MOS rhythm: Difference between revisions
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Wikispaces>xenjacob **Imported revision 53937546 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 54066678 - 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>2009-01-19 23:22:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>54066678</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 | 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//. '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 | |||
The durations in MOS 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 [[http://en.wikipedia.org/wiki/Modular_arithmetic|Modular arithmetic]] with a modulus of 1.) | 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): | ||
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<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 | 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>. '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 | <br /> | ||
The durations in MOS 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 /> | |||
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 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 /> | ||
<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: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 /> | <!-- 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 /> | ||
<!-- 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> | <!-- 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> | ||
Revision as of 23:22, 19 January 2009
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenjacob and made on 2009-01-19 23:22:56 UTC.
- The original revision id was 54066678.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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 //period//. '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 //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 [[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 <em>period</em>. '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 /> <br /> The durations in MOS 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 /> 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 /> <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>