Periodic scale: Difference between revisions
Wikispaces>guest **Imported revision 199011154 - Original comment: ** |
Wikispaces>guest **Imported revision 199011694 - 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:guest|guest]] and made on <tt>2011-02-05 21: | : This revision was by author [[User:guest|guest]] and made on <tt>2011-02-05 21:35:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>199011694</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> | ||
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(3) i < j | (3) i < j\text{ implies }s[i] < s[j] | ||
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We may define an important function **class(i)** on the integers which gives the //generic intervals// of a periodic scale. This is defined by s[j] - s[i] is in class(k) if j - i = k. Since s is quasiperiodic, class(nP) consists only of {nO}, but the rest define sets of numbers in terms of which we can define some important scale properties. In particular we have: | We may define an important function **class(i)** on the integers which gives the //generic intervals// of a periodic scale. This is defined by s[j] - s[i] is in class(k) if j - i = k. Since s is quasiperiodic, class(nP) consists only of {nO}, but the rest define sets of numbers in terms of which we can define some important scale properties. In particular we have: | ||
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We may define an important function <strong>class(i)</strong> on the integers which gives the <em>generic intervals</em> of a periodic scale. This is defined by s[j] - s[i] is in class(k) if j - i = k. Since s is quasiperiodic, class(nP) consists only of {nO}, but the rest define sets of numbers in terms of which we can define some important scale properties. In particular we have:<br /> | We may define an important function <strong>class(i)</strong> on the integers which gives the <em>generic intervals</em> of a periodic scale. This is defined by s[j] - s[i] is in class(k) if j - i = k. Since s is quasiperiodic, class(nP) consists only of {nO}, but the rest define sets of numbers in terms of which we can define some important scale properties. In particular we have:<br /> | ||