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Wikispaces>Andrew_Heathwaite **Imported revision 277296388 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 277964308 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-11- | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-11-21 22:41:03 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>277964308</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">Equal Divisions of the Double Octave -- frequency ratio 4/1 -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1 -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are: | <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">Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are: | ||
0 240 480 720 960 1200 1440 1680 1920 2160 2400... | 0 240 480 720 960 1200 1440 1680 1920 2160 2400... | ||
| Line 23: | Line 23: | ||
See: [[Equal Temperaments]]</pre></div> | See: [[Equal Temperaments]]</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>ed4</title></head><body>Equal Divisions of the Double Octave -- frequency ratio 4/1 -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1 -- in other words, ED2 or <a class="wiki_link" href="/EDO">EDO</a> scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka <a class="wiki_link" href="/5edo">5edo</a>), two octaves of which, in cents are:<br /> | <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>ed4</title></head><body>Equal Divisions of the Double Octave -- frequency ratio 4/1, aka &quot;Quadruple&quot; -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka &quot;Duple&quot; -- in other words, ED2 or <a class="wiki_link" href="/EDO">EDO</a> scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka <a class="wiki_link" href="/5edo">5edo</a>), two octaves of which, in cents are:<br /> | ||
<br /> | <br /> | ||
0 240 480 720 960 1200 1440 1680 1920 2160 2400...<br /> | 0 240 480 720 960 1200 1440 1680 1920 2160 2400...<br /> | ||
Revision as of 22:41, 21 November 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2011-11-21 22:41:03 UTC.
- The original revision id was 277964308.
- 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:
Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are: 0 240 480 720 960 1200 1440 1680 1920 2160 2400... ...taking every other tone yields: 0 240 **480** 720 **960** 1200 **1440** 1680 **1920** 2160 **2400...** **0 480 960 1440 1920 2400...** The resultant scale we can call 5ED4. This approach yields more useful scales starting with ED2 systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 37ED2 (aka [[37edo]]), which is well known to be an excellent temperament in the 2.5.7.11.13.27 subgroup, but whose single degree, approximately 32.4¢, might be "too small" in some context (eg. guitar frets). Taking every other step of 37ED2 produces [[37ED4]], an equal-stepped scale which repeats at 4/1, the double octave, and has a single step of 64.9¢. (See also [[65cET]].) ED4 scales also have the feature that they ascend the pitch continuum twice as fast as ED2 systems. 37 tones of 37ED2 is one octave, while 37 tones of ED4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc. See: [[Equal Temperaments]]
Original HTML content:
<html><head><title>ed4</title></head><body>Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or <a class="wiki_link" href="/EDO">EDO</a> scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka <a class="wiki_link" href="/5edo">5edo</a>), two octaves of which, in cents are:<br /> <br /> 0 240 480 720 960 1200 1440 1680 1920 2160 2400...<br /> <br /> ...taking every other tone yields:<br /> <br /> 0 240 <strong>480</strong> 720 <strong>960</strong> 1200 <strong>1440</strong> 1680 <strong>1920</strong> 2160 <strong>2400...</strong><br /> <strong>0 480 960 1440 1920 2400...</strong><br /> <br /> The resultant scale we can call 5ED4.<br /> <br /> This approach yields more useful scales starting with ED2 systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 37ED2 (aka <a class="wiki_link" href="/37edo">37edo</a>), which is well known to be an excellent temperament in the 2.5.7.11.13.27 subgroup, but whose single degree, approximately 32.4¢, might be "too small" in some context (eg. guitar frets). Taking every other step of 37ED2 produces <a class="wiki_link" href="/37ED4">37ED4</a>, an equal-stepped scale which repeats at 4/1, the double octave, and has a single step of 64.9¢. (See also <a class="wiki_link" href="/65cET">65cET</a>.)<br /> <br /> ED4 scales also have the feature that they ascend the pitch continuum twice as fast as ED2 systems. 37 tones of 37ED2 is one octave, while 37 tones of ED4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.<br /> <br /> See: <a class="wiki_link" href="/Equal%20Temperaments">Equal Temperaments</a></body></html>