Tritone - Revision history

Lucius Chiaraviglio: /* In edos */ Add link to semioctave

2025-07-18T08:46:56Z

In edos: Add link to semioctave

← Older revision		Revision as of 08:46, 18 July 2025
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	== In edos ==		== In edos ==
	The following table lists the tunings of 11/8, 7/5, and their octave complements, as well as other tritones if present, in various significant [[edo]]s. Note that many edos map 7/5 and 10/7 to the semioctave.		The following table lists the tunings of 11/8, 7/5, and their octave complements, as well as other tritones if present, in various significant [[edo]]s. Note that many edos map 7/5 and 10/7 to the [[semioctave]].

	{\| class="wikitable"		{\| class="wikitable"

VectorGraphics: Rewrite to be consistent with the new major third page

2025-05-05T23:37:29Z

Rewrite to be consistent with the new major third page

Show changes

FloraC: Cleanup

2025-03-14T11:16:25Z

Cleanup

← Older revision		Revision as of 11:16, 14 March 2025
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	{{Infobox interval region\|Name=Tritone, augmented fourth, diminished fifth\|Cents lower=570\|Cents lower wide=540\|Cents upper=630\|Cents upper wide=660\|JI intervals=7/5, 10/7\|MOSes=[[2L 5s]], [[2L 7s]]\|Complement=[[Tritone]]\|Lower region=[[Semi-augmented fourth]] <br> [[Perfect fourth]]\|Higher region=[[~~Semi-diminished~~ fifth]] <br> [[Perfect fifth]]}}{{Wikipedia}}		{{Infobox interval region
			\| Name = Tritone, augmented fourth, diminished fifth
			\| Cents lower = 570
			\| Cents lower wide = 540
			\| Cents upper = 630
			\| Cents upper wide = 660
			\| JI intervals = 7/5, 10/7
			\| MOSes = [[2L 5s]], [[2L 7s]]
			\| Complement = [[Tritone]]
			\| Lower region = [[Semi-augmented fourth]] <br> [[Perfect fourth]]
			\| Higher region = [[Semidiminished fifth]] <br> [[Perfect fifth]]
			}}
			{{Wikipedia}}
	A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.		A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.

	As a concrete [[interval region]], it is typically near 600 [[cent]]s in size. A rough tuning range for the tritone is about 560 to 640 cents according to [[Margo Schulter]]'s theory of interval regions. ''Tritone'' in this sense can also refer to the semi-octave, a tritone of exactly 600 cents found in every even [[edo]], due to the fact that it is [[2edo\|1\2edo]].		As a concrete [[interval region]], it is typically near 600 [[cent]]s in size. A rough tuning range for the tritone is about 560 to 640 cents according to [[Margo Schulter]]'s theory of interval regions. ''Tritone'' in this sense can also refer to the semi-octave, a tritone of exactly 600 cents found in every even [[edo]], due to the fact that it is [[2edo\|1\2edo]].

	For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and ~~frankly~~ for having more than one pair of simple ratios to use in the ~~EDO~~ section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].		For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity and for having more than one pair of simple ratios to use in the edo section. More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].

	As such, this article covers intervals from 560 to 640 cents, but intervals between 540-560 and 640-660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.		As such, this article covers intervals from 560 to 640 cents, but intervals between 540-560 and 640-660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.
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	* The 11-limit '''superfourth''' and '''subfifth''' are ratios of 11/8 and 16/11 respectively, and are about 551{{c}} and 649{{c}} respectively; they are listed here because they barely do not make the cutoff (550{{c}} and 650{{c}}) to be included in the pages on fourths and fifths.		* The 11-limit '''superfourth''' and '''subfifth''' are ratios of 11/8 and 16/11 respectively, and are about 551{{c}} and 649{{c}} respectively; they are listed here because they barely do not make the cutoff (550{{c}} and 650{{c}}) to be included in the pages on fourths and fifths.

