Fokker block: Difference between revisions
Wikispaces>genewardsmith **Imported revision 508626008 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 509470914 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2014-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-17 01:14:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>509470914</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> | ||
| Line 30: | Line 30: | ||
Hence S satisfies the conditions for being a [[Periodic scale|periodic scale]], and since our unit of measurement is the octave, ie we are using log base two to define intervals, the repetition interval 1 represents an octave. This gives us our first definition of Fokker block. | Hence S satisfies the conditions for being a [[Periodic scale|periodic scale]], and since our unit of measurement is the octave, ie we are using log base two to define intervals, the repetition interval 1 represents an octave. This gives us our first definition of Fokker block. | ||
By choosing various ak satisfying 0 ≤ ak < P, for any Fokker block we may find the various [[Periodic scale#Definition-Rotations|rotations]], of the block. However, other choices lead to blocks which are not rotations of our initial block, but instead belong to [[Dome|domes]], which are disjoint from the dome of the initial block. The collection of all Fokker blocks for any of the allowed values of the ak offsets is an //arena//; a Fokker arena is defined entirely by its chromas. | |||
=Second definition of a Fokker block= | =Second definition of a Fokker block= | ||
| Line 137: | Line 137: | ||
Hence S satisfies the conditions for being a <a class="wiki_link" href="/Periodic%20scale">periodic scale</a>, and since our unit of measurement is the octave, ie we are using log base two to define intervals, the repetition interval 1 represents an octave. This gives us our first definition of Fokker block.<br /> | Hence S satisfies the conditions for being a <a class="wiki_link" href="/Periodic%20scale">periodic scale</a>, and since our unit of measurement is the octave, ie we are using log base two to define intervals, the repetition interval 1 represents an octave. This gives us our first definition of Fokker block.<br /> | ||
<br /> | <br /> | ||
By choosing various ak satisfying 0 ≤ ak &lt; P, for any Fokker block we may find the various <a class="wiki_link" href="/Periodic%20scale#Definition-Rotations">rotations</a>, of the block. However, other choices lead to blocks which are not rotations of our initial block, but instead belong to <a class="wiki_link" href="/Dome">domes</a>, which are disjoint from the dome of the initial block. The collection of all Fokker blocks for any of the allowed values of the ak offsets is an <em>arena</em>; a Fokker arena is defined entirely by its chromas.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Second definition of a Fokker block"></a><!-- ws:end:WikiTextHeadingRule:4 -->Second definition of a Fokker block</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Second definition of a Fokker block"></a><!-- ws:end:WikiTextHeadingRule:4 -->Second definition of a Fokker block</h1> | ||