|
|
| (11 intermediate revisions by 6 users not shown) |
| Line 1: |
Line 1: |
| <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>2009-01-18 18:06:47 UTC</tt>.<br>
| | |
| : The original revision id was <tt>53937546</tt>.<br>
| | 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. |
| : The revision comment was: <tt></tt><br>
| | |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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 [https://en.wikipedia.org/wiki/Modular_arithmetic Modular arithmetic] with a modulus of 1. (Clocks and twelve-tone theory use a modulus of 12.) |
| <h4>Original Wikitext content:</h4>
| | |
| <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=
| |
| 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): | | 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"]] | | [[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"]]</pre></div> | | [[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 | | |
| <h4>Original HTML content:</h4>
| | |
| <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>
| | == Generators == |
| 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 />
| | 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. |
| 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 />
| | == History == |
| 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 />
| | 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: |
| <br />
| | |
| <!-- ws:start:WikiTextLocalImageRule:2:&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: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 />
| | * [http://anaphoria.com/hora.pdf A Rhythmic Application of the Horagrams] from ''[[Xenharmonikon]] 16'' |
| <!-- ws:start:WikiTextLocalImageRule:3:&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:3 --></body></html></pre></div>
| | * [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]] |