	== In ~~EDOs~~ ==		== In edos ==
	The following table lists the tunings of 11/8, 7/5, and their octave complements, as well as other tritones if present, in various significant [[~~EDO\|EDOs~~]]. Note that many ~~EDOs~~ map 7/5 and 10/7 to the semioctave.		The following table lists the tunings of 11/8, 7/5, and their octave complements, as well as other tritones if present, in various significant [[edo]]s. Note that many edos map 7/5 and 10/7 to the semioctave.

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! ~~EDO~~		! Edo
	! 11/8		! 11/8
	! 7/5		! 7/5
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	=== Temperaments that use 7/5 as a generator ===		=== Temperaments that use 7/5 as a generator ===
	{{todo\|complete section\|inline=1\|text=(see [[~~List_of_rank_two_temperaments_by_generator_and_period~~#~~Generator_~~.7E7.2F5]])}}		{{todo\|complete section\|inline=1\|text=(see [[List of rank two temperaments by generator and period #Generator .7E7.2F5]])}}

	== In ~~moment-of-symmetry~~ scales ==		== In mos scales ==
	Intervals between 545 and 654 cents generate the following [[~~MOS~~]] scales:		Intervals between 545 and 654 cents generate the following [[mos]] scales:

	These tables start from the last monolarge [[~~MOS~~]] generated by the interval range.		These tables start from the last monolarge [[mos]] generated by the interval range.

	~~MOSes~~ with more than 12 notes are not included.		Scales with more than 12 notes are not included.

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! Range		! Range
	! colspan="6" \| ~~MOS~~		! colspan="6" \| Mos
	\|-		\|-
	\| 545–654{{c}}		\| 545–654{{c}}
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	\| [[2L 9s]]		\| [[2L 9s]]
	\|}		\|}
	{{Navbox intervals}} ~~<!-- Main article -->~~		{{Navbox intervals}}

	[[Category:Tritone]]		[[Category:Tritone]] <!-- Main article -->

VectorGraphics at 10:18, 14 March 2025

2025-03-14T10:18:17Z

← Older revision		Revision as of 10:18, 14 March 2025
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	{{Infobox interval region\|Name=Tritone, augmented fourth, diminished fifth\|Cents lower=~~540~~\|Cents lower wide=~~570~~\|Cents upper=630\|Cents upper wide=660\|JI intervals=7/5, 10/7\|MOSes=[[2L 5s]], [[2L 7s]]\|Complement=[[Tritone]]\|Lower region=[[Semi-augmented fourth]] <br> [[Perfect fourth]]\|Higher region=[[Semi-diminished fifth]] <br> [[Perfect fifth]]}}{{Wikipedia}}		{{Infobox interval region\|Name=Tritone, augmented fourth, diminished fifth\|Cents lower=570\|Cents lower wide=540\|Cents upper=630\|Cents upper wide=660\|JI intervals=7/5, 10/7\|MOSes=[[2L 5s]], [[2L 7s]]\|Complement=[[Tritone]]\|Lower region=[[Semi-augmented fourth]] <br> [[Perfect fourth]]\|Higher region=[[Semi-diminished fifth]] <br> [[Perfect fifth]]}}{{Wikipedia}}
	A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.		A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.

VectorGraphics at 10:12, 14 March 2025

2025-03-14T10:12:30Z

← Older revision		Revision as of 10:12, 14 March 2025
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	{{Wikipedia}}		{{Infobox interval region\|Name=Tritone, augmented fourth, diminished fifth\|Cents lower=540\|Cents lower wide=570\|Cents upper=630\|Cents upper wide=660\|JI intervals=7/5, 10/7\|MOSes=[[2L 5s]], [[2L 7s]]\|Complement=[[Tritone]]\|Lower region=[[Semi-augmented fourth]] <br> [[Perfect fourth]]\|Higher region=[[Semi-diminished fifth]] <br> [[Perfect fifth]]}}{{Wikipedia}}
	A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.		A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.

