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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | == Assumptions == |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | 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. |
| : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2009-01-21 10:31:01 UTC</tt>.<br>
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| : The original revision id was <tt>54254194</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Assumptions=
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| 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//. 'Cyclyclical 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 cyclyclical rhythm. In our examples, the magnitude of the duration of the period will remain fixed. | |
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| The durations in cyclyclical 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. | | 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. |
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| 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.) |
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| 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): | | 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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| [[image:mr_line.png align="center"]] | | [[File:mr_line.png|alt=mr_line.png|mr_line.png]]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): |
| 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"]] | | [[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 | | |
| 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 == |
| Cyclyclical 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 cyclyclical rhythms is specified. When how many multiples and which multiples are specified, a single cyclyclical rhythm is specified.</pre></div>
| | 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. |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>MOS Rhythm Tutorial</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Assumptions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Assumptions</h1>
| | == History == |
| 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 <em>period</em>. 'Cyclyclical 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 cyclyclical rhythm. In our examples, the magnitude of the duration of the period will remain fixed.<br />
| | 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: |
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| The durations in cyclyclical rhythms are specified not in <em>absolute</em> terms of time interval (minutes, seconds, beats of a metronome), but <em>relative</em> 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 />
| | * [http://anaphoria.com/hora.pdf A Rhythmic Application of the Horagrams] from ''[[Xenharmonikon]] 16'' |
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| | * [http://anaphoria.com/horo2.pdf More on Horogram Rhythms] |
| 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 <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Modular_arithmetic" rel="nofollow">Modular arithmetic</a> with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.)<br />
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| | [[Category:Non-scale applications of MOS]] |
| 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 />
| | [[Category:Rhythm]] |
| <br />
| | [[Category:todo:expand]] |
| <!-- ws:start:WikiTextLocalImageRule:4:&lt;div style=&quot;text-align: center&quot;&gt;&lt;img src=&quot;/file/view/mr_line.png/54241800/mr_line.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/div&gt; --><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:4 -->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 />
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| <!-- ws:start:WikiTextLocalImageRule:5:&lt;div style=&quot;text-align: center&quot;&gt;&lt;img src=&quot;/file/view/mr_cycle.png/54241802/mr_cycle.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt;&lt;/div&gt; --><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:5 -->When we want to refer to an interval <em>from zero</em>, which also specifies a single pulse within a period, we will use unadorned expressions (e.g. <em>a</em> and <em>1-a</em>). When we want to talk about an interval <em>from anywhere</em>, emphasizing only the magnitude of it, we will enclose it within vertical slashes | | <br />
| | == See also == |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Generators"></a><!-- ws:end:WikiTextHeadingRule:2 -->Generators</h1>
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| Cyclyclical rhythms are calculated by taking <em>multiples</em> of a single interval, called the <em>generating interval</em> or <em>generator</em>. When one interval is called a <em>generator</em> interval relative to a period, a <em>family</em> of cyclyclical rhythms is specified. When how many multiples and which multiples are specified, a single cyclyclical rhythm is specified.</body></html></pre></div>
| | * [[Gallery of MOS patterns]] |