Millioctave: Difference between revisions

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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 [[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 ==

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 ==

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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.

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

== External links ==

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

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

[[Category:~~Logarithmic measure~~]]

[[Category:~~Measure~~]]

[[Category:Interval size measures]]

[[Category:~~Unit~~]]

[[Category:Terms]]

[[Category:1000edo]]

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 {{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 [[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 ==
-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 ==
@@ Line 13: / Line 13: @@
 * 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]]
+== External links ==
-[[Category:Interval size measure]]
+* [http://tonalsoft.com/enc/m/millioctave.aspx millioctave / m8ve / μ8ve / moct / μoct] on [[Tonalsoft Encyclopedia]] (includes a ratio-to-millioctaves calculator)
-[[Category:Logarithmic measure]]
-[[Category:Measure]]
+[[Category:Interval size measures]]
-[[Category:Unit]]
+[[Category:Terms]]
+[[Category:1000edo]]