Interval class - Revision history

FloraC: + link

2025-07-21T09:48:27Z

+ link

← Older revision		Revision as of 09:48, 21 July 2025
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	== See also ==		== See also ==
			* [[Pitch class]]
	* [[Interval size measure]]		* [[Interval size measure]]
	* [[Interval region]]		* [[Interval region]]

BudjarnLambeth: /* See also */ add link to orphaned page

2025-06-07T07:53:29Z

ArrowHead294: {{Wikipedia}} template is fixed and updated now

2024-10-29T03:01:14Z

{{Wikipedia}} template is fixed and updated now

← Older revision		Revision as of 03:01, 29 October 2024
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	{{Wikipedia\|Interval class}}		{{Wikipedia\|Interval class\|Generic and specific intervals}}
	~~{{Wikipedia~~\|Generic and specific intervals}}
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.

Fitzgerald Lee: Fixed Wikipedia thingy

2024-10-28T11:07:28Z

Fixed Wikipedia thingy

← Older revision		Revision as of 11:07, 28 October 2024
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	{{Wikipedia}}		{{Wikipedia\|Interval class}}
	{{Wikipedia\|Generic and specific intervals}}		{{Wikipedia\|Generic and specific intervals}}
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:

Inthar at 01:48, 24 January 2024

2024-01-24T01:48:06Z

← Older revision		Revision as of 01:48, 24 January 2024
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	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
	# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''~~. The newer term '''''ordinal category''''' has also been used for this second sense~~. For example, the interval class~~, or ordinal category,~~ of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.		# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. For example, the interval class of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

	== See also ==		== See also ==

Inthar at 00:39, 25 August 2023

2023-08-25T00:39:33Z

← Older revision		Revision as of 00:39, 25 August 2023
Line 3:		Line 3:
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
	# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all [[interval qualities]] at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.		# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals ([[interval qualities]]) at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

	== See also ==		== See also ==

Inthar at 00:39, 25 August 2023

2023-08-25T00:39:03Z

← Older revision		Revision as of 00:39, 25 August 2023
Line 3:		Line 3:
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
	# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all ~~specific intervals~~ at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.		# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all [[interval qualities]] at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

	== See also ==		== See also ==

Inthar at 00:37, 25 August 2023

2023-08-25T00:37:43Z

← Older revision		Revision as of 00:37, 25 August 2023
Line 2:		Line 2:
	{{Wikipedia\|Generic and specific intervals}}		{{Wikipedia\|Generic and specific intervals}}
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful and less generalizable than the second definition.
	# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.		# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

Inthar: The term "class" has varying definitions in math; the term often refers to equivalence classes, which does fit the musical set theory definition.

2023-08-25T00:36:40Z

The term "class" has varying definitions in math; the term often refers to equivalence classes, which does fit the musical set theory definition.

← Older revision		Revision as of 00:36, 25 August 2023
Line 2:		Line 2:
	{{Wikipedia\|Generic and specific intervals}}		{{Wikipedia\|Generic and specific intervals}}
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on ~~two~~ grounds~~: it is not a class in the vocabulary of mathematics, and~~ it is less useful than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on the grounds that it is less useful than the second definition.
	# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.		# The second definition, used for example by [[Scala]], defines the ''interval class'', or the '''''generic interval''''', as the set of all specific intervals at a certain number of scale steps apart. More formally, an interval class is the set of all intervals that occur in the scale as ''k''-step intervals, or ''k''-steps, for a specific fixed integer ''k''. The newer term '''''ordinal category''''' has also been used for this second sense. For example, the interval class, or ordinal category, of 2-steps in the diatonic scale ([[5L 2s]]) is the set {2L, L + s} = {major third, minor third}.

Fredg999: Add second Wikipedia box, update internal link

2023-08-24T00:49:48Z

Add second Wikipedia box, update internal link

← Older revision		Revision as of 00:49, 24 August 2023
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	{{Wikipedia\| ~~Interval class~~ }}		{{Wikipedia}}
			{{Wikipedia\|Generic and specific intervals}}
	'''Interval class''' is used in the following ways:		'''Interval class''' is used in the following ways:
	# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on two grounds: it is not a class in the vocabulary of mathematics, and it is less useful than the second definition.		# First, common in academic [[Wikipedia: Set theory (music)\|set theory]], defines it as the [[Octave #Octave equivalence\|octave-equivalent]] distance between two pitch classes, measured by the shortest distance. Thus C to G may be the interval of 7, but its interval class is 5. The largest interval class or "ic" – in [[12edo]] – is the tritone (6). This may be criticized on two grounds: it is not a class in the vocabulary of mathematics, and it is less useful than the second definition.
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	== See also ==		== See also ==
	* [[Interval size measure]]		* [[Interval size measure]]
	* [[Interval ~~category~~]]		* [[Interval region]]

	[[Category:Interval]]		[[Category:Interval]]

← Older revision		Revision as of 07:53, 7 June 2025
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	* [[Interval size measure]]		* [[Interval size measure]]
	* [[Interval region]]		* [[Interval region]]
			* [[Functional systems]]

	[[Category:Interval]]		[[Category:Interval]]