Microtemperament
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- This revision was by author genewardsmith and made on 2010-05-16 02:40:10 UTC.
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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>