Octave (interval region) - Revision history

VectorGraphics at 06:55, 18 June 2025

2025-06-18T06:55:52Z

← Older revision		Revision as of 06:55, 18 June 2025
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	{{About\|the interval region\|the octave as a just ratio\|2/1}}		{{About\|the interval region\|the octave as a just ratio\|2/1}}
	{{Wikipedia\|Octave}}		{{Wikipedia\|Octave}}
	A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure\|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to ~~[[7edo\|7\7]] and [[24edo\|24\24]] (precisely~~ seven steps of the diatonic scale and twelve steps of the chromatic scale). ~~The use~~ of ~~24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s~~ 12~~\12 better captures~~ the ~~characteristics~~ of ~~many intervals in~~ the ~~[[11-limit\|11-]]~~ and ~~[[13-limit]]~~.		A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure\|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to seven steps of the diatonic scale and twelve steps of the chromatic scale, reflecting the period and equave of both. Enharmonic intervals may be found at multiples of 12 steps along the chain of fifths, such as the diminished ninth (mapped to 8\7) and augmented seventh (6\7).

	The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave~~. Enharmonic intervals may be found at multiples of 12 steps along the chain of fifths, such as the diminished ninth and augmented seventh~~.		The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave.

	Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].		Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].

VectorGraphics at 06:54, 18 June 2025

2025-06-18T06:54:44Z

← Older revision		Revision as of 06:54, 18 June 2025
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	A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure\|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to [[7edo\|7\7]] and [[24edo\|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure\|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to [[7edo\|7\7]] and [[24edo\|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave.		The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave. Enharmonic intervals may be found at multiples of 12 steps along the chain of fifths, such as the diminished ninth and augmented seventh.

	Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].		Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].

VectorGraphics at 06:53, 18 June 2025

2025-06-18T06:53:46Z

← Older revision		Revision as of 06:53, 18 June 2025
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	Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].		Because of that, this page only covers intervals of 1200 cents and flatter, as sharper intervals octave-reduce to [[commas and dieses]].

	For the sake of simplicity, this page also covers '''interseptimal seventh-octaves''', which are approximately 1150 cents in size. Thus, the interval region considered as "octave" for the purpose of this page is 1140-1200 cents.		For the sake of simplicity, this page also covers '''interseptimal seventh-octaves''', which are approximately 1150 cents in size and are the complements of [[Comma and diesis\|dieses]]. Thus, the interval region considered as "octave" for the purpose of this page is 1140-1200 cents.

	~~{{todo\|inline=1\|review\|comment=Mention concordance before harmonic entropy, since harmonic entropy is a single model of concordance}}~~

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

Xenllium at 11:17, 18 April 2025

2025-04-18T11:17:13Z

← Older revision		Revision as of 11:17, 18 April 2025
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	2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).		2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).

			== See also ==
			* [[Octave]] (disambiguation page)

	{{Navbox intervals}}		{{Navbox intervals}}

Xenllium at 23:33, 11 April 2025

2025-04-11T23:33:47Z

← Older revision		Revision as of 23:33, 11 April 2025
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	{{About\|the interval region\|the octave as a just ratio\|2/1}}		{{About\|the interval region\|the octave as a just ratio\|2/1}}
	{{Wikipedia}}		{{Wikipedia\|Octave}}
	A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure\|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo\|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].		A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure\|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to [[7edo\|7\7]] and [[24edo\|24\24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24\24 as the mapping criteria here rather than [[12edo]]'s 12\12 better captures the characteristics of many intervals in the [[11-limit\|11-]] and [[13-limit]].

	The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave.		The aforementioned function is the interval of equivalence, or [[equave]], because tones separated by an octave are perceived to have the same or similar [[pitch class]] to the average human listener. The reason for this phenomenon is probably due to the strong concordance of the octave or the strong amplitude of the second [[harmonic]] in most harmonic instruments. As such, it is common practice to [[octave-reduce]] intervals so that they lie within the octave.

Lériendil: don't really think there's a need to make xenllium-sized tables here

2025-04-05T03:05:48Z

don't really think there's a need to make xenllium-sized tables here

← Older revision		Revision as of 03:05, 5 April 2025
Line 116:		Line 116:

	2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).		2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).

	~~{{todo\|inline=1\|complete table}}~~

	{{Navbox intervals}}		{{Navbox intervals}}

Lériendil: partial revert of xenllium's changes

2025-04-05T03:04:56Z

partial revert of xenllium's changes

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Lériendil: will readd the table, will remove anything w/ red links

2025-04-05T03:04:00Z

will readd the table, will remove anything w/ red links

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Lériendil: Lériendil moved page Octave to Octave (interval region) over redirect: undoing edits by normal llium

2025-04-05T02:58:10Z

Lériendil moved page Octave to Octave (interval region) over redirect: undoing edits by normal llium

← Older revision	Revision as of 02:58, 5 April 2025
(No difference)

Lériendil: Undo revision 189882 by Xenllium (talk)

2025-04-05T02:57:43Z

Undo revision 189882 by Xenllium (talk)

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