39edt
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2011-11-19 20:03:21 UTC.
- The original revision id was 277286414.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
The 39 equal division of 3, the tritave, divides it into 39 equal parts of 48.678 cents each, a [[nonoctave]] tuning corresponding to 24.606 edo. It is a strong no-twos 13-limit system, a fact first noted by [[Paul Erlich]], and like [[26edt]] and [[52edt]] it is a multiple of [[13edt]] and so contains the [[Bohlen-Pierce]] scale. It is contorted in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&172f temperament tempering out 245/243, 275/273, 847/845 and 1575/1573, which has map [<1 0 0 0 0 0|, <0 39 57 69 85 91|]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth [[The Riemann Zeta Function and Tuning#Removing%20primes|no-twos zeta peak edt]]. ==Intervals of 39EDT== ||~ Degrees of 39EDT ||~ Cents Value ||~ ¢ Octave-Reduced ||~ Degrees of [[BP]] ||~ Comments || || 0 || 0.000 || || 0 || 1/1 || || 1 || 48.768 || || || 39th root of 3 || || 2 || 97.536 || || || || || 3 || 146.304 || || 1 || 13th root of 3 || || 4 || 195.072 || || || || || 5 || 243.840 || || || || || 6 || 292.608 || || 2 || || || 7 || 341.377 || || || || || 8 || 390.145 || || || || || 9 || 438.913 || || 3 || || || 10 || 487.681 || || || || || 11 || 536.449 || || || || || 12 || 585.217 || || 4 || || || 13 || 633.985 || || || cube root of 3 || || 14 || 682.753 || || || || || 15 || 731.521 || || 5 || || || 16 || 780.289 || || || || || 17 || 829.057 || || || || || 18 || 877.825 || || 6 || || || 19 || 926.593 || || || || || 20 || 975.362 || || || || || 21 || 1024.130 || || 7 || || || 22 || 1072.898 || || || || || 23 || 1121.666 || || || || || 24 || 1170.434 || || 8 || || || 25 || 1219.202 || 19.202 || || || || 26 || 1267.970 || 67.970 || || || || 27 || 1316.738 || 116.738 || 9 || || || 28 || 1365.506 || 165.506 || || || || 29 || 1414.274 || 214.274 || || || || 30 || 1463.042 || 263.042 || 10 || || || 31 || 1511.810 || 311.810 || || || || 32 || 1560.578 || 360.578 || || || || 33 || 1609.347 || 409.347 || 11 || || || 34 || 1658.115 || 458.115 || || || || 35 || 1706.883 || 506.883 || || || || 36 || 1755.651 || 555.651 || 12 || || || 37 || 1804.419 || 604.419 || || || || 38 || 1853.187 || 653.187 || || || || 39 || 1901.955 || 701.955 || 13 || 3/1 (tritave) || || 40 || 1950.723 || 750.723 || || || || 41 || 1999.491 || 799.491 || || || || 42 || 2048.259 || 848.259 || 14 || || || 43 || 2097.027 || 897.027 || || || || 44 || 2145.795 || 945.795 || || || || 45 || 2194.563 || 994.563 || 15 || || || 46 || 2243.332 || 1043.332 || || || || 47 || 2292.100 || 1092.100 || || || || 48 || 2340.868 || 1140.868 || 16 || || || 49 || 2389.636 || 1189.636 || || || || 50 || 2438.404 || 38.404 || || || || 51 || 2487.172 || 87.172 || 17 || || || 52 || 2535.940 || 135.940 || || || || 53 || 2584.708 || 184.708 || || || || 54 || 2633.476 || 233.476 || 18 || || || 55 || 2682.244 || 282.244 || || || || 56 || 2731.012 || 331.012 || || || || 57 || 2779.780 || 379.780 || 19 || || || 58 || 2828.548 || 428.548 || || || || 59 || 2877.317 || 477.317 || || || || 60 || 2926.085 || 526.085 || 20 || || || 61 || 2974.853 || 574.853 || || || || 62 || 3023.621 || 623.621 || || || || 63 || 3072.389 || 672.389 || 21 || || || 64 || 3121.157 || 721.157 || || || || 65 || 3169.925 || 769.925 || || || || 66 || 3218.693 || 818.693 || 22 || || || 67 || 3267.461 || 867.461 || || || || 68 || 3316.229 || 916.229 || || || || 69 || 3364.997 || 964.997 || 23 || || || 70 || 3413.765 || 1013.765 || || || || 71 || 3462.533 || 1062.533 || || || || 72 || 3511.302 || 1111.302 || 24 || || || 73 || 3560.070 || 1160.070 || || || || 74 || 3608.838 || 8.838 || || || || 75 || 3657.606 || 57.606 || 25 || || || 76 || 3706.374 || 106.374 || || || || 77 || 3755.142 || 155.142 || || || || 78 || 3803.910 || 203.910 || 26 || 9/1 ||
Original HTML content:
<html><head><title>39edt</title></head><body>The 39 equal division of 3, the tritave, divides it into 39 equal parts of 48.678 cents each, a <a class="wiki_link" href="/nonoctave">nonoctave</a> tuning corresponding to 24.606 edo. It is a strong no-twos 13-limit system, a fact first noted by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>, and like <a class="wiki_link" href="/26edt">26edt</a> and <a class="wiki_link" href="/52edt">52edt</a> it is a multiple of <a class="wiki_link" href="/13edt">13edt</a> and so contains the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale. It is contorted in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&172f temperament tempering out 245/243, 275/273, 847/845 and 1575/1573, which has map [<1 0 0 0 0 0|, <0 39 57 69 85 91|]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes">no-twos zeta peak edt</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Intervals of 39EDT"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals of 39EDT</h2>
<br />
<table class="wiki_table">
<tr>
<th>Degrees of 39EDT<br />
</th>
<th>Cents Value<br />
</th>
<th>¢ Octave-Reduced<br />
</th>
<th>Degrees of <a class="wiki_link" href="/BP">BP</a><br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>0<br />
</td>
<td>0.000<br />
</td>
<td><br />
</td>
<td>0<br />
</td>
<td>1/1<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>48.768<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>39th root of 3<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>97.536<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>146.304<br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>13th root of 3<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>195.072<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>243.840<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>292.608<br />
</td>
<td><br />
</td>
<td>2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>341.377<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>390.145<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>438.913<br />
</td>
<td><br />
</td>
<td>3<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>487.681<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>536.449<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>585.217<br />
</td>
<td><br />
</td>
