Cent - Revision history

FloraC: "1/100" or "100th", not "1/100th"

2025-12-23T11:13:23Z

"1/100" or "100th", not "1/100th"

← Older revision		Revision as of 11:13, 23 December 2025
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	}}		}}
	{{Wikipedia\|Cent (music)}}		{{Wikipedia\|Cent (music)}}
	The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/~~100th~~ (or 1%) of a [[12edo]] [[semitone (interval size measure)\|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w\|Alexander John Ellis\|Alexander J. Ellis}}, the cent may also be defined as the {{w\|logarithm}} base 1200th root of 2 of a ratio.		The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100 (or 1%) of a [[12edo]] [[semitone (interval size measure)\|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w\|Alexander John Ellis\|Alexander J. Ellis}}, the cent may also be defined as the {{w\|logarithm}} base 1200th root of 2 of a ratio.

	Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.		Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.

FloraC: /* Conversion */ + see also

2025-11-25T11:54:58Z

Conversion: + see also

← Older revision		Revision as of 11:54, 25 November 2025
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	== Conversion ==		== Conversion ==
			{{See also\| Ratio #Conversion }}

	=== Ratio to cents ===		=== Ratio to cents ===
	To find the size ''s'' of an interval in cents from its ratio ''r'', calculate the [[log2\|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply it by 1200.		To find the size ''s'' of an interval in cents from its ratio ''r'', calculate the [[log2\|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply it by 1200.

FloraC: /* Conversion */ cleanup

2025-11-25T11:50:41Z

Conversion: cleanup

← Older revision		Revision as of 11:50, 25 November 2025
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	== Conversion ==		== Conversion ==
	=== Ratio to cents ===		=== Ratio to cents ===
	To find the size ''s'' of an interval in cents from its ratio ''c'', ~~you have to~~ calculate the [[log2\|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply ~~this~~ by 1200.		To find the size ''s'' of an interval in cents from its ratio ''r'', calculate the [[log2\|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply it by 1200.

	<math>\displaystyle s = 1200\log_2 (c)</math>		<math>\displaystyle s = 1200 \cdot \log_2 (r)</math>

	~~Example (~~just perfect fifth~~): log~~<sub>2</sub>(3/2) × ~~1200 ≈~~ 0.584 ~~× 1200~~ ≈ 701.955 cents.		For example, the size in cents of a just perfect fifth is 1200⋅log<sub>2</sub>(3/2) ≈ 1200 × 0.584 ≈ 701.955 cents.

	If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way:		If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way:

FloraC: Update linking

2025-02-26T16:47:47Z

Update linking

← Older revision		Revision as of 16:47, 26 February 2025
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	}}		}}
	{{Wikipedia\|Cent (music)}}		{{Wikipedia\|Cent (music)}}
	The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100th (or 1%) of a [[12edo]] [[semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w\|Alexander John Ellis\|Alexander J. Ellis}}, the cent may also be defined as the {{w\|logarithm}} base 1200th root of 2 of a ratio.		The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100th (or 1%) of a [[12edo]] [[semitone (interval size measure)\|semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w\|Alexander John Ellis\|Alexander J. Ellis}}, the cent may also be defined as the {{w\|logarithm}} base 1200th root of 2 of a ratio.

	Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.		Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.

Pailiaq: typo correction

2025-02-18T19:11:05Z

typo correction

← Older revision		Revision as of 19:11, 18 February 2025
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	<math>\displaystyle s = 1200\log_2 (c)</math>		<math>\displaystyle s = 1200\log_2 (c)</math>

	Example (just perfect fifth): log<~~sub>2</~~sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents.		Example (just perfect fifth): log<sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents.

	If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way:		If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way:

FloraC: Minor style improvements. -review tag

2024-12-18T11:36:37Z

Minor style improvements. -review tag

← Older revision		Revision as of 11:36, 18 December 2024
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	Example (just perfect fifth): log<sub>2</sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents.		Example (just perfect fifth): log<sub>2</sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents.

