MOS rhythm: Difference between revisions
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change cyclyclical into cyclical assuming it a mistake originating from copy&past or search&replace (even google found only this page 🎉🥳) |
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=Assumptions= | == Assumptions == | ||
Assume, for now, that a rhythm is specified as a set of pulses within an interval of time. Assume that a pulse is an instant of attack. Call the total interval of time a ''period''. ' | Assume, for now, that a rhythm is specified as a set of pulses within an interval of time. Assume that a pulse is an instant of attack. Call the total interval of time a ''period''. '''Cyclical rhythms'' as defined here are distinguished by the exact spacing of pulses within a period; the tempo or tempo change of the period is not (yet) relevant to the cyclical rhythm. In our examples, the magnitude of the duration of the period will remain fixed. | ||
The durations in | 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 [http://en.wikipedia.org/wiki/Modular_arithmetic Modular arithmetic] with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.) | ||
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[[File:mr_cycle.png|alt=mr_cycle.png|mr_cycle.png]]When we want to refer to an interval ''from zero'', which also specifies a single pulse within a period, we will use unadorned expressions (e.g. ''a'' and ''1-a''). When we want to talk about an interval ''from anywhere'', emphasizing only the magnitude of it, we will enclose it within vertical slashes | | | [[File:mr_cycle.png|alt=mr_cycle.png|mr_cycle.png]]When we want to refer to an interval ''from zero'', which also specifies a single pulse within a period, we will use unadorned expressions (e.g. ''a'' and ''1-a''). When we want to talk about an interval ''from anywhere'', emphasizing only the magnitude of it, we will enclose it within vertical slashes | | | ||
=Generators= | == 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. | |||