantone]] \|\| [[81/80]]		\| [[Didymic chords]] \|\| [[Meantone]] \|\| [[81/80]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Mothwellsmic chords]] \|\| [[Mothwellsmic]] \|\| [[99/98]]		\| [[Mothwellsmic chords]] \|\| [[Mothwellsmic]] \|\| [[99/98]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Buzurgismic chords]] \|\| [[Buzurgismic]] \|\| [[169/168]]		\| [[Buzurgismic chords]] \|\| [[Buzurgismic]] \|\| [[169/168]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Island chords]] \|\| [[The Archipelago\|Island]] \|\| [[676/675]]		\| [[Island chords]] \|\| [[The Archipelago\|Island]] \|\| [[676/675]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Augustmic chords]] \|\| [[Augustmic]] \|\| [[154/153]]		\| [[Augustmic chords]] \|\| [[Augustmic]] \|\| [[154/153]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Photismic chords]] \|\| [[Photismic]] \|\| [[324/323]]		\| [[Photismic chords]] \|\| [[Photismic]] \|\| [[324/323]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Slendric pentad]] \|\| [[~~Gamelismic clan\|~~Gamelismic]] \|\| [[1029/1024]]		\| [[Slendric pentad]] \|\| [[Gamelismic]] \|\| [[1029/1024]]
	\|-		\|-
	\| [[Palingenetic chords]] \|\| [[Palingenetic]] \|\| [[1701/1700]]		\| [[Palingenetic chords]] \|\| [[Palingenetic]] \|\| [[1701/1700]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Scanismic chords]] \|\| [[Scanismic]] \|\| [[460/459]]		\| [[Scanismic chords]] \|\| [[Scanismic]] \|\| [[460/459]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Tunbarsmic chords]] \|\| [[Tunbarsmic]] \|\| [[625/624]]		\| [[Tunbarsmic chords]] \|\| [[Tunbarsmic]] \|\| [[625/624]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Ragismic chords]] \|\| [[~~Ragismic microtemperaments\|~~Ragismic]] \|\| [[4375/4374]]		\| [[Ragismic chords]] \|\| [[Ragismic]] \|\| [[4375/4374]]
	\|-		\|-
	\| [[Hagendorfismic chords]] \|\| [[Hagendorfismic]] \|\| [[8075/8073]]		\| [[Hagendorfismic chords]] \|\| [[Hagendorfismic]] \|\| [[8075/8073]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Vinecute chords]] \|\| [[Vinecute]] \|\| [[4641/4640]]		\| [[Vinecute chords]] \|\| [[Vinecute]] \|\| [[4641/4640]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Kibismic chords]] \|\| [[Kibismic]] \|\| [[1024/1023]]		\| [[Kibismic chords]] \|\| [[Kibismic]] \|\| [[1024/1023]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Wizardharry chords]] \|\| [[Wizardharry]] \|\| [[4000/3993]]		\| [[Wizardharry chords]] \|\| [[Wizardharry]] \|\| [[4000/3993]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Lummic chords]] \|\| [[Lummic]] \|\| [[1716/1715]]		\| [[Lummic chords]] \|\| [[Lummic]] \|\| [[1716/1715]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Bullionismic chords]] \|\| [[Bullionismic]] \|\| [[5292/5291]]		\| [[Bullionismic chords]] \|\| [[Bullionismic]] \|\| [[5292/5291]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
	\|-		\|-
	\| [[Harmonismic chords]] \|\| [[Harmonismic]] \|\| [[10648/10647]]		\| [[Harmonismic chords]] \|\| [[Harmonismic]] \|\| [[10648/10647]]
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Chords !! Associated ~~Temperament~~ !! Associated ~~Commas~~		! Chords !! Associated temperament !! Associated commas
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	\| [[Jacobin chords]] \|\| [[The Jacobins\|Jacobin]] \|\| [[6656/6655]]		\| [[Jacobin chords]] \|\| [[The Jacobins\|Jacobin]] \|\| [[6656/6655]]

FloraC: /* List of essentially tempered dyadic chords */ +1

2026-01-07T10:23:01Z

List of essentially tempered dyadic chords: +1

← Older revision		Revision as of 10:23, 7 January 2026
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	\| [[Marveltwin chords]] \|\| [[Marveltwin]] \|\| [[325/324]]		\| [[Marveltwin chords]] \|\| [[Marveltwin]] \|\| [[325/324]]
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			\| [[Sooty fox chords]] \|\| [[Sooty fox]] \|\| [[343/338]]
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	\| [[Ratwolfsmic chords]] \|\| [[Ratwolfsmic]] \|\| [[351/350]]		\| [[Ratwolfsmic chords]] \|\| [[Ratwolfsmic]] \|\| [[351/350]]

FloraC: The split doesn't quite make sense cuz the "types" should cover every type but doesn't.

2025-12-18T10:46:57Z

The split doesn't quite make sense cuz the "types" should cover every type but doesn't.

← Older revision		Revision as of 10:46, 18 December 2025
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	The significance of dyadic chords and of the paradigm where all interval pairs are examined in the chord has the psychoacoustic basis of timbral fusion and emergence of the [[virtual fundamental]]. In the above examples, it can be shown that the lower harmonics of each note in the first chord blends better than in the second. Meanwhile, the virtual fundamental of the first chord appears 5/1 below the bass, whereas that of the second appears much lower, at 35/1 below the bass as the denominators "fight" each other. For these reasons we tend to find the first chord more consonant than the second.		The significance of dyadic chords and of the paradigm where all interval pairs are examined in the chord has the psychoacoustic basis of timbral fusion and emergence of the [[virtual fundamental]]. In the above examples, it can be shown that the lower harmonics of each note in the first chord blends better than in the second. Meanwhile, the virtual fundamental of the first chord appears 5/1 below the bass, whereas that of the second appears much lower, at 35/1 below the bass as the denominators "fight" each other. For these reasons we tend to find the first chord more consonant than the second.