	If your pocket calculator has no ''log2'' key, but does have a ''log'' (log<sub>10</sub>) or ''ln'' (log<sub>e</sub>) key, you can key it this way:		If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way:

	(frequency ratio) log ÷ 2 log =		<code>(frequency ratio)</code> <code>log</code> <code>÷</code> <code>2</code> <code>log</code> <code>=</code>

	(This makes use of the property of logarithms that log<sub>2</sub>(''x'') = log<sub>''n''</sub>(''x'') / log<sub>''n''</sub>(2).)		This makes use of the property of logarithms that log<sub>2</sub>(''x'') = log<sub>''n''</sub>(''x'') / log<sub>''n''</sub>(2).

	For scientific calculators, the order of buttons may be different, and a right parenthesis may be needed.		For scientific calculators, the order of buttons may be different, and a right parenthesis may be needed.
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	=== Monzo to cents ===		=== Monzo to cents ===
	To find the size ''s'' of a just interval in cents from its [[monzo]] '''m''' = {{monzo\| m<sub>1</sub> m<sub>2</sub> m<sub>3</sub> … }}, left-multiply '''m''' by the [[just tuning map]] in cents ''T''<sub>''J''</sub> = {{val\| 1200.000 1901.955 2786.314 … }}		To find the size ''s'' of a just interval in cents from its [[monzo]] '''m''' = {{monzo\| ''m''<sub>1</sub> ''m''<sub>2</sub> ''m''<sub>3</sub> … }}, left-multiply '''m''' by the [[just tuning map]] in cents ''T''<sub>''J''</sub> = {{val\| 1200.000 1901.955 2786.314 … }}

	<math>\displaystyle s = T_J \cdot \vec m</math>		<math>\displaystyle s = T_J \cdot \vec m</math>
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	[[Category:Elementary math]]		[[Category:Elementary math]]
	[[Category:Terms]]		[[Category:Terms]]

	~~[[Category:Todo:review]]~~

FloraC: +interwiki, linking, and style

2024-12-18T08:14:51Z

+interwiki, linking, and style

← Older revision		Revision as of 08:14, 18 December 2024
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	\| ja = セント		\| ja = セント
	\| ko = 센트		\| ko = 센트
			\| ro = Centisunet
	}}		}}
	{{Wikipedia\|Cent (music)}}		{{Wikipedia\|Cent (music)}}
	The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100th (or 1%) of a [[12edo]] semitone. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w\|Alexander John Ellis\|Alexander J. Ellis}}, the cent may also be defined as the {{w\|logarithm}} base 1200th root of 2 of a ratio.		The '''cent''' (symbol: '''¢''') is a [[unit of interval size]] equal to exactly 1/100th (or 1%) of a [[12edo]] [[semitone]]. In other words, cents divide the half step (semitone) of 12edo into 100 equal parts. First proposed in the late 19th century by {{w\|Alexander John Ellis\|Alexander J. Ellis}}, the cent may also be defined as the {{w\|logarithm}} base 1200th root of 2 of a ratio.

	Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.		Cents are often used to express the size of intervals in different tuning systems, sometimes to express the accuracy of the representation of a [[just intonation]] [[interval]] in a given system.
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	=== Monzo to cents ===		=== Monzo to cents ===
	To find the size ''s'' of a just interval in cents from its [[monzo]] '''m''' = {{monzo\| m<sub>1</sub> m<sub>2</sub> m<sub>3</sub> … }}, left-multiply '''m''' by the [[just tuning map]] in cents T<sub>J</sub> = {{val\| 1200.000 1901.955 2786.314 … }}		To find the size ''s'' of a just interval in cents from its [[monzo]] '''m''' = {{monzo\| m<sub>1</sub> m<sub>2</sub> m<sub>3</sub> … }}, left-multiply '''m''' by the [[just tuning map]] in cents ''T''<sub>''J''</sub> = {{val\| 1200.000 1901.955 2786.314 … }}

