Millioctave - Revision history

Fredg999: Categories

2024-07-05T04:54:06Z

Fredg999: External link

2024-07-05T04:20:04Z

External link

← Older revision		Revision as of 04:20, 5 July 2024
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	* Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .		* Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .
	* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.		* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.

			== External links ==
			* [http://tonalsoft.com/enc/m/millioctave.aspx millioctave / m8ve / μ8ve / moct / μoct] on [[Tonalsoft Encyclopedia]] (includes a ratio-to-millioctaves calculator)

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

Eliora at 12:37, 26 November 2023

2023-11-26T12:37:25Z

← Older revision		Revision as of 12:37, 26 November 2023
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	{{Wikipedia}}		{{Wikipedia}}
	The '''millioctave''' ('''moct''') is a [[unit of interval size]] that divides the [[octave]] (2/1) into 1000 logarithmically equal parts. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 2<sup>0.001</sup>. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[wikipedia:International System of Units\|SI units]], have led some ethnomusicologists and microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples.		The '''millioctave''' ('''moct''') is a [[unit of interval size]] that divides the [[octave]] (2/1) into [[1000edo\|1000 logarithmically equal parts]]. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 2<sup>0.001</sup>. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[wikipedia:International System of Units\|SI units]], have led some ethnomusicologists and microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples.

	== History ==		== History ==
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	[[Category:Logarithmic measures]]		[[Category:Logarithmic measures]]
	[[Category:Terms]]		[[Category:Terms]]
			[[Category:1000edo]]

FloraC: Recategorize

2023-11-26T11:21:01Z

Recategorize

← Older revision		Revision as of 11:21, 26 November 2023
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	* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.		* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.

	[[Category:Interval size ~~measure~~]]		[[Category:Interval size measures]]
	[[Category:Logarithmic ~~measure~~]]		[[Category:Logarithmic measures]]
	[[Category:Terms]]		[[Category:Terms]]

Fredg999: Minor improvement to lead section

2023-08-22T04:20:32Z

Minor improvement to lead section

← Older revision		Revision as of 04:20, 22 August 2023
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	{{Wikipedia}}		{{Wikipedia}}
	The '''millioctave''' ('''moct''') is a ~~logarithmic~~ [[interval size ~~measure~~]]~~. It~~ divides the octave (2/1) into 1000 logarithmically equal parts. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 2^0.001. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[wikipedia:International System of Units\|SI units]], have led some ethnomusicologists and microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples.		The '''millioctave''' ('''moct''') is a [[unit of interval size]] that divides the [[octave]] (2/1) into 1000 logarithmically equal parts. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 2<sup>0.001</sup>. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[wikipedia:International System of Units\|SI units]], have led some ethnomusicologists and microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples.

	== History ==		== History ==

Fredg999: Categories

2023-08-22T04:11:54Z

Fredg999 category edits: Removing from Category:Unit using Cat-a-lot

2023-04-26T02:22:08Z

Removing from Category:Unit using Cat-a-lot

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	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
	~~[[Category:Unit]]~~

Fredg999 category edits: Removing from Category:Measure using Cat-a-lot

2023-02-26T06:34:33Z

Removing from Category:Measure using Cat-a-lot

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	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
	~~[[Category:Measure]]~~
	[[Category:Unit]]		[[Category:Unit]]

Fredg999: Fixed typo

2022-02-26T18:29:11Z

Fixed typo

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	== History ==		== History ==
	The ~~millioctace~~ (German abbreviation '''mO''') was introduced by the German physicist Arthur von Oettingen in his book ''Das duale Harmoniesystem (1913)''.		The millioctave (German abbreviation '''mO''') was introduced by the German physicist Arthur von Oettingen in his book ''Das duale Harmoniesystem (1913)''.

	== Usage convention ==		== Usage convention ==

Xenwolf: reworked

2022-02-26T18:26:50Z

reworked

← Older revision		Revision as of 18:26, 26 February 2022
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	{{Wikipedia}}		{{Wikipedia}}
	The '''millioctave''' ('''moct''') is a logarithmic [[interval size measure]]. It divides the octave (2/1) into 1000 logarithmically equal parts. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[~~http~~:~~//en.wikipedia.org/wiki/International_System_of_Units~~ SI] ~~units~~, have led some microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples~~. The millioctace (''mO'') was introduced by the German physicist Arthur von Oettingen in his book ''Das duale Harmoniesystem (1913)''~~.		The '''millioctave''' ('''moct''') is a logarithmic [[interval size measure]]. It divides the octave (2/1) into 1000 logarithmically equal parts. So, the millioctave can be defined as a frequency ratio of the 1000th root of 2, or 2^0.001. Its independence from the "classical"/"standard" [[12edo]] tuning, and its similarity to other metric/[[wikipedia:International System of Units\|SI units]], have led some ethnomusicologists and microtonalists to prefer it over similar measures such as [[cents]]. However, others note that it naturally favors [[10edo]] and its multiples, just as cents favor 12edo and its multiples.

	~~When comparing the approximations of [[just interval]]s between different systems,~~ mO ~~values can be used equally well as [[cent]] values. Also,~~ the ~~absolute size of [[comma]]s can be given~~ in ~~millioctave steps~~.		== History ==
			The millioctace (German abbreviation '''mO''') was introduced by the German physicist Arthur von Oettingen in his book ''Das duale Harmoniesystem (1913)''.

	~~1 millioctave may~~ be ~~defined as~~ a ~~frequency ratio~~ of ~~the 1000th root~~ of ~~2, or 2^0.001~~.		== Usage convention ==
			In this wiki, the cent is the preferred unit for interval sizes and differences, approximations, etc., and alternative units are usually tolerated only when the good reasons are obvious. But it cannot be ruled out that there are also a few places where the use of millioctaves as opposed to cents proves advantageous in terms of clarity and comprehensibility.

	To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log<span style="font-size: 80%; vertical-align: sub;">2</span>(n/d) .		== Conversion ==
			* To convert a just interval (n/d) to millioctaves (m), use the formula m = 1000 * log<span style="font-size: 80%; vertical-align: sub;">2</span>(n/d) .
	Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .		* Or, if your calculator or software does not have a log2 function, use m = 1000 * log(n/d) / log(2) .
			* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.
	1 mO is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 mO.

	[[Category:Absolute measure]]		[[Category:Absolute measure]]

← Older revision		Revision as of 04:54, 5 July 2024
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	[[Category:Interval size measures]]		[[Category:Interval size measures]]
	~~[[Category:Logarithmic measures]]~~
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:1000edo]]		[[Category:1000edo]]

← Older revision		Revision as of 04:11, 22 August 2023
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	* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.		* 1 moct is equal to exactly 1.2 cents. Conversely, 1 cent is equal to exactly 5/6 or ~0.8333 moct.

	~~[[Category:Absolute measure]]~~
	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Logarithmic measure]]		[[Category:Logarithmic measure]]
			[[Category:Terms]]