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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | Garibaldi is a 7-limit (and higher) temperament of the [[Schismatic_family#Garibaldi|schismatic family]]. It is an extension of [[Helmholtz|helmholtz]] temperament beyond the 5 limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, 5/4 is mapped to the diminished fourth (e.g. A-Db), and the new mapping specific to garibaldi is that 7/4 is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a [[Marvel_temperaments|marvel temperament]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-11-20 10:51:30 UTC</tt>.<br>
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| : The original revision id was <tt>470742574</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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">Garibaldi is a 7-limit (and higher) temperament of the [[schismatic family#Garibaldi]]. It is an extension of [[helmholtz]] temperament beyond the 5 limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, 5/4 is mapped to the diminished fourth (e.g. A-Db), and the new mapping specific to garibaldi is that 7/4 is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a [[marvel temperaments|marvel temperament]].
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| =Spectrum of Garibaldi Tunings by Eigenmonzos= | | =Spectrum of Garibaldi Tunings by Eigenmonzos= |
| ||~ Eigenmonzo ||~ Fifth ||
| |
| || 16/15 || 701.676 ||
| |
| || 69\118 || 701.695 ||
| |
| || 5/4 || 701.711 ||
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| || [0 -10 17> || 701.728 (5 limit least squares) ||
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| || 6/5 || 701.738 (5 limit minimax) ||
| |
| || 100\171 || 701.754 ||
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| || 10/9 || 701.760 ||
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| || 31\53 || 701.887 ||
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| || 15/13 || 701.9355 ||
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| || 13/10 || 701.9362 ||
| |
| || 4/3 || 701.955 ||
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| || 16/13 || 702.026 ||
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| || 13/12 || 702.030 ||
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| || 18/13 || 702.034 ||
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| || 86\147 || 702.041 ||
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| || 11/10 || 702.097 ||
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| || 15/11 || 702.102 ||
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| || 14/13 || 702.109 (13 and 15 limit minimax) ||
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| || [0 -95 -137 -129 167 143> || 702.112 (15 limit least squares) ||
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| || [0 -27 7 17> || 702.114 (9 limit least squares) ||
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| || 55\94 || 702.12766 ||
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| || [0 -38 -80 -122 137 116> || 702.12770 (13 limit least squares) ||
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| || [0 -25 11 35> || 702.140 (7 limit least squares) ||
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| || [0 17 -52 -88 134> || 702.183 (11 limit least squares) ||
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| || 9/7 || 702.193 (9 and 11 limit minimax) ||
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| || 7/6 || 702.209 (7 limit minimax) ||
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| || 79\135 || 702.222 ||
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| || 8/7 || 702.227 ||
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| || 14/11 || 702.230 ||
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| || 11/8 || 702.231 ||
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| || 12/11 || 702.244 ||
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| || 11/9 || 702.258 ||
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| || 24\41 || 702.439 ||
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| || 15/14 || 702.778 ||
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| || 7/5 || 702.915 ||
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| || 17\29 || 703.448 ||
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| || 13/11 || 703.597 ||</pre></div>
