MOS rhythm
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- This revision was by author xenjacob and made on 2009-01-18 18:06:47 UTC.
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Original Wikitext content:
=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 <span class="Apple-style-span">//period//</span>. 'MOS 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 MOS rhythm. In our examples, the magnitude of the duration of the period will remain fixed. The durations in MOS rhythms are specified not in <span class="Apple-style-span">//absolute//</span> terms of time interval (minutes, seconds, beats of a metronome), but <span class="Apple-style-span">//relative//</span> 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 [[http://en.wikipedia.org/wiki/Modular_arithmetic|Modular arithmetic]] with a modulus of 1.) 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): [[image:mr_line.png align="center"]] Furthermore, we can emphasize the cyclical nature of our arithmetic if we bend the line segment into a circle (drawing a point at the top for 0/1): [[image:mr_cycle.png align="center"]]
Original HTML content:
<html><head><title>MOS Rhythm Tutorial</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Assumptions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Assumptions</h1> 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 <span class="Apple-style-span"><em>period</em></span>. 'MOS 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 MOS rhythm. In our examples, the magnitude of the duration of the period will remain fixed.<br /> The durations in MOS rhythms are specified not in <span class="Apple-style-span"><em>absolute</em></span> terms of time interval (minutes, seconds, beats of a metronome), but <span class="Apple-style-span"><em>relative</em></span> 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.<br /> 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 class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Modular_arithmetic" rel="nofollow">Modular arithmetic</a> with a modulus of 1.)<br /> 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):<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:2:<div style="text-align: center"><img src="/file/view/mr_line.png/54241800/mr_line.png" alt="" title="" /></div> --><div style="text-align: center"><img src="/file/view/mr_line.png/54241800/mr_line.png" alt="mr_line.png" title="mr_line.png" /></div><!-- ws:end:WikiTextLocalImageRule:2 -->Furthermore, we can emphasize the cyclical nature of our arithmetic if we bend the line segment into a circle (drawing a point at the top for 0/1):<br /> <!-- ws:start:WikiTextLocalImageRule:3:<div style="text-align: center"><img src="/file/view/mr_cycle.png/54241802/mr_cycle.png" alt="" title="" /></div> --><div style="text-align: center"><img src="/file/view/mr_cycle.png/54241802/mr_cycle.png" alt="mr_cycle.png" title="mr_cycle.png" /></div><!-- ws:end:WikiTextLocalImageRule:3 --></body></html>