MOS rhythm: Difference between revisions
Wikispaces>xenjacob **Imported revision 54066678 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 54254194 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2009-01- | : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2009-01-21 10:31:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>54254194</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : 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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <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= | <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 //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//. '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. | ||
The durations in | 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. | ||
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. | 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 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"]] | [[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): | 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> | [[image:mr_cycle.png align="center"]] | ||
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= | |||
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> | |||
<h4>Original HTML content:</h4> | <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> | <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> | ||
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>. ' | 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 /> | ||
<br /> | <br /> | ||
The durations in | 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 /> | ||
<br /> | <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. | 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 /> | ||
<br /> | <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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- 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 /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- 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 /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Generators"></a><!-- ws:end:WikiTextHeadingRule:2 -->Generators</h1> | |||
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> | |||