	<math>\displaystyle s = T_J \cdot \vec m</math>		<math>\displaystyle s = T_J \cdot \vec m</math>

FloraC: +interwiki

2024-10-12T07:35:50Z

+interwiki

← Older revision		Revision as of 07:35, 12 October 2024
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	{{interwiki		{{interwiki
			\| en = Cent
	\| de = Cent		\| de = Cent
	~~\| en = Cent~~
	\| es = Centésimas		\| es = Centésimas
	\| ja =		\| ja = セント
			\| ko = 센트
	}}		}}
	{{Wikipedia\|Cent (music)}}		{{Wikipedia\|Cent (music)}}

Fredg999: Categories

2024-07-05T04:53:46Z

Fredg999: External link, misc. edits

2024-06-30T21:42:26Z

External link, misc. edits

← Older revision		Revision as of 21:42, 30 June 2024
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	== Examples ==		== Examples ==

	The 12edo perfect fifth is exactly 700 cents, and the 12edo major third is exactly 400 cents. In contrast, the just perfect fifth, which corresponds to two notes in a frequency ratio of [[3/2]], is approximately 702 cents, and the just major third of [[5/4]] is about 386 cents. The [[24edo]] neutral third is exactly 350 cents. The [[22edo]] approximation to 3/2 is approximately 709 cents.		The 12edo perfect fifth is exactly 700 cents, and the 12edo major third is exactly 400 cents. In contrast, the just perfect fifth, which corresponds to two notes in a frequency ratio of [[3/2]], is approximately 702 cents, and the just major third of [[5/4]] is about 386 cents. The [[24edo]] neutral third is exactly 350 cents. The [[22edo]] approximation to 3/2 is approximately 709 cents.

	== Conversion ==		== Conversion ==
	=== Ratio to cents ===		=== Ratio to cents ===

	To find the size ''s'' of an interval in cents from its ratio ''c'', you have to calculate the [[log2\|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply this by 1200.		To find the size ''s'' of an interval in cents from its ratio ''c'', you have to calculate the [[log2\|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply this by 1200.

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	== Other interval size units ==		== Other interval size units ==

	The cent is commonly used because of its ease in communicating information about intervals to a 12edo-savvy audience. However, some have suggested that the cent be deprecated, as other than societal convention there's no reason to give 12edo inherent importance over any other decent tuning. In contrast, others have suggested that cents are a useful unit of interval measure for purely mathematical reasons, even despite of 12edo's current status as the dominant tuning in Western society.		The cent is commonly used because of its ease in communicating information about intervals to a 12edo-savvy audience. However, some have suggested that the cent be deprecated, as other than societal convention there's no reason to give 12edo inherent importance over any other decent tuning. In contrast, others have suggested that cents are a useful unit of interval measure for purely mathematical reasons, even despite of 12edo's current status as the dominant tuning in Western society.

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

	* [[Relative cent]] – a useful generalization for the cent measure to ''any'' [[equal]] tuning		* [[Relative cent]] – a useful generalization for the cent measure to ''any'' [[equal]] tuning
	* [[Millioctave]] – one prominent alternative interval measure		* [[Millioctave]] – one prominent alternative interval measure
	* [[Interval size measure]] – overview		* [[Interval size measure]] – overview

			== External links ==
			* [http://tonalsoft.com/enc/c/cent.aspx cent, ¢, 1200-ed2] on [[Tonalsoft Encyclopedia]]

	[[Category:Interval size measures]]		[[Category:Interval size measures]]

← Older revision		Revision as of 04:53, 5 July 2024
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	[[Category:Interval size measures]]		[[Category:Interval size measures]]
	~~[[Category:Logarithmic measures]]~~
	[[Category:Elementary math]]		[[Category:Elementary math]]
	[[Category:Terms]]		[[Category:Terms]]

	[[Category:Todo:review]]		[[Category:Todo:review]]