Microtemperament: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 142269977 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 142270117 - 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:genewardsmith|genewardsmith]] and made on <tt>2010-05-16 02: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-16 02:40:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>142270117</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">Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a **microtemperament**. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a //nanotemperament//. | <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">Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a **microtemperament**. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a //nanotemperament//. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 236, 270 ... are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 ... are 7-limit microtemperaments; 764, 836, 1084, 1106 ... are 11-limit microtemperaments, and that 1171, 1178, 1186 ... are 13-limit microtemperaments. | ||
Putting 118 and 171 together, we see that the 5-limit [[http://en.wikipedia.org/wiki/Schismatic_temperament|schismatic temperament]], which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal temperament|ennealimmal temperament]], which tempers out the [[http://en.wikipedia.org/wiki/Breedsma|breedsma]] 2401/2400 and the [[http://en.wikipedia.org/wiki/Ragisma|ragisma]] 4375/4374 is also a microtemperament. </pre></div> | Putting 118 and 171 together, we see that the 5-limit [[http://en.wikipedia.org/wiki/Schismatic_temperament|schismatic temperament]], which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal temperament|ennealimmal temperament]], which tempers out the [[http://en.wikipedia.org/wiki/Breedsma|breedsma]] 2401/2400 and the [[http://en.wikipedia.org/wiki/Ragisma|ragisma]] 4375/4374 is also a microtemperament. </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>Microtempering</title></head><body>Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a <strong>microtemperament</strong>. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a <em>nanotemperament</em>. | <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>Microtempering</title></head><body>Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a <strong>microtemperament</strong>. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a <em>nanotemperament</em>. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 236, 270 ... are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 ... are 7-limit microtemperaments; 764, 836, 1084, 1106 ... are 11-limit microtemperaments, and that 1171, 1178, 1186 ... are 13-limit microtemperaments.<br /> | ||
<br /> | <br /> | ||
Putting 118 and 171 together, we see that the 5-limit <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">schismatic temperament</a>, which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that <a class="wiki_link" href="/Ennealimmal%20temperament">ennealimmal temperament</a>, which tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Breedsma" rel="nofollow">breedsma</a> 2401/2400 and the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Ragisma" rel="nofollow">ragisma</a> 4375/4374 is also a microtemperament.</body></html></pre></div> | Putting 118 and 171 together, we see that the 5-limit <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">schismatic temperament</a>, which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that <a class="wiki_link" href="/Ennealimmal%20temperament">ennealimmal temperament</a>, which tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Breedsma" rel="nofollow">breedsma</a> 2401/2400 and the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Ragisma" rel="nofollow">ragisma</a> 4375/4374 is also a microtemperament.</body></html></pre></div> | ||
Revision as of 02:40, 16 May 2010
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2010-05-16 02:40:10 UTC.
- The original revision id was 142270117.
- 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:
Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a **microtemperament**. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a //nanotemperament//. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 236, 270 ... are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 ... are 7-limit microtemperaments; 764, 836, 1084, 1106 ... are 11-limit microtemperaments, and that 1171, 1178, 1186 ... are 13-limit microtemperaments. Putting 118 and 171 together, we see that the 5-limit [[http://en.wikipedia.org/wiki/Schismatic_temperament|schismatic temperament]], which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that [[Ennealimmal temperament|ennealimmal temperament]], which tempers out the [[http://en.wikipedia.org/wiki/Breedsma|breedsma]] 2401/2400 and the [[http://en.wikipedia.org/wiki/Ragisma|ragisma]] 4375/4374 is also a microtemperament.
Original HTML content:
<html><head><title>Microtempering</title></head><body>Any system of temperament in which all of the intervals considered to be consonances of the system are so closely approximated as to be effectively just is a <strong>microtemperament</strong>. There is no agreed on value for the threshold to microtempering, and here we will use less than a cent in error as our line of demarcation, which some people would call a <em>nanotemperament</em>. Using this definition and the tonality diamond as our consonance set, we find that the equal temperaments 118, 171, 236, 270 ... are 5-limit microtmeperaments; that 171, 270, 441, 612, 643 ... are 7-limit microtemperaments; 764, 836, 1084, 1106 ... are 11-limit microtemperaments, and that 1171, 1178, 1186 ... are 13-limit microtemperaments.<br /> <br /> Putting 118 and 171 together, we see that the 5-limit <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Schismatic_temperament" rel="nofollow">schismatic temperament</a>, which tempers out the schisma of 32805/32768, is a microtemperament when appropriately tuned. Putting 171 and 270 together, we see that <a class="wiki_link" href="/Ennealimmal%20temperament">ennealimmal temperament</a>, which tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Breedsma" rel="nofollow">breedsma</a> 2401/2400 and the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Ragisma" rel="nofollow">ragisma</a> 4375/4374 is also a microtemperament.</body></html>