9/8 - Revision history

Overthink: /* Temperaments */ - antitonic; expand description

2026-03-12T04:25:16Z

Temperaments: - antitonic; expand description

← Older revision		Revision as of 04:25, 12 March 2026
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	== Temperaments ==		== Temperaments ==
	~~When this ratio~~ is ~~taken as a comma to be~~ [[~~tempering out\|tempered out~~]], ~~it produces~~ [[~~Very low accuracy temperaments #Antitonic\|antitonic~~]] ~~temperament~~. ~~Edos that temper~~ it ~~out include~~ [[~~2edo~~]] ~~and~~ [[~~4edo~~]]. If it ~~is instead used as~~ a generator, it ~~produces, among others,~~ [[Subgroup temperaments #Baldy\|baldy]].		In [[meantone]], 9/8 is equated with [[10/9]], so that two instances of 9/8~10/9 stack to ~[[5/4]]. [[Superpyth]] instead sharpens 9/8 to equate it with [[8/7]].

			Since 9/8 is reached by stacking two instances of [[3/2]], temperaments in subgroups that include 3 cannot be generated by ~9/8. However, it can be a generator in subgroups such as [[2.9.5.7 subgroup\|2.9.5.7]], where it generates [[Subgroup temperaments #Baldy\|baldy]] for example.

	== Approximation ==		== Approximation ==

Overthink: move info to correct section; slight rewrite

2026-03-12T04:17:04Z

move info to correct section; slight rewrite

← Older revision		Revision as of 04:17, 12 March 2026
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	Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.		Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.

	9/8 is well-represented in [[6edo]] and its multiples. [[Edo]]s which tune [[3/2]] close to just ([[29edo]], [[41edo]], [[53edo]], to name three) will tune 9/8 close to just as well. The difference between six ~~instances~~ of 9/8 ~~and~~ the octave is the [[Pythagorean comma]].		A stack of six intervals of 9/8 exceeds the octave by the [[Pythagorean comma]].

	== History ==		== History ==
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	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].		When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].

	== Approximation ==		== Approximation ==
			9/8 is well-represented in [[6edo]] and its multiples, though only multiples of [[12edo]] (up to [[300edo]]) map 9/8 to 1\6 by [[patent val]]. [[Edo]]s which tune [[3/2]] close to just, such as [[29edo]], [[41edo]], and [[53edo]], will tune 9/8 close to just as well.

	{{Interval edo approximation\|9/8}}		{{Interval edo approximation\|9/8}}

Overthink: /* Notation */ make statement more concise and readable

2026-03-12T04:13:48Z

Notation: make statement more concise and readable

← Older revision		Revision as of 04:13, 12 March 2026
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	== Notation ==		== Notation ==
	In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between ~~A and B~~, ~~between C and D~~, ~~between D and E~~, ~~between F and G~~, ~~as well as between G~~ and A.		In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between the notes A–B, C–D, D–E, F–G, and G–A.

	The scale is structured with the following step pattern:		The scale is structured with the following step pattern:

Lucius Chiaraviglio: /* Approximation */ Fix typo that made Interval edo approximation not work

2025-11-10T01:57:54Z

Approximation: Fix typo that made Interval edo approximation not work

← Older revision		Revision as of 01:57, 10 November 2025
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	When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].		When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].
	== Approximation ==		== Approximation ==
	{{Interval edo approximation\|9/8}		{{Interval edo approximation\|9/8}}

	== Notation ==		== Notation ==
	In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between A and B, between C and D, between D and E, between F and G, as well as between G and A.		In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between A and B, between C and D, between D and E, between F and G, as well as between G and A.

FloraC: Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

2025-11-03T13:02:46Z

Text replacement - " {{Interval_Edo_Approximation | " to "{{Interval edo approximation|"

← Older revision		Revision as of 13:02, 3 November 2025
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	When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].		When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].
	== Approximation ==		== Approximation ==
	{{~~Interval_Edo_Approximation~~ \| 9/8}		{{Interval edo approximation\|9/8}
	== Notation ==		== Notation ==
	In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between A and B, between C and D, between D and E, between F and G, as well as between G and A.		In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between A and B, between C and D, between D and E, between F and G, as well as between G and A.

Pailiaq at 06:55, 3 November 2025

2025-11-03T06:55:12Z

← Older revision		Revision as of 06:55, 3 November 2025
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	== Temperaments ==		== Temperaments ==
	When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].		When this ratio is taken as a comma to be [[tempering out\|tempered out]], it produces [[Very low accuracy temperaments #Antitonic\|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy\|baldy]].
			== Approximation ==
			{{Interval_Edo_Approximation \| 9/8}
	== Notation ==		== Notation ==
	In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between A and B, between C and D, between D and E, between F and G, as well as between G and A.		In musical notations that employ the [[5L 2s\|diatonic]] [[chain-of-fifths notation\|chain-of-fifths]], such as the [[ups and downs notation]], the whole tone is represented by the distances between A and B, between C and D, between D and E, between F and G, as well as between G and A.

VectorGraphics at 08:34, 19 October 2025

2025-10-19T08:34:01Z

← Older revision		Revision as of 08:34, 19 October 2025
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	{{Wikipedia\|Major second}}		{{Wikipedia\|Major second}}

	'''9/8''', the '''Pythagorean whole tone''' or '''major second,''' is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.		'''9/8''', the '''Pythagorean whole tone''' or '''major second''', is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.

	Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.		Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.

VectorGraphics at 08:33, 19 October 2025

2025-10-19T08:33:38Z

← Older revision		Revision as of 08:33, 19 October 2025
Line 7:		Line 7:
	{{Wikipedia\|Major second}}		{{Wikipedia\|Major second}}

	'''9/8''', the '''Pythagorean whole tone''' or '''major second''', is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.		'''9/8''', the '''Pythagorean whole tone''' or '''major second,''' is an interval measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context, though because of its relatively close proximity to the [[unison]], it is the largest [[superparticular]] interval known to cause crowding, which lends more to it being considered a type of dissonance- at least in historical Western Classical traditions and in the xenharmonic traditions derived from them.

	Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.		Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments.

FloraC: Undo revision 211124 by M1k1 H2tsun2 (talk)

2025-09-27T11:47:41Z

Undo revision 211124 by M1k1 H2tsun2 (talk)

← Older revision		Revision as of 11:47, 27 September 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~Threerish major second,~~ Pythagorean whole tone, Pythagorean major second		\| Name = Pythagorean whole tone, Pythagorean major second
	\| Color name = w2, wa 2nd		\| Color name = w2, wa 2nd
	\| Sound = jid_9_8_pluck_adu_dr220.mp3		\| Sound = jid_9_8_pluck_adu_dr220.mp3

M1k1 H2tsun2: add it in the first, rather than the other place.

2025-09-27T10:39:32Z

add it in the first, rather than the other place.

← Older revision		Revision as of 10:39, 27 September 2025
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	{{Infobox Interval		{{Infobox Interval
	\| Name = Pythagorean whole tone, Pythagorean major second		\| Name = Threerish major second, Pythagorean whole tone, Pythagorean major second
	\| Color name = w2, wa 2nd		\| Color name = w2, wa 2nd
	\| Sound = jid_9_8_pluck_adu_dr220.mp3		\| Sound = jid_9_8_pluck_adu_dr220.mp3