Valentine
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Gedankenwelt and made on 2015-02-02 21:10:57 UTC.
- The original revision id was 539439684.
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Original Wikitext content:
See [[Starling temperaments#Valentine%20temperament]]. =Generator Chain= ||~ Generators ||~ Cents* ||~ 11-limit ratios (valentine mapping) ||~ 13-limit ratios (valentino mapping) ||~ 13-limit ratios (lupercalia mapping) ||~ 13-limit ratios (dwynwen mapping) || || 0 ||> 0.00 || 1/1 || || || || || 1 ||> 77.88 || 21/20, 22/21, 25/24 || || 26/25 || 27/26 || || 2 ||> 155.76 || 12/11, 11/10, 35/32 || || 13/12 || || || 3 ||> 233.64 || 8/7 || || 15/13 || || || 4 ||> 311.52 || 6/5 || || 13/11 || || || 5 ||> 389.41 || 5/4 || || 26/21, 33/26 || || || 6 ||> 467.29 || 21/16 || || 13/10 || || || 7 ||> 545.17 || 11/8, 15/11 || || 18/13 || || || 8 ||> 623.05 || 10/7 || 56/39 || || 13/9 || || 9 ||> 700.93 || 3/2 || || 52/35 || || || 10 ||> 778.81 || 11/7, 25/16 || || || 52/33 || || 11 ||> 856.69 || 18/11 || 64/39 || 13/8 || || || 12 ||> 934.57 || 12/7 || || || 26/15 || || 13 ||> 1012.46 || 9/5, 25/14 || || || || || 14 ||> 1090.34 || 15/8 || || 13/7 || || || 15 ||> 1168.22 || 63/32, 96/49, 55/28, 108/55, 125/64 || || 39/20 || || || 16 ||> 46.10 || 33/32, 36/35, 50/49 || 40/39 || 27/26 || 26/25 || || 17 ||> 123.98 || 15/14, 27/25 || 14/13 || || 13/12 || || 18 ||> 201.86 || 9/8 || || || || || 19 ||> 279.74 || 33/28 || || || 13/11 || || 20 ||> 357.62 || 27/22 || 16/13 || 39/32 || 26/21 || || 21 ||> 435.51 || 9/7 || || || 13/10 || || 22 ||> 513.39 || 27/20 || 35/26 || || || || 23 ||> 591.27 || 45/32 || || 39/28 || || || 24 ||> 669.15 || 72/49 || || || 52/35 || || 25 ||> 747.03 || 54/35 || 20/13 || || || || 26 ||> 824.91 || 45/28 || 21/13 || || 13/8 || || 27 ||> 902.79 || 27/16 || 22/13 || || || || 28 ||> 980.67 || || || || || || 29 ||> 1058.56 || 90/49 || 24/13 || || 13/7 || || 30 ||> 1136.44 || 27/14 || 25/13 || || 39/20 || || 31 ||> 14.32 || 81/80, 99/98 || || || || *in 11-limit POTE tuning =Spectrum of Valentine Tunings by Eigenmonzos= ||~ Eigenmonzo ||~ Minor Semitone || || 12/11 || 75.319 || || 8/7 || 77.058 || || 7/5 || 77.186 || || 5/4 || 77.263 || || 11/9 || 77.508 || || 7/6 || 77.761 (7 limit minimax) || || 9/7 || 77.861 (9 limit minimax) || || 4/3 || 77.995 (5 limit minimax, Carlos Alpha tuning) || || 14/11 || 78.249 (11 limit minimax) || || 10/9 || 78.277 || || 11/8 || 78.760 || || 6/5 || 78.910 || || 11/10 || 82.502 ||
Original HTML content:
<html><head><title>Valentine</title></head><body>See <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament">Starling temperaments</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Generator Chain"></a><!-- ws:end:WikiTextHeadingRule:0 -->Generator Chain</h1>
<table class="wiki_table">
<tr>
<th>Generators<br />
</th>
<th>Cents*<br />
</th>
<th>11-limit ratios<br />
(valentine mapping)<br />
</th>
<th>13-limit ratios<br />
(valentino mapping)<br />
</th>
<th>13-limit ratios<br />
(lupercalia mapping)<br />
</th>
<th>13-limit ratios<br />
(dwynwen mapping)<br />
</th>
</tr>
<tr>
<td>0<br />
</td>
<td style="text-align: right;">0.00<br />
</td>
<td>1/1<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td style="text-align: right;">77.88<br />
</td>
<td>21/20, 22/21, 25/24<br />
</td>
<td><br />
</td>
<td>26/25<br />
</td>
<td>27/26<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td style="text-align: right;">155.76<br />
</td>
<td>12/11, 11/10, 35/32<br />
</td>
<td><br />
</td>
<td>13/12<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td style="text-align: right;">233.64<br />
</td>
<td>8/7<br />
</td>
<td><br />
</td>
<td>15/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td style="text-align: right;">311.52<br />
</td>
<td>6/5<br />
</td>
<td><br />
</td>
<td>13/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td style="text-align: right;">389.41<br />
</td>
<td>5/4<br />
</td>
<td><br />
</td>
<td>26/21, 33/26<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td style="text-align: right;">467.29<br />
</td>
<td>21/16<br />
</td>
<td><br />
</td>
<td>13/10<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td style="text-align: right;">545.17<br />
</td>
<td>11/8, 15/11<br />
</td>
<td><br />
</td>
<td>18/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td style="text-align: right;">623.05<br />
</td>
<td>10/7<br />
</td>
<td>56/39<br />
</td>
<td><br />
</td>
<td>13/9<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td style="text-align: right;">700.93<br />
</td>
<td>3/2<br />
</td>
<td><br />
</td>