FloraC: The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition

2025-03-14T10:01:24Z

The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition

← Older revision		Revision as of 10:01, 14 March 2025
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	{{Wikipedia}}		{{Wikipedia}}
	A '''tritone'''~~, as~~ a ~~concrete~~ [[~~interval region~~]], is ~~typically near 600~~ [[~~Cent~~\|~~cents~~]] ~~in size~~. ~~A rough tuning range for~~ the ~~tritone is about 560 to 640 cents according to~~ [[~~Margo Schulter~~]]'s ~~theory~~ of ~~interval regions. ''Tritone''~~ in ~~this sense can also refer to~~ the ~~semi~~-~~octave, a tritone of exactly 600 cents found in every even~~ [[~~edo~~]], ~~due to~~ the ~~fact that it is~~ [[~~2edo~~\|~~1\2edo~~]].		A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo\|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.

	~~Functionally,~~ a ~~tritone is an interval that spans six steps of a 12-tone~~ [[~~chromatic~~]] ~~scale. In~~ [[~~just intonation~~]]~~, an interval may be classified as a~~ tritone ~~if it~~ is ~~reasonably mapped~~ to ~~6 steps~~ of ~~the chromatic scale~~. ~~Tritones come in octave-complementary pairs, called~~ '''~~augmented fourth~~'~~'' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number~~ of ~~steps~~ in the [[~~5L 2s~~\|~~diatonic~~]] ~~scale~~.		As a concrete [[interval region]], it is typically near 600 [[cent]]s in size. A rough tuning range for the tritone is about 560 to 640 cents according to [[Margo Schulter]]'s theory of interval regions. ''Tritone'' in this sense can also refer to the semi-octave, a tritone of exactly 600 cents found in every even [[edo]], due to the fact that it is [[2edo\|1\2edo]].

	For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and frankly for having more than one pair of simple ratios to use in the EDO section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].		For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and frankly for having more than one pair of simple ratios to use in the EDO section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].
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	Due to being close to 600{{c}}, tritones come in octave-complementary pairs. For low-limit harmony, these pairs are often referred to as "augmented fourth" (A4) and "diminished fifth" (d5) based on their function in diatonic harmony, but in higher limits, the tritones are usually just distinguished by size.		Due to being close to 600{{c}}, tritones come in octave-complementary pairs. For low-limit harmony, these pairs are often referred to as "augmented fourth" (A4) and "diminished fifth" (d5) based on their function in diatonic harmony, but in higher limits, the tritones are usually just distinguished by size.

	Historically, the term "tritone" referred to the '''Pythagorean augmented fourth,''' the ratio of 729/512 reached by stacking three Pythagorean whole tones (hence "tri-tone"), or equivalently, six [[3/2]]~~<nowiki/>~~s, which is an interval of about 612{{c}}. There is also the octave complement, the '''Pythagorean diminished fifth''' of 1024/729, which is about 588{{c}} in size.		Historically, the term "tritone" referred to the '''Pythagorean augmented fourth,''' the ratio of 729/512 reached by stacking three Pythagorean whole tones (hence "tri-tone"), or equivalently, six [[3/2]]'s, which is an interval of about 612{{c}}. There is also the octave complement, the '''Pythagorean diminished fifth''' of 1024/729, which is about 588{{c}} in size.