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| <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>Garibaldi temperament</title></head><body>Garibaldi is a 7-limit (and higher) temperament of the <a class="wiki_link" href="/schismatic%20family#Garibaldi">schismatic family</a>. It is an extension of <a class="wiki_link" href="/helmholtz">helmholtz</a> temperament beyond the 5 limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, 5/4 is mapped to the diminished fourth (e.g. A-Db), and the new mapping specific to garibaldi is that 7/4 is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a <a class="wiki_link" href="/marvel%20temperaments">marvel temperament</a>.<br />
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| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Spectrum of Garibaldi Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:0 -->Spectrum of Garibaldi Tunings by Eigenmonzos</h1>
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| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>Eigenmonzo<br />
| | ! | Eigenmonzo |
| </th>
| | ! | Fifth |
| <th>Fifth<br />
| | |- |
| </th>
| | | | 16/15 |
| </tr>
| | | | 701.676 |
| <tr>
| | |- |
| <td>16/15<br />
| | | | 69\118 |
| </td>
| | | | 701.695 |
| <td>701.676<br />
| | |- |
| </td>
| | | | 5/4 |
| </tr>
| | | | 701.711 |
| <tr>
| | |- |
| <td>69\118<br />
| | | | [0 -10 17> |
| </td>
| | | | 701.728 (5 limit least squares) |
| <td>701.695<br />
| | |- |
| </td>
| | | | 6/5 |
| </tr>
| | | | 701.738 (5 limit minimax) |
| <tr>
| | |- |
| <td>5/4<br />
| | | | 100\171 |
| </td>
| | | | 701.754 |
| <td>701.711<br />
| | |- |
| </td>
| | | | 10/9 |
| </tr>
| | | | 701.760 |
| <tr>
| | |- |
| <td>[0 -10 17&gt;<br />
| | | | 31\53 |
| </td>
| | | | 701.887 |
| <td>701.728 (5 limit least squares)<br />
| | |- |
| </td>
| | | | 15/13 |
| </tr>
| | | | 701.9355 |
| <tr>
| | |- |
| <td>6/5<br />
| | | | 13/10 |
| </td>
| | | | 701.9362 |
| <td>701.738 (5 limit minimax)<br />
| | |- |
| </td>
| | | | 4/3 |
| </tr>
| | | | 701.955 |
| <tr>
| | |- |
| <td>100\171<br />
| | | | 16/13 |
| </td>
| | | | 702.026 |
| <td>701.754<br />
| | |- |
| </td>
| | | | 13/12 |
| </tr>
| | | | 702.030 |
| <tr>
| | |- |
| <td>10/9<br />
| | | | 18/13 |
| </td>
| | | | 702.034 |
| <td>701.760<br />
| | |- |
| </td>
| | | | 86\147 |
| </tr>
| | | | 702.041 |
| <tr>
| | |- |
| <td>31\53<br />
| | | | 11/10 |
| </td>
| | | | 702.097 |
| <td>701.887<br />
| | |- |
| </td>
| | | | 15/11 |
| </tr>
| | | | 702.102 |
| <tr>
| | |- |
| <td>15/13<br />
| | | | 14/13 |
| </td>
| | | | 702.109 (13 and 15 limit minimax) |
| <td>701.9355<br />
| | |- |
| </td>
| | | | [0 -95 -137 -129 167 143> |
| </tr>
| | | | 702.112 (15 limit least squares) |
| <tr>
| | |- |
| <td>13/10<br />
| | | | [0 -27 7 17> |
| </td>
| | | | 702.114 (9 limit least squares) |
| <td>701.9362<br />
| | |- |
| </td>
| | | | 55\94 |
| </tr>
| | | | 702.12766 |
| <tr>
| | |- |
| <td>4/3<br />
| | | | [0 -38 -80 -122 137 116> |
| </td>
| | | | 702.12770 (13 limit least squares) |
| <td>701.955<br />
| | |- |
| </td>
| | | | [0 -25 11 35> |
| </tr>
| | | | 702.140 (7 limit least squares) |
| <tr>
| | |- |
| <td>16/13<br />
| | | | [0 17 -52 -88 134> |
| </td>
| | | | 702.183 (11 limit least squares) |
| <td>702.026<br />
| | |- |
| </td>
| | | | 9/7 |
| </tr>
| | | | 702.193 (9 and 11 limit minimax) |
| <tr>
| | |- |
| <td>13/12<br />
| | | | 7/6 |
| </td>
| | | | 702.209 (7 limit minimax) |
| <td>702.030<br />
| | |- |
| </td>
| | | | 79\135 |
| </tr>
| | | | 702.222 |
| <tr>
| | |- |
| <td>18/13<br />
| | | | 8/7 |
| </td>
| | | | 702.227 |
| <td>702.034<br />
| | |- |
| </td>
| | | | 14/11 |
| </tr>
| | | | 702.230 |
| <tr>
| | |- |
| <td>86\147<br />
| | | | 11/8 |
| </td>
| | | | 702.231 |
| <td>702.041<br />
| | |- |
| </td>
| | | | 12/11 |
| </tr>
| | | | 702.244 |
| <tr>
| | |- |
| <td>11/10<br />
| | | | 11/9 |
| </td>
| | | | 702.258 |
| <td>702.097<br />
| | |- |
| </td>
| | | | 24\41 |
| </tr>
| | | | 702.439 |
| <tr>
| | |- |
| <td>15/11<br />
| | | | 15/14 |
| </td>
| | | | 702.778 |
| <td>702.102<br />
| | |- |
| </td>
| | | | 7/5 |
| </tr>
| | | | 702.915 |
| <tr>
| | |- |
| <td>14/13<br />
| | | | 17\29 |
| </td>
| | | | 703.448 |
| <td>702.109 (13 and 15 limit minimax)<br />
| | |- |
| </td>
| | | | 13/11 |
| </tr>
| | | | 703.597 |
| <tr>
| | |} |
| <td>[0 -95 -137 -129 167 143&gt;<br />
| | [[Category:7-limit]] |
