Interval span - Revision history

BudjarnLambeth: Added a ‘not to be confused with’ line at the top as a temporary band aid response to the discussion in the talk page. My edit doesn’t attempt to resolve the debate about the term, it just makes all this less confusing for readers in the mean time and buys other editors time to sort it out calmly without worrying about doing readers a disservice in the mean time.

2024-12-12T20:55:13Z

Added a ‘not to be confused with’ line at the top as a temporary band aid response to the discussion in the talk page. My edit doesn’t attempt to resolve the debate about the term, it just makes all this less confusing for readers in the mean time and buys other editors time to sort it out calmly without worrying about doing readers a disservice in the mean time.

← Older revision		Revision as of 20:55, 12 December 2024
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			''Not to be confused with [[Fifthspan]], which is an unrelated concept.''

	The '''span''' of an interval is a technical term referring to the [[Interval size measure\|size of an interval]], typically in some logarithmic unit such as cents, octaves, or something else. The [[JIP]] can give the span of any just interval, whereas within regular temperaments, this is typically given by a [[tuning map]].		The '''span''' of an interval is a technical term referring to the [[Interval size measure\|size of an interval]], typically in some logarithmic unit such as cents, octaves, or something else. The [[JIP]] can give the span of any just interval, whereas within regular temperaments, this is typically given by a [[tuning map]].

ArrowHead294: Update links

2024-11-02T18:51:26Z

Update links

← Older revision		Revision as of 18:51, 2 November 2024
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	The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.		The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.

	[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]]. For a units analysis of interval size, see [[Dave Keenan & Douglas Blumeyer's guide to RTT~~: units~~ analysis#Size of JI interval]] and the following section for [[~~Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_units_analysis~~#~~Size_of_tempered_interval~~\|the size of a tempered interval]].		[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]]. For a units analysis of interval size, see [[Dave Keenan & Douglas Blumeyer's guide to RTT/Units analysis#Size of JI interval]] and the following section for [[Dave Keenan & Douglas Blumeyer's guide to RTT/Units analysis#Size of tempered interval\|the size of a tempered interval]].

	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].

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

BudjarnLambeth: Moved from category "theory" to "terms"

2023-04-26T09:23:22Z

Moved from category "theory" to "terms"

← Older revision		Revision as of 09:23, 26 April 2023
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	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].
	~~[[Category:Theory]]~~
	[[Category:Interval]]		[[Category:Interval]]
			[[Category:Terms]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-25T11:57:04Z

Categorised this uncategorised page

← Older revision		Revision as of 11:57, 25 April 2023
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	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].
	[[Category:Theory]]		[[Category:Theory]]
			[[Category:Interval]]

BudjarnLambeth: Categorised this uncategorised page

2023-04-25T11:56:38Z

Categorised this uncategorised page

← Older revision		Revision as of 11:56, 25 April 2023
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	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].
			[[Category:Theory]]

Cmloegcmluin: add another link

2022-12-16T15:53:34Z

add another link

← Older revision		Revision as of 15:53, 16 December 2022
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	The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.		The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.

	[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]].		[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]]. For a units analysis of interval size, see [[Dave Keenan & Douglas Blumeyer's guide to RTT: units analysis#Size of JI interval]] and the following section for [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_units_analysis#Size_of_tempered_interval\|the size of a tempered interval]].

	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].

Cmloegcmluin: link to relevant article, and fix formatting of Wikipedia link

2022-12-14T22:44:05Z

link to relevant article, and fix formatting of Wikipedia link

← Older revision		Revision as of 22:44, 14 December 2022
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	The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.		The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.

	Various units have been used for the span of an interval. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]].		[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]].

	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].

Dummy index: +link

2022-02-09T15:11:01Z

+link

← Older revision		Revision as of 15:11, 9 February 2022
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	The '''span''' of an interval is a technical term referring to the size of an interval, typically in some logarithmic unit such as cents, octaves, or something else. The [[JIP]] can give the span of any just interval, whereas within regular temperaments, this is typically given by a [[tuning map]].		The '''span''' of an interval is a technical term referring to the [[Interval size measure\|size of an interval]], typically in some logarithmic unit such as cents, octaves, or something else. The [[JIP]] can give the span of any just interval, whereas within regular temperaments, this is typically given by a [[tuning map]].

	The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.		The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.

Cmloegcmluin: I think it's less confusing to say "different" here, since the linear span meaning is not really a broadening of the interval span meaning

2021-12-30T17:31:06Z

I think it's less confusing to say "different" here, since the linear span meaning is not really a broadening of the interval span meaning

← Older revision		Revision as of 17:31, 30 December 2021
Line 5:		Line 5:
	Various units have been used for the span of an interval. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]].		Various units have been used for the span of an interval. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]].

	The term span is also used in a ~~broader~~ mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span]].

Mike Battaglia: Mike Battaglia moved page Span to Interval span

2021-12-23T21:33:59Z

Mike Battaglia moved page Span to Interval span

← Older revision	Revision as of 21:33, 23 December 2021
(No difference)

← Older revision		Revision as of 15:53, 16 December 2022
Line 3:		Line 3:
	The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.		The span of some comma can be thought of as a very simple metric to measure the usefulness of the temperament vanishing that comma. This is because the formula for the [[TE simple badness\|simple badness]], which is the product of the best-case tuning error and the complexity of the temperament, happens to reduce to the span of the comma in the situation where there is only one comma tempered out.

	[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]].		[[Interval size unit\|Various units have been used for the span of an interval]]. Typically [[cents]] are used, which can be thought of as the logarithm taken to the base <math>2^{1/1200}</math>. However, in mathematical situations it is often useful to work with the log base 2, meaning units of octaves, or even simply in the natural logarithm of base e, meaning units of "[[Wikipedia:Neper\|nepers]]". [[Martin Gough]] introduced the unit of a "dineper" in his work on [[Logarithmic approximants]]. For a units analysis of interval size, see [[Dave Keenan & Douglas Blumeyer's guide to RTT: units analysis#Size of JI interval]] and the following section for [[Dave_Keenan_%26_Douglas_Blumeyer%27s_guide_to_RTT:_units_analysis#Size_of_tempered_interval\|the size of a tempered interval]].

	The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].		The term span is also used in a different mathematical sense to refer to the linear span of a set of vectors, see [[Wikipedia:Linear span\|linear span]].