	Much [[Odd limit\|simpler]] tritones exist in higher [[Prime limit\|limits]], however, for example:		Much [[Odd limit\|simpler]] tritones exist in higher [[Prime limit\|limits]], however, for example:

VectorGraphics at 06:59, 14 March 2025

2025-03-14T06:59:25Z

← Older revision		Revision as of 06:59, 14 March 2025
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	{{Wikipedia}}		{{Wikipedia}}
	A '''tritone''' ~~is an interval that spans six steps of~~ a ~~12-tone~~ [[~~chromatic]] scale. In [[just intonation~~]], ~~an interval may be classified as a tritone if it~~ is ~~reasonably mapped to~~ [[~~24edo~~\|~~12\24~~]]. ~~The use of 24edo's 12\24 as~~ the ~~mapping criteria here rather than~~ [[~~12edo~~]]'s ~~6\12 better captures the characteristics~~ of ~~many intervals~~ in the ~~[[11~~-~~limit\|11-]] and~~ [[~~13-limit~~]]~~. Tritones come in octave-complementary pairs~~, ~~called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in~~ the [[~~5L 2s~~\|~~diatonic~~]] ~~scale~~.		A '''tritone''', as a concrete [[interval region]], is typically near 600 [[Cent\|cents]] in size. A rough tuning range for the tritone is about 560 to 640 cents according to [[Margo Schulter]]'s theory of interval regions. ''Tritone'' in this sense can also refer to the semi-octave, a tritone of exactly 600 cents found in every even [[edo]], due to the fact that it is [[2edo\|1\2edo]].

	As a ~~concrete~~ [[~~interval region~~]]~~, it is typically near 600~~ [[~~Cent\|cents~~]] ~~in size. A rough tuning range for the~~ tritone is ~~about 560~~ to ~~640 cents according to [[Margo Schulter]]'s theory~~ of ~~interval regions~~. ''~~Tritone~~'' ~~in this sense can also refer to the semi-octave, a tritone~~ of ~~exactly 600 cents found~~ in ~~every even [[edo]], due to~~ the ~~fact that it is~~ [[~~2edo~~\|~~1\2edo~~]].		Functionally, a tritone is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to 6 steps of the chromatic scale. Tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s\|diatonic]] scale.

	For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and frankly for having more than one pair of simple ratios to use in the EDO section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].		For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and frankly for having more than one pair of simple ratios to use in the EDO section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].

ArrowHead294: /* In moment-of-symmetry scales */

2025-03-11T14:16:50Z

In moment-of-symmetry scales

← Older revision		Revision as of 14:16, 11 March 2025
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	\|-		\|-
	\| 545–654{{c}}		\| 545–654{{c}}
	\| 1L 1s		\| [[1L 1s]]
	\| 2L 1s		\| [[2L 1s]]
	\| 2L 3s		\| [[2L 3s]]
	\| 2L 5s		\| [[2L 5s]]
	\| 2L 7s		\| [[2L 7s]]
	\| 2L 9s		\| [[2L 9s]]
	\|}		\|}
	{{Navbox intervals}} <!-- Main article -->		{{Navbox intervals}} <!-- Main article -->

	[[Category:Tritone]]		[[Category:Tritone]]

ArrowHead294 at 13:52, 10 March 2025

2025-03-10T13:52:43Z

← Older revision		Revision as of 13:52, 10 March 2025
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	== Tritones as approximations of the semioctave ==		== Tritones as approximations of the semioctave ==
			In some tuning systems having an even number of divisions of the octave (equal or well-tempered), the tritone (defined as three whole tones) is the same as the half-octave; if the divisions of the octave are equal and the octave is tuned pure, the tritone will therefore be exactly the square root of 2. The following table compares selected JI tritone pairs that approximate the half-octave and the commas separating them:
	In some tuning systems having an even number of divisions of the octave (equal or well-tempered), the tritone (defined as three whole tones) is the same as the half-octave; if the divisions of the octave are equal and the octave is tuned pure, the tritone will therefore be exactly the square root of 2. The following table compares selected JI tritone pairs that approximate the half-octave and the commas separating them:

	{\| class="wikitable sortable center-all right-3"		{\| class="wikitable sortable center-all right-3"
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	However, it is possible for a tuning system to have an even number of notes and a pair of tritones that is not the same as the semioctave.		However, it is possible for a tuning system to have an even number of notes and a pair of tritones that is not the same as the semioctave.