<td>52/35<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td style="text-align: right;">778.81<br />
</td>
<td>11/7, 25/16<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>52/33<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td style="text-align: right;">856.69<br />
</td>
<td>18/11<br />
</td>
<td>64/39<br />
</td>
<td>13/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td style="text-align: right;">934.57<br />
</td>
<td>12/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>26/15<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td style="text-align: right;">1012.46<br />
</td>
<td>9/5, 25/14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td style="text-align: right;">1090.34<br />
</td>
<td>15/8<br />
</td>
<td><br />
</td>
<td>13/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td style="text-align: right;">1168.22<br />
</td>
<td>63/32, 96/49, 55/28, 108/55, 125/64<br />
</td>
<td><br />
</td>
<td>39/20<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td style="text-align: right;">46.10<br />
</td>
<td>33/32, 36/35, 50/49<br />
</td>
<td>40/39<br />
</td>
<td>27/26<br />
</td>
<td>26/25<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td style="text-align: right;">123.98<br />
</td>
<td>15/14, 27/25<br />
</td>
<td>14/13<br />
</td>
<td><br />
</td>
<td>13/12<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td style="text-align: right;">201.86<br />
</td>
<td>9/8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td style="text-align: right;">279.74<br />
</td>
<td>33/28<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13/11<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td style="text-align: right;">357.62<br />
</td>
<td>27/22<br />
</td>
<td>16/13<br />
</td>
<td>39/32<br />
</td>
<td>26/21<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td style="text-align: right;">435.51<br />
</td>
<td>9/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13/10<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td style="text-align: right;">513.39<br />
</td>
<td>27/20<br />
</td>
<td>35/26<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td style="text-align: right;">591.27<br />
</td>
<td>45/32<br />
</td>
<td><br />
</td>
<td>39/28<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td style="text-align: right;">669.15<br />
</td>
<td>72/49<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>52/35<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td style="text-align: right;">747.03<br />
</td>
<td>54/35<br />
</td>
<td>20/13<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td style="text-align: right;">824.91<br />
</td>
<td>45/28<br />
</td>
<td>21/13<br />
</td>
<td><br />
</td>
<td>13/8<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td style="text-align: right;">902.79<br />
</td>
<td>27/16<br />
</td>
<td>22/13<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td style="text-align: right;">980.67<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td style="text-align: right;">1058.56<br />
</td>
<td>90/49<br />
</td>
<td>24/13<br />
</td>
<td><br />
</td>
<td>13/7<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td style="text-align: right;">1136.44<br />
</td>
<td>27/14<br />
</td>
<td>25/13<br />
</td>
<td><br />
</td>
<td>39/20<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td style="text-align: right;">14.32<br />
</td>
<td>81/80, 99/98<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
*in 11-limit POTE tuning<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Spectrum of Valentine Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:2 -->Spectrum of Valentine Tunings by Eigenmonzos</h1>
<table class="wiki_table">
<tr>
<th>Eigenmonzo<br />
</th>
<th>Minor Semitone<br />
</th>
</tr>
<tr>
<td>12/11<br />
</td>
<td>75.319<br />
</td>
</tr>
<tr>
<td>8/7<br />
</td>
<td>77.058<br />
</td>
</tr>
<tr>
<td>7/5<br />
</td>
<td>77.186<br />
</td>
</tr>
<tr>
<td>5/4<br />
</td>
<td>77.263<br />
</td>
</tr>
<tr>
<td>11/9<br />
</td>
<td>77.508<br />
</td>
</tr>
<tr>
<td>7/6<br />
</td>
<td>77.761 (7 limit minimax)<br />
</td>
</tr>
<tr>
<td>9/7<br />
</td>
<td>77.861 (9 limit minimax)<br />
</td>
</tr>
<tr>
<td>4/3<br />
</td>
<td>77.995 (5 limit minimax, Carlos Alpha tuning)<br />
</td>
</tr>
<tr>
<td>14/11<br />
</td>
<td>78.249 (11 limit minimax)<br />
</td>
</tr>
<tr>
<td>10/9<br />
</td>
<td>78.277<br />
</td>
</tr>
<tr>
<td>11/8<br />
</td>
<td>78.760<br />
</td>
</tr>
<tr>
<td>6/5<br />
</td>
<td>78.910<br />
</td>
</tr>
<tr>
<td>11/10<br />
</td>
<td>82.502<br />
</td>
</tr>
</table>
</body></html>