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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>2010-05-29 00:55:44 UTC</tt>.<br> | | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-05-29 00:56:45 UTC</tt>.<br> |
| : The original revision id was <tt>145581889</tt>.<br> | | : The original revision id was <tt>145581925</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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| [[Paul Erlich]] has given us a [[Catalog of five-limit rank two temperaments|catalog of 5-limit rank two temperaments]]. | | [[Paul Erlich]] has given us a [[Catalog of five-limit rank two temperaments|catalog of 5-limit rank two temperaments]]. |
|
| |
| || Vanishing Interval's Ratio || V.I. Vector || V.I. cents || Horagram name || TOP per. || TOP gen. || Mapp. of 2 || Mapp. of 3 || Mapp. of 5 || Cmplx. || TOP Dmg. ||
| |
| || TWO EXOTEMPERAMENTS: || || || || || || || || || || ||
| |
| || 15:16 || [4, -1, -1> || 111.7 || Father || 1185.9 || 447.4 || 1, 0 || || || || ||
| |
| || || || || Bug || 1200.0 || 260.3 || 1, 0 || || || || ||
| |
| || MAIN SEQUENCE || || || || || || || || || || ||
| |
| || || || || Dicot || 1207.66 || 353.22 || 1, 0 || || || || ||
| |
| || || || || Meantone || 1201.70 || 504.13 || 1, 0 || || || || ||
| |
| || || || || Augmented || 399.02 || 93.15 || 3, 0 || || || || ||
| |
| || || || || Mavila || 1206.55 || 685.03 || 1, 0 || || || || ||
| |
| || || || || Porcupine || 1196.91 || 1034.59 || 1, 0 || || || || ||
| |
| || || || || Blackwood || 238.87 || 158.78 || 5, 0 || || || || ||
| |
| || || || || Dimipent || 299.16 || 197.49 || 4, 0 || || || || ||
| |
| || || || || Srutal || 599.56 || 494.86 || 2, 0 || || || || ||
| |
| || || || || Magic || 1201.28 || 380.80 || 1, 0 || || || || ||
| |
| || || || || Ripple || 1203.32 || 101.99 || 1, 0 || || || || ||
| |
| || || || || Hanson || 1200.29 || 317.07 || 1, 0 || || || || ||
| |
| || || || || Negripent || 1201.82 || 1075.68 || 1, 0 || || || || ||
| |
| || || || || Tetracot || 1199.03 || 176.11 || 1, 0 || || || || ||
| |
| || || || || Superpyth || 1197.60 || 708.17 || 1, 0 || || || || ||
| |
| || || || || Helmholtz || 1200.07 || 701.79 || 1, 0 || || || || ||
| |
| || || || || Sensipent || 1199.59 || 756.60 || 1, 0 || || || || ||
| |
| || || || || Passion || 1198.31 || 98.40 || 1, 0 || || || || ||
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| || || || || Würschmidt || 1199.69 || 812.05 || 1, 0 || || || || ||
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| || || || || Compton || 100.05 || 15.13 || 12, 0 || || || || ||
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| || || || || Amity || 1199.85 || 860.38 || 1, 0 || || || || ||
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| || || || || Orson || 1200.24 || 271.65 || 1, 0 || || || || ||
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| || TWO BONUS TEMPS || || || || || || || || || || ||
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| || || || || Vishnu || 599.97 || 71.15 || 2, 0 || || || || ||
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| || || || || Luna || 1199.98 || 193.196 || 1, 0 || || || || ||
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| [[Meantone]] is a familar historical temperament based on a chain of fifths (or fourths), but it is only one of many possibilities for temperaments based on a chain of generating intervals. These are referred to as "rank 2" temperaments, since they are based on a set of two linearly independent intervals. One of these intervals (typically an octave or fraction of an octave) can be selected as the "period", and another interval, smaller than the period, is referred to as the "generator". | | [[Meantone]] is a familar historical temperament based on a chain of fifths (or fourths), but it is only one of many possibilities for temperaments based on a chain of generating intervals. These are referred to as "rank 2" temperaments, since they are based on a set of two linearly independent intervals. One of these intervals (typically an octave or fraction of an octave) can be selected as the "period", and another interval, smaller than the period, is referred to as the "generator". |
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| <br /> | | <br /> |
| <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> has given us a <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>.<br /> | | <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> has given us a <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>.<br /> |
| <br />
| |
|
| |
|
| |
| <table class="wiki_table">
| |
| <tr>
| |
| <td>Vanishing Interval's Ratio<br />
| |
| </td>
| |
| <td>V.I. Vector<br />
| |
| </td>
| |
| <td>V.I. cents<br />
| |
| </td>
| |
| <td>Horagram name<br />
| |
| </td>
| |
| <td>TOP per.<br />
| |
| </td>
| |
| <td>TOP gen.<br />
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| </td>
| |
| <td>Mapp. of 2<br />
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| </td>
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| <td>Mapp. of 3<br />
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| </td>
| |
| <td>Mapp. of 5<br />
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| </td>
| |
| <td>Cmplx.<br />
| |
| </td>
| |
| <td>TOP Dmg.<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>TWO EXOTEMPERAMENTS:<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td>15:16<br />
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| </td>
| |
| <td>[4, -1, -1&gt;<br />
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| </td>
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| <td>111.7<br />
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| </td>
| |
| <td>Father<br />
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| </td>
| |
| <td>1185.9<br />
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| </td>
| |
| <td>447.4<br />
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| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td>Bug<br />
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| </td>