	An example of a tuning system having an even number of notes and a pair of tritones that is not the same as the semioctave is [[26edo]]. In [[flattone]] tuning systems such as 26edo, 11/8 is ~~C-F♯~~, which is the lesser tritone mapping to 12\26 (not the semioctave 13\26); 16/11 is ~~C-G♭~~, which is the greater tritone mapping to 14\26. Note that these tritones are not necessarily valid generators for tuning systems analogous to flattone but substituting 11/8 for [[4/3]]; for instance, these are not valid generators for 26edo with a whole-octave period, because they instead produce [[13edo]].		An example of a tuning system having an even number of notes and a pair of tritones that is not the same as the semioctave is [[26edo]]. In [[flattone]] tuning systems such as 26edo, 11/8 is C–F♯, which is the lesser tritone mapping to 12\26 (not the semioctave 13\26); 16/11 is C–G♭, which is the greater tritone mapping to 14\26. Note that these tritones are not necessarily valid generators for tuning systems analogous to flattone but substituting 11/8 for [[4/3]]; for instance, these are not valid generators for 26edo with a whole-octave period, because they instead produce [[13edo]].

	== Temperaments that can use tritones as generators ==		== Temperaments that can use tritones as generators ==

	=== Temperaments that use 11/8 as a generator ===		=== Temperaments that use 11/8 as a generator ===
			In 13edo, 11/8 and 16/11 map to the tritones 6\13 and 7\13, respectively, and are valid generators for it. Furthermore, although 12\26 is not valid as a generator for 26edo with a whole-octave period, it ''is'' valid with a half-octave period, for a temperament analogous to [[Injera]] but substituting 11/8 for 4/3.
	In 13edo, 11/8 and 16/11 map to the tritones 6\13 and 7\13, respectively, and are valid generators for it. Furthermore, although 12\26 is not valid as a generator for 26edo with a whole-octave period, it ''is'' valid with a half-octave period, for a temperament analogous to [[Injera]] but substituting 11/8 for 4/3.

	{{todo\|complete section\|inline=1}}		{{todo\|complete section\|inline=1}}

	=== Temperaments that use 7/5 as a generator ===		=== Temperaments that use 7/5 as a generator ===

	{{todo\|complete section\|inline=1\|text=(see [[List_of_rank_two_temperaments_by_generator_and_period#Generator_.7E7.2F5]])}}		{{todo\|complete section\|inline=1\|text=(see [[List_of_rank_two_temperaments_by_generator_and_period#Generator_.7E7.2F5]])}}

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	MOSes with more than 12 notes are not included.		MOSes with more than 12 notes are not included.

	{\| class="wikitable"		{\| class="wikitable"
	\|+
	~~!Range~~
	~~! colspan="6" \|MOS~~
	\|-		\|-
	\|~~545~~-~~654c~~		! Range
	\|1L 1s		! colspan="6" \| MOS
	\|2L 1s		\|-
	\|2L 3s		\| 545–654{{c}}
	\|2L 5s		\| 1L 1s
	\|2L 7s		\| 2L 1s
	\|2L 9s		\| 2L 3s
			\| 2L 5s
			\| 2L 7s
			\| 2L 9s
	\|}		\|}
	{{Navbox intervals}} <!-- Main article -->		{{Navbox intervals}} <!-- Main article -->

	[[Category:Tritone]]		[[Category:Tritone]]

VectorGraphics at 02:49, 9 March 2025

2025-03-09T02:49:19Z

← Older revision		Revision as of 02:49, 9 March 2025
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	For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and frankly for having more than one pair of simple ratios to use in the EDO section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].		For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity (and frankly for having more than one pair of simple ratios to use in the EDO section). More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]].

			As such, this article covers intervals from 560 to 640 cents, but intervals between 540-560 and 640-660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles.

	== In just intonation ==		== In just intonation ==