Clipper
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- This revision was by author genewardsmith and made on 2012-02-01 15:33:15 UTC.
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Original Wikitext content:
If c is a [[comma]], then clipper(c) is defined as Euler(Benedetti(c)), tempered by the codimension one temperament tempering out c. Here Euler(N) is the [[Euler genera|Euler genus]], the divisors of the integer N reduced to the octave, and Benedetti(c) is the [[Benedetti height]] of c = p/q, which is p*q if p/q is reduced to its lowest terms. Euler(Benedetti(c)) has exactly one interval of size c, which mis removed when c is tempered out. Two [[Transversal|transversals]] of clipper(c) are obtained by leaving out either one or the other of the pair of scale intervals separated by c. A comma such that the smallest interval in Euler(Benedetti(c)) is c may be called a //clipper comma//; clipper commas would seem to make for superior clippers, avoiding very small intervals. Some 7-limit clipper commas are 16807/16384, 525/512, 128/125, 49/48, 50/49, 3125/3072, 64/63, 81/80, 2048/2025, 245/243, 2109375/2097152, 1029/1024, 15625/15552, 225/224, 3136/3125, 5120/5103, 6144/6125, 2100875/2097152, 5250987/5242880, 65625/65536, 32805/32768, 703125/702464, 2401/2400, 4375/4374 and 250047/250000. =Links= [[http://tech.groups.yahoo.com/group/tuning-math/message/11429]] [[http://tech.groups.yahoo.com/group/tuning-math/message/11432]] [[http://tech.groups.yahoo.com/group/tuning-math/message/11439]] [[http://tech.groups.yahoo.com/group/tuning-math/message/11441]]
Original HTML content:
<html><head><title>Clippers</title></head><body>If c is a <a class="wiki_link" href="/comma">comma</a>, then clipper(c) is defined as Euler(Benedetti(c)), tempered by the codimension one temperament tempering out c. Here Euler(N) is the <a class="wiki_link" href="/Euler%20genera">Euler genus</a>, the divisors of the integer N reduced to the octave, and Benedetti(c) is the <a class="wiki_link" href="/Benedetti%20height">Benedetti height</a> of c = p/q, which is p*q if p/q is reduced to its lowest terms. Euler(Benedetti(c)) has exactly one interval of size c, which mis removed when c is tempered out. Two <a class="wiki_link" href="/Transversal">transversals</a> of clipper(c) are obtained by leaving out either one or the other of the pair of scale intervals separated by c.<br /> <br /> A comma such that the smallest interval in Euler(Benedetti(c)) is c may be called a <em>clipper comma</em>; clipper commas would seem to make for superior clippers, avoiding very small intervals. Some 7-limit clipper commas are 16807/16384, 525/512, 128/125, 49/48, 50/49, 3125/3072, 64/63, 81/80, 2048/2025, 245/243, 2109375/2097152, 1029/1024, 15625/15552, 225/224, 3136/3125, 5120/5103, 6144/6125, 2100875/2097152, 5250987/5242880, 65625/65536, 32805/32768, 703125/702464, 2401/2400, 4375/4374 and <br /> 250047/250000.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:0 -->Links</h1> <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11429" rel="nofollow">http://tech.groups.yahoo.com/group/tuning-math/message/11429</a><br /> <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11432" rel="nofollow">http://tech.groups.yahoo.com/group/tuning-math/message/11432</a><br /> <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11439" rel="nofollow">http://tech.groups.yahoo.com/group/tuning-math/message/11439</a><br /> <a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/11441" rel="nofollow">http://tech.groups.yahoo.com/group/tuning-math/message/11441</a></body></html>