	== ~~Types of~~ dyadic ~~chords~~ ==		== Essentially tempered dyadic chord ==
	In [[regular temperament theory]], we may speak of a just or tempered dyadic chord. By a ''just'' dyadic chord is meant a chord in just intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. An ''essentially just'' dyadic chord is a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, [[4:5:6\|1 – 5/4 – 3/2]] is a just dyadic chord when the consonance set is the [[5-odd-limit]] diamond with [[octave equivalence]], and 0 – 10 – 18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1 – 5/4 – 3/2.		In [[regular temperament theory]], we may speak of a just or tempered dyadic chord. By a ''just'' dyadic chord is meant a chord in just intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. An ''essentially just'' dyadic chord is a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, [[4:5:6\|1 – 5/4 – 3/2]] is a just dyadic chord when the consonance set is the [[5-odd-limit]] diamond with [[octave equivalence]], and 0 – 10 – 18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1 – 5/4 – 3/2.

	~~== Essentially tempered dyadic chord ==~~

	[[File:Essentially tempered chord.png\|400px\|thumb\|right\|A more in-depth work-through of the starling 1-6/5-10/7 essentially tempered chord example]]		[[File:Essentially tempered chord.png\|400px\|thumb\|right\|A more in-depth work-through of the starling 1-6/5-10/7 essentially tempered chord example]]

Overthink: /* Essentially tempered dyadic chord */ split section

2025-12-18T05:38:52Z

Essentially tempered dyadic chord: split section

← Older revision		Revision as of 05:38, 18 December 2025
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	The significance of dyadic chords and of the paradigm where all interval pairs are examined in the chord has the psychoacoustic basis of timbral fusion and emergence of the [[virtual fundamental]]. In the above examples, it can be shown that the lower harmonics of each note in the first chord blends better than in the second. Meanwhile, the virtual fundamental of the first chord appears 5/1 below the bass, whereas that of the second appears much lower, at 35/1 below the bass as the denominators "fight" each other. For these reasons we tend to find the first chord more consonant than the second.		The significance of dyadic chords and of the paradigm where all interval pairs are examined in the chord has the psychoacoustic basis of timbral fusion and emergence of the [[virtual fundamental]]. In the above examples, it can be shown that the lower harmonics of each note in the first chord blends better than in the second. Meanwhile, the virtual fundamental of the first chord appears 5/1 below the bass, whereas that of the second appears much lower, at 35/1 below the bass as the denominators "fight" each other. For these reasons we tend to find the first chord more consonant than the second.

			== Types of dyadic chords ==
			In [[regular temperament theory]], we may speak of a just or tempered dyadic chord. By a ''just'' dyadic chord is meant a chord in just intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. An ''essentially just'' dyadic chord is a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, [[4:5:6\|1 – 5/4 – 3/2]] is a just dyadic chord when the consonance set is the [[5-odd-limit]] diamond with [[octave equivalence]], and 0 – 10 – 18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1 – 5/4 – 3/2.

	== Essentially tempered dyadic chord ==		== Essentially tempered dyadic chord ==
	In [[regular temperament theory]], we may speak of a just or tempered dyadic chord. By a ''just'' dyadic chord is meant a chord in just intonation which is dyadic, so that each of its notes in relation to the lowest note is a rational number belonging to the set of consonances, and moreover each interval between the notes belongs to the set of consonances. An ''essentially just'' dyadic chord is a chord which is considered to be an approximation of a just dyadic chord, such that each of its intervals is considered to be an approximation of the corresponding interval in the just dyadic chord. So, for instance, [[4:5:6\|1 – 5/4 – 3/2]] is a just dyadic chord when the consonance set is the [[5-odd-limit]] diamond with [[octave equivalence]], and 0 – 10 – 18 in 31edo with consonance set {8, 10, 13, 18, 21, 23, 31} modulo 31 is an essentially just dyadic chord approximating 1 – 5/4 – 3/2.

	[[File:Essentially tempered chord.png\|400px\|thumb\|right\|A more in-depth work-through of the starling 1-6/5-10/7 essentially tempered chord example]]		[[File:Essentially tempered chord.png\|400px\|thumb\|right\|A more in-depth work-through of the starling 1-6/5-10/7 essentially tempered chord example]]

FloraC: /* List of essentially tempered dyadic chords */ guanyin chords are 15-odd-limit

2025-12-15T07:47:58Z

List of essentially tempered dyadic chords: guanyin chords are 15-odd-limit

← Older revision		Revision as of 07:47, 15 December 2025
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	\| [[Keemic chords]] \|\| [[Keemic]] \|\| 100/99, 385/384		\| [[Keemic chords]] \|\| [[Keemic]] \|\| 100/99, 385/384
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	\| [[Orwell tetrad]] \|\| [[~~Guanyin~~]] \|\| ~~176~~/~~175~~, ~~540~~/~~539~~		\| [[Orwell tetrad]] \|\| [[Orwellian]] \|\| 99/98, 385/384
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	\| [[Tutonic hexad\|Tutonic hexads]] \|\| [[Meantone]] \|\| 81/80, 99/98, 126/125		\| [[Tutonic hexad\|Tutonic hexads]] \|\| [[Meantone]] \|\| 81/80, 99/98, 126/125