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| <td>1200.0<br />
| |
| </td>
| |
| <td>260.3<br />
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| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td>MAIN SEQUENCE<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
| |
| <td>Dicot<br />
| |
| </td>
| |
| <td>1207.66<br />
| |
| </td>
| |
| <td>353.22<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Meantone<br />
| |
| </td>
| |
| <td>1201.70<br />
| |
| </td>
| |
| <td>504.13<br />
| |
| </td>
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| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Augmented<br />
| |
| </td>
| |
| <td>399.02<br />
| |
| </td>
| |
| <td>93.15<br />
| |
| </td>
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| <td>3, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Mavila<br />
| |
| </td>
| |
| <td>1206.55<br />
| |
| </td>
| |
| <td>685.03<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
| |
| <td><br />
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| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| <td>Porcupine<br />
| |
| </td>
| |
| <td>1196.91<br />
| |
| </td>
| |
| <td>1034.59<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Blackwood<br />
| |
| </td>
| |
| <td>238.87<br />
| |
| </td>
| |
| <td>158.78<br />
| |
| </td>
| |
| <td>5, 0<br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
| |
| <td>Dimipent<br />
| |
| </td>
| |
| <td>299.16<br />
| |
| </td>
| |
| <td>197.49<br />
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| </td>
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| <td>4, 0<br />
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| </td>
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| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Srutal<br />
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| </td>
| |
| <td>599.56<br />
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| </td>
| |
| <td>494.86<br />
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| </td>
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| <td>2, 0<br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Magic<br />
| |
| </td>
| |
| <td>1201.28<br />
| |
| </td>
| |
| <td>380.80<br />
| |
| </td>
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| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Ripple<br />
| |
| </td>
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| <td>1203.32<br />
| |
| </td>
| |
| <td>101.99<br />
| |
| </td>
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| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Hanson<br />
| |
| </td>
| |
| <td>1200.29<br />
| |
| </td>
| |
| <td>317.07<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| </tr>
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| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td>Negripent<br />
| |
| </td>
| |
| <td>1201.82<br />
| |
| </td>
| |
| <td>1075.68<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
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| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Tetracot<br />
| |
| </td>
| |
| <td>1199.03<br />
| |
| </td>
| |
| <td>176.11<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Superpyth<br />
| |
| </td>
| |
| <td>1197.60<br />
| |
| </td>
| |
| <td>708.17<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Helmholtz<br />
| |
| </td>
| |
| <td>1200.07<br />
| |
| </td>
| |
| <td>701.79<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| </tr>
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| <tr>
| |
| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| <td><br />
| |
| </td>
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| <td>Sensipent<br />
| |
| </td>
| |
| <td>1199.59<br />
| |
| </td>
| |
| <td>756.60<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Passion<br />
| |
| </td>
| |
| <td>1198.31<br />
| |
| </td>
| |
| <td>98.40<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Würschmidt<br />
| |
| </td>
| |
| <td>1199.69<br />
| |
| </td>
| |
| <td>812.05<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Compton<br />
| |
| </td>
| |
| <td>100.05<br />
| |
| </td>
| |
| <td>15.13<br />
| |
| </td>
| |
| <td>12, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Amity<br />
| |
| </td>
| |
| <td>1199.85<br />
| |
| </td>
| |
| <td>860.38<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Orson<br />
| |
| </td>
| |
| <td>1200.24<br />
| |
| </td>
| |
| <td>271.65<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>TWO BONUS TEMPS<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Vishnu<br />
| |
| </td>
| |
| <td>599.97<br />
| |
| </td>
| |
| <td>71.15<br />
| |
| </td>
| |
| <td>2, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>Luna<br />
| |
| </td>
| |
| <td>1199.98<br />
| |
| </td>
| |
| <td>193.196<br />
| |
| </td>
| |
| <td>1, 0<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
| <br />
| |
| <br /> | | <br /> |
| <a class="wiki_link" href="/Meantone">Meantone</a> is a familar historical temperament based on a chain of fifths (or fourths), but it is only one of many possibilities for temperaments based on a chain of generating intervals. These are referred to as &quot;rank 2&quot; temperaments, since they are based on a set of two linearly independent intervals. One of these intervals (typically an octave or fraction of an octave) can be selected as the &quot;period&quot;, and another interval, smaller than the period, is referred to as the &quot;generator&quot;.<br /> | | <a class="wiki_link" href="/Meantone">Meantone</a> is a familar historical temperament based on a chain of fifths (or fourths), but it is only one of many possibilities for temperaments based on a chain of generating intervals. These are referred to as &quot;rank 2&quot; temperaments, since they are based on a set of two linearly independent intervals. One of these intervals (typically an octave or fraction of an octave) can be selected as the &quot;period&quot;, and another interval, smaller than the period, is referred to as the &quot;generator&quot;.<br /> |