Minkowski block: Difference between revisions
Wikispaces>genewardsmith **Imported revision 173622511 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 173622645 - 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>2010-10-26 01: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-10-26 01:18:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>173622645</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"> | <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"> | ||
A Minkowski block is a particular kind of [[Fokker block]] which tends to be a good candidate form tempering by a particular regular temperament T. Suppose we have a val v supporting T, and the [[http://mathworld.wolfram.com/Seminorm.html|seminorm]] on [[Monzos and Interval Space|interval space]] defined from the temperament; that is, the seminorm defined by orthogonal projection in interval space orthogonal to the commas of T and 2, the octave. | A Minkowski block is a particular kind of [[Fokker blocks|Fokker block]] which tends to be a good candidate form tempering by a particular regular temperament T. Suppose we have a val v supporting T, and the [[http://mathworld.wolfram.com/Seminorm.html|seminorm]] on [[Monzos and Interval Space|interval space]] defined from the temperament; that is, the seminorm defined by orthogonal projection in interval space orthogonal to the commas of T and 2, the octave. | ||
We can find a subgroup of just intonation in which every member of the notes of the temperament, for a particular just tuning, has a unique representative. In that case, the seminorm becomes a norm. The commas of the val v belonging to the subgroup have a unique [[http://www.farcaster.com/papers/sm-thesis/node6.html|Minkowski basis]] in terms of this norm, and we may use these commas, and the reduction of v to the subgroup, to define Fokker blocks in the usual way. The tempering of these blocks by the temperament are the Minkowski blocks. This often but not always includes the [[Hobbits|hobbit]] associated with T and v. </pre></div> | We can find a subgroup of just intonation in which every member of the notes of the temperament, for a particular just tuning, has a unique representative. In that case, the seminorm becomes a norm. The commas of the val v belonging to the subgroup have a unique [[http://www.farcaster.com/papers/sm-thesis/node6.html|Minkowski basis]] in terms of this norm, and we may use these commas, and the reduction of v to the subgroup, to define Fokker blocks in the usual way. The tempering of these blocks by the temperament are the Minkowski blocks. This often but not always includes the [[Hobbits|hobbit]] associated with T and v. </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>Minkowski blocks</title></head><body><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>Minkowski blocks</title></head><body><br /> | ||
A Minkowski block is a particular kind of <a class="wiki_link" href="/Fokker% | A Minkowski block is a particular kind of <a class="wiki_link" href="/Fokker%20blocks">Fokker block</a> which tends to be a good candidate form tempering by a particular regular temperament T. Suppose we have a val v supporting T, and the <a class="wiki_link_ext" href="http://mathworld.wolfram.com/Seminorm.html" rel="nofollow">seminorm</a> on <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">interval space</a> defined from the temperament; that is, the seminorm defined by orthogonal projection in interval space orthogonal to the commas of T and 2, the octave.<br /> | ||
<br /> | <br /> | ||
We can find a subgroup of just intonation in which every member of the notes of the temperament, for a particular just tuning, has a unique representative. In that case, the seminorm becomes a norm. The commas of the val v belonging to the subgroup have a unique <a class="wiki_link_ext" href="http://www.farcaster.com/papers/sm-thesis/node6.html" rel="nofollow">Minkowski basis</a> in terms of this norm, and we may use these commas, and the reduction of v to the subgroup, to define Fokker blocks in the usual way. The tempering of these blocks by the temperament are the Minkowski blocks. This often but not always includes the <a class="wiki_link" href="/Hobbits">hobbit</a> associated with T and v.</body></html></pre></div> | We can find a subgroup of just intonation in which every member of the notes of the temperament, for a particular just tuning, has a unique representative. In that case, the seminorm becomes a norm. The commas of the val v belonging to the subgroup have a unique <a class="wiki_link_ext" href="http://www.farcaster.com/papers/sm-thesis/node6.html" rel="nofollow">Minkowski basis</a> in terms of this norm, and we may use these commas, and the reduction of v to the subgroup, to define Fokker blocks in the usual way. The tempering of these blocks by the temperament are the Minkowski blocks. This often but not always includes the <a class="wiki_link" href="/Hobbits">hobbit</a> associated with T and v.</body></html></pre></div> | ||