MOS rhythm: Difference between revisions

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The durations in cyclical rhythms are specified not in ''absolute'' terms of time interval (minutes, seconds, beats of a metronome), but ''relative'' to the period, and thus expressed as a (unitless) proportion. For example, '1/2' (or '0.5') will represent a duration (interval of time) of exactly half the duration of the period.

We are concerned with durations that are shorter than the duration of the period; i.e., greater than or equal to zero (no interval) and less than one (period). We can easily convert numbers outside that range by adding or subtracting 1 until they are in the range. This is tantamount to using a [~~http~~://en.wikipedia.org/wiki/Modular_arithmetic Modular arithmetic] with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.)

We are concerned with durations that are shorter than the duration of the period; i.e., greater than or equal to zero (no interval) and less than one (period). We can easily convert numbers outside that range by adding or subtracting 1 until they are in the range. This is tantamount to using a [https://en.wikipedia.org/wiki/Modular_arithmetic Modular arithmetic] with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.)

We can use the metaphor of a timeline, assuming that a line segment (representing a period) can be broken up into smaller line segments (durations or intervals) as delineated by the placement of points (pulses):

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== Generators ==

Cyclical rhythms are calculated by taking ''multiples'' of a single interval, called the ''generating interval'' or ''generator''. When one interval is called a ''generator'' interval relative to a period, a ''family'' of cyclical rhythms is specified. When how many multiples and which multiples are specified, a single cyclical rhythm is specified.

== History ==

David Canright was the first to suggest Fibonacci Rhythms in 1/1. This led to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here:

* [http://anaphoria.com/hora.pdf A Rhythmic Application of the Horagrams] from ''[[Xenharmonikon]] 16''

* [http://anaphoria.com/horo2.pdf More on Horogram Rhythms]

[[Category:Non-scale applications of MOS]]

[[Category:Rhythm]]

[[Category:todo:expand]]

== See also ==

* [[Gallery of MOS patterns]]

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 The durations in cyclical rhythms are specified not in ''absolute'' terms of time interval (minutes, seconds, beats of a metronome), but ''relative'' to the period, and thus expressed as a (unitless) proportion. For example, '1/2' (or '0.5') will represent a duration (interval of time) of exactly half the duration of the period.
-We are concerned with durations that are shorter than the duration of the period; i.e., greater than or equal to zero (no interval) and less than one (period). We can easily convert numbers outside that range by adding or subtracting 1 until they are in the range. This is tantamount to using a [http://en.wikipedia.org/wiki/Modular_arithmetic Modular arithmetic] with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.)
+We are concerned with durations that are shorter than the duration of the period; i.e., greater than or equal to zero (no interval) and less than one (period). We can easily convert numbers outside that range by adding or subtracting 1 until they are in the range. This is tantamount to using a [https://en.wikipedia.org/wiki/Modular_arithmetic Modular arithmetic] with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.)
 We can use the metaphor of a timeline, assuming that a line segment (representing a period) can be broken up into smaller line segments (durations or intervals) as delineated by the placement of points (pulses):
@@ Line 14: / Line 14: @@
 == Generators ==
 Cyclical rhythms are calculated by taking ''multiples'' of a single interval, called the ''generating interval'' or ''generator''. When one interval is called a ''generator'' interval relative to a period, a ''family'' of cyclical rhythms is specified. When how many multiples and which multiples are specified, a single cyclical rhythm is specified.
+== History ==
+David Canright was the first to suggest Fibonacci Rhythms in 1/1. This led to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here:
+* [http://anaphoria.com/hora.pdf A Rhythmic Application of the Horagrams] from ''[[Xenharmonikon]] 16''
+* [http://anaphoria.com/horo2.pdf More on Horogram Rhythms]
+[[Category:Non-scale applications of MOS]]
+[[Category:Rhythm]]
+[[Category:todo:expand]]
+== See also ==
+* [[Gallery of MOS patterns]]