39edo
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Original Wikitext content:
=<span style="color: #007a22; font-size: 118%;">39 tone equal temperament</span>= If we take 22/39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, Hornbostel Temperament (23EDO) and allied systems. However, its 23/39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat--in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some ways allied to 12EDO in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find 39et tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|. **39-EDO Intervals:** || **NOMENCLATURE** || || **|** = Semisharp **t** = Semiflat || || **DEGREE** || **NOTE** || **CENTS** || **[[Nearest just interval|Nearest JI]]** || **Cents** || **Error** || || **0** || **1** || **0** || **1/1** || **0** || **None** || || 1 || 1| || 30.7692 || 58/57 || 30.1092 || +0.66 || || 2 || 1# || 61.5385 || 28/27 || 62.9609 || - 1.4224 || || 3 || 2b || 92.3077 || 58/55 || 91.9455 || +0.3622 || || 4 || 2t || 123.0769 || 29/27 || 123.7122 || -0.6353 || || 5 || 2 || 153.8462 || 82/75 || 154.48 || -0.6338 || || 6 || 2| || 184.6154 || 10/9 || 182.4037 || +2.2117 || || **7·** || **2#** || **215.3846** || **17/15** || **216.6867** || **-1.3021** || || 8 || 3b || 246.1538 || 15/13 || 247.7411 || -1.5873 || || 9 || 3t || 276.9231 || 27/23 || 277.5907 || -0.6676 || || 10 || 3 || 307.6923 || 49/41 || 308.5894 || -0.8971 || || 11 || 3| || 338.4615 || 62/51 || 338.1252 || +0.3363 || || **12·** || **3#** || **369.2308** || **26/21** || **369.7468** || **-0.516** || || 13 || 4b || 400 || 34/27 || 399.0904 || +0.9096 || || 14 || 4t || 430.7692 || 41/32 || 429.0624 || +1.7068 || || 15 || 4 || 461.5385 || 43/33 || 458.2448 || +3.2937 || || 16 || 4| (5t) || 492.3077 || 85/64 || 491.2691 || +1.0386 || || **17·** || **5** || **523.0769** || **23/17** || **523.3189** || **-0.242** || || 18 || 5| || 553.8462 || 11/8 || 551.3179 || +2.5283 || || 19 || 5# || 584.6154 || 7/5 || 582.5122 || +2.1032 || || 20 || 6b || 615.3846 || 10/7 || 617.4878 || -2.1032 || || 21 || 6t || 646.1538 || 16/11 || 648.6821 || -2.5283 || || **22·** || **6** || **676.9231** || **34/23** || **676.6811** || **+0.242** || || 23 || 6| || 707.6923 || 128/85 || 708.7309 || -1.0386 || || 24 || 6# || 738.4615 || 66/43 || 741.7552 || -3.2937 || || 25 || 7b || 769.2308 || 64/41 || 770.9376 || -1.7068 || || 26 || 7t || 800 || 27/17 || 800.9096 || -0.9096 || || **27·** || **7** || **830.7692** || **21/13** || **830.2532** || **+0.516** || || 28 || 7| || 861.5385 || 51/31 || 861.8748 || -0.3363 || || 29 || 7# (A) || 892.3077 || 82/49 || 891.4106 || +0.8971 || || 30 || 8b || 923.0769 || 46/27 || 922.4093 || +0.6676 || || 31 || 8t || 953.8462 || 26/15 || 952.2589 || +1.5873 || || **32·** || **8** || **984.6154** || **30/17** || **983.3133** || **+1.3021** || || 33 || 8| || 1015.3846 || 9/5 || 1017.5963 || -2.2117 || || 34 || 8# || 1046.1538 || 75/41 || 1045.52 || +0.6338 || || 35 || 9b || 1076.9231 || 54/29 || 1076.2878 || +0.6353 || || 36 || 9t || 1107.6923 || 55/29 || 1108.0545 || -0.3622 || || 37 || 9 || 1138.4615 || 27/14 || 1137.0391 || +1.4224 || || 38 || 9| (1t) || 1169.2308 || 57/29 || 1169.8908 || -0.66 || || **39··(or 0)** || **1** || **1200** || **2/1** || **1200** || **None** || **39 tone equal modes:** 15 15 9 14 14 11 13 13 13 11 11 11 6 10 10 10 9 9 9 9 9 3 8 8 8 8 7 7 7 7 7 7 4 5 5 7 5 5 5 7 5 5 5 7 5 5 7 5 5 5 7 5 7 5 5 5 5 5 5 5 5 4 **5 5 5 2 5 5 5 5 2** 5 5 2 5 5 5 5 2 5 5 5 3 5 5 3 5 5 3 5 4 4 5 4 4 5 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 **3 3 3 2 3 3 3 3 2 3 3 3 3 2** 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1
Original HTML content:
<html><head><title>39edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x39 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #007a22; font-size: 118%;">39 tone equal temperament</span></h1>
<br />
If we take 22/39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group interested in 16EDO, Hornbostel Temperament (23EDO) and allied systems. However, its 23/39 fifth, five and three-quarters cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat--in this case, 25 cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO in some ways allied to 12EDO in supporting augene temperament, and is in fact an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find 39et tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|.<br />
