Millioctave: Difference between revisions

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The '''millioctave''' ('''moct''') is a logarithmic [[interval size measure]]. ~~which~~ 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 '''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)''.

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.

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.

1 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.

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 {{Wikipedia}}
-The '''millioctave''' ('''moct''') is a logarithmic [[interval size measure]]. which 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 '''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)''.
-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.
+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.
 millioctave may be defined as a frequency ratio of the 1000th root of 2, or 2^0.001.