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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 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. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-27 10:14:48 UTC</tt>.<br>
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| : The original revision id was <tt>205384210</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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.
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| 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 [[Breedsmic temperaments|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 [[Breedsmic_temperaments|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. |
| <h4>Original HTML content:</h4>
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| <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 />
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| 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="/Breedsmic%20temperaments">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>
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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 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, which tempers out the breedsma 2401/2400 and the ragisma 4375/4374 is also a microtemperament.