<td>4<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>633.985<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>cube root of 3<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>682.753<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>731.521<br />
</td>
<td><br />
</td>
<td>5<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>780.289<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>829.057<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>877.825<br />
</td>
<td><br />
</td>
<td>6<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>926.593<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>975.362<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>1024.130<br />
</td>
<td><br />
</td>
<td>7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>1072.898<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>1121.666<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1170.434<br />
</td>
<td><br />
</td>
<td>8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1219.202<br />
</td>
<td>19.202<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1267.970<br />
</td>
<td>67.970<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1316.738<br />
</td>
<td>116.738<br />
</td>
<td>9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>1365.506<br />
</td>
<td>165.506<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>1414.274<br />
</td>
<td>214.274<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>1463.042<br />
</td>
<td>263.042<br />
</td>
<td>10<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>1511.810<br />
</td>
<td>311.810<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>1560.578<br />
</td>
<td>360.578<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>1609.347<br />
</td>
<td>409.347<br />
</td>
<td>11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>1658.115<br />
</td>
<td>458.115<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>1706.883<br />
</td>
<td>506.883<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>1755.651<br />
</td>
<td>555.651<br />
</td>
<td>12<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>1804.419<br />
</td>
<td>604.419<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>1853.187<br />
</td>
<td>653.187<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>1901.955<br />
</td>
<td>701.955<br />
</td>
<td>13<br />
</td>
<td>3/1 (tritave)<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>1950.723<br />
</td>
<td>750.723<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>1999.491<br />
</td>
<td>799.491<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>2048.259<br />
</td>
<td>848.259<br />
</td>
<td>14<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>2097.027<br />
</td>
<td>897.027<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>2145.795<br />
</td>
<td>945.795<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>2194.563<br />
</td>
<td>994.563<br />
</td>
<td>15<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>2243.332<br />
</td>
<td>1043.332<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>2292.100<br />
</td>
<td>1092.100<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>2340.868<br />
</td>
<td>1140.868<br />
</td>
<td>16<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>2389.636<br />
</td>
<td>1189.636<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>2438.404<br />
</td>
<td>38.404<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>2487.172<br />
</td>
<td>87.172<br />
</td>
<td>17<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>2535.940<br />
</td>
<td>135.940<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>2584.708<br />
</td>
<td>184.708<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>2633.476<br />
</td>
<td>233.476<br />
</td>
<td>18<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>2682.244<br />
</td>
<td>282.244<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>2731.012<br />
</td>
<td>331.012<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>2779.780<br />
</td>
<td>379.780<br />
</td>
<td>19<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>2828.548<br />
</td>
<td>428.548<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>2877.317<br />
</td>
<td>477.317<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>2926.085<br />
</td>
<td>526.085<br />
</td>
<td>20<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>61<br />
</td>
<td>2974.853<br />
</td>
<td>574.853<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>62<br />
</td>
<td>3023.621<br />
</td>
<td>623.621<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>63<br />
</td>
<td>3072.389<br />
</td>
<td>672.389<br />
</td>
<td>21<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>64<br />
</td>
<td>3121.157<br />
</td>
<td>721.157<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>65<br />
</td>
<td>3169.925<br />
</td>
<td>769.925<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>66<br />
</td>
<td>3218.693<br />
</td>
<td>818.693<br />
</td>
<td>22<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>67<br />
</td>
<td>3267.461<br />
</td>
<td>867.461<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>68<br />
</td>
<td>3316.229<br />
</td>
<td>916.229<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>69<br />
</td>
<td>3364.997<br />
</td>
<td>964.997<br />
</td>
<td>23<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>70<br />
</td>
<td>3413.765<br />
</td>
<td>1013.765<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>71<br />
</td>
<td>3462.533<br />
</td>
<td>1062.533<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>72<br />
</td>
<td>3511.302<br />
</td>
<td>1111.302<br />
</td>
<td>24<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>73<br />
</td>
<td>3560.070<br />
</td>
<td>1160.070<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>74<br />
</td>
<td>3608.838<br />
</td>
<td>8.838<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>75<br />
</td>
<td>3657.606<br />
</td>
<td>57.606<br />
</td>
<td>25<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>76<br />
</td>
<td>3706.374<br />
</td>
<td>106.374<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>77<br />
</td>
<td>3755.142<br />
</td>
<td>155.142<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>78<br />
</td>
<td>3803.910<br />
</td>
<td>203.910<br />
</td>
<td>26<br />
</td>
<td>9/1<br />
</td>
</tr>
</table>
</body></html>