| </td>
| | [[Category:garibaldi]] |
| <td>702.112 (15 limit least squares)<br />
| | [[Category:marvel]] |
| </td>
| | [[Category:schismatic]] |
| </tr>
| | [[Category:temperament]] |
| <tr>
| |
| <td>[0 -27 7 17&gt;<br />
| |
| </td>
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| <td>702.114 (9 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>55\94<br />
| |
| </td>
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| <td>702.12766<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>[0 -38 -80 -122 137 116&gt;<br />
| |
| </td>
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| <td>702.12770 (13 limit least squares)<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>[0 -25 11 35&gt;<br />
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| </td>
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| <td>702.140 (7 limit least squares)<br />
| |
| </td>
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| </tr>
| |
| <tr>
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| <td>[0 17 -52 -88 134&gt;<br />
| |
| </td>
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| <td>702.183 (11 limit least squares)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>9/7<br />
| |
| </td>
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| <td>702.193 (9 and 11 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>702.209 (7 limit minimax)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>79\135<br />
| |
| </td>
| |
| <td>702.222<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>8/7<br />
| |
| </td>
| |
| <td>702.227<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>14/11<br />
| |
| </td>
| |
| <td>702.230<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>11/8<br />
| |
| </td>
| |
| <td>702.231<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>702.244<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>11/9<br />
| |
| </td>
| |
| <td>702.258<br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td>24\41<br />
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| </td>
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| <td>702.439<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>15/14<br />
| |
| </td>
| |
| <td>702.778<br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td>7/5<br />
| |
| </td>
| |
| <td>702.915<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>17\29<br />
| |
| </td>
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| <td>703.448<br />
| |
| </td>
| |
| </tr>
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| <tr>
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| <td>13/11<br />
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| </td>
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| <td>703.597<br />
| |
| </td>
| |
| </tr>
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| </table>
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| </body></html></pre></div>
| |
Garibaldi is a 7-limit (and higher) temperament of the schismatic family. It is an extension of helmholtz temperament beyond the 5 limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, 5/4 is mapped to the diminished fourth (e.g. A-Db), and the new mapping specific to garibaldi is that 7/4 is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a marvel temperament.
Spectrum of Garibaldi Tunings by Eigenmonzos
| Eigenmonzo
|
Fifth
|
| 16/15
|
701.676
|
| 69\118
|
701.695
|
| 5/4
|
701.711
|
| [0 -10 17>
|
701.728 (5 limit least squares)
|
| 6/5
|
701.738 (5 limit minimax)
|
| 100\171
|
701.754
|
| 10/9
|
701.760
|
| 31\53
|
701.887
|
| 15/13
|
701.9355
|
| 13/10
|
701.9362
|
| 4/3
|
701.955
|
| 16/13
|
702.026
|
| 13/12
|
702.030
|
| 18/13
|
702.034
|
| 86\147
|
702.041
|
| 11/10
|
702.097
|
| 15/11
|
702.102
|
| 14/13
|
702.109 (13 and 15 limit minimax)
|
| [0 -95 -137 -129 167 143>
|
702.112 (15 limit least squares)
|
| [0 -27 7 17>
|
702.114 (9 limit least squares)
|
| 55\94
|
702.12766
|
| [0 -38 -80 -122 137 116>
|
702.12770 (13 limit least squares)
|
| [0 -25 11 35>
|
702.140 (7 limit least squares)
|
| [0 17 -52 -88 134>
|
702.183 (11 limit least squares)
|
| 9/7
|
702.193 (9 and 11 limit minimax)
|
| 7/6
|
702.209 (7 limit minimax)
|
| 79\135
|
702.222
|
| 8/7
|
702.227
|
| 14/11
|
702.230
|
| 11/8
|
702.231
|
| 12/11
|
702.244
|
| 11/9
|
702.258
|
| 24\41
|
702.439
|
| 15/14
|
702.778
|
| 7/5
|
702.915
|
| 17\29
|
703.448
|
| 13/11
|
703.597
|