<br />
<br />
<br />
<strong>39-EDO Intervals:</strong><br />
<table class="wiki_table">
<tr>
<td><strong>NOMENCLATURE</strong><br />
</td>
</tr>
<tr>
<td><strong>|</strong> = Semisharp<br />
<strong>t</strong> = Semiflat<br />
</td>
</tr>
</table>
<br />
<table class="wiki_table">
<tr>
<td><strong>DEGREE</strong><br />
</td>
<td><strong>NOTE</strong><br />
</td>
<td><strong>CENTS</strong><br />
</td>
<td><strong><a class="wiki_link" href="/Nearest%20just%20interval">Nearest JI</a></strong><br />
</td>
<td><strong>Cents</strong><br />
</td>
<td><strong>Error</strong><br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td><strong>1</strong><br />
</td>
<td>0<br />
</td>
<td><strong>1/1</strong><br />
</td>
<td>0<br />
</td>
<td><strong>None</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>1|<br />
</td>
<td>30.7692<br />
</td>
<td>58/57<br />
</td>
<td>30.1092<br />
</td>
<td>+0.66<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>1#<br />
</td>
<td>61.5385<br />
</td>
<td>28/27<br />
</td>
<td>62.9609<br />
</td>
<td>- 1.4224<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>2b<br />
</td>
<td>92.3077<br />
</td>
<td>58/55<br />
</td>
<td>91.9455<br />
</td>
<td>+0.3622<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>2t<br />
</td>
<td>123.0769<br />
</td>
<td>29/27<br />
</td>
<td>123.7122<br />
</td>
<td>-0.6353<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>2<br />
</td>
<td>153.8462<br />
</td>
<td>82/75<br />
</td>
<td>154.48<br />
</td>
<td>-0.6338<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>2|<br />
</td>
<td>184.6154<br />
</td>
<td>10/9<br />
</td>
<td>182.4037<br />
</td>
<td>+2.2117<br />
</td>
</tr>
<tr>
<td><strong>7·</strong><br />
</td>
<td><strong>2#</strong><br />
</td>
<td><strong>215.3846</strong><br />
</td>
<td><strong>17/15</strong><br />
</td>
<td><strong>216.6867</strong><br />
</td>
<td><strong>-1.3021</strong><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>3b<br />
</td>
<td>246.1538<br />
</td>
<td>15/13<br />
</td>
<td>247.7411<br />
</td>
<td>-1.5873<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>3t<br />
</td>
<td>276.9231<br />
</td>
<td>27/23<br />
</td>
<td>277.5907<br />
</td>
<td>-0.6676<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>3<br />
</td>
<td>307.6923<br />
</td>
<td>49/41<br />
</td>
<td>308.5894<br />
</td>
<td>-0.8971<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>3|<br />
</td>
<td>338.4615<br />
</td>
<td>62/51<br />
</td>
<td>338.1252<br />
</td>
<td>+0.3363<br />
</td>
</tr>
<tr>
<td><strong>12·</strong><br />
</td>
<td><strong>3#</strong><br />
</td>
<td><strong>369.2308</strong><br />
</td>
<td><strong>26/21</strong><br />
</td>
<td><strong>369.7468</strong><br />
</td>
<td><strong>-0.516</strong><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>4b<br />
</td>
<td>400<br />
</td>
<td>34/27<br />
</td>
<td>399.0904<br />
</td>
<td>+0.9096<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>4t<br />
</td>
<td>430.7692<br />
</td>
<td>41/32<br />
</td>
<td>429.0624<br />
</td>
<td>+1.7068<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>4<br />
</td>
<td>461.5385<br />
</td>
<td>43/33<br />
</td>
<td>458.2448<br />
</td>
<td>+3.2937<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>4| (5t)<br />
</td>
<td>492.3077<br />
</td>
<td>85/64<br />
</td>
<td>491.2691<br />
</td>
<td>+1.0386<br />
</td>
</tr>
<tr>
<td><strong>17·</strong><br />
</td>
<td><strong>5</strong><br />
</td>
<td><strong>523.0769</strong><br />
</td>
<td><strong>23/17</strong><br />
</td>
<td><strong>523.3189</strong><br />
</td>
<td><strong>-0.242</strong><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>5|<br />
</td>
<td>553.8462<br />
</td>
<td>11/8<br />
</td>
<td>551.3179<br />
</td>
<td>+2.5283<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>5#<br />
</td>
<td>584.6154<br />
</td>
<td>7/5<br />
</td>
<td>582.5122<br />
</td>
<td>+2.1032<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>6b<br />
</td>
<td>615.3846<br />
</td>
<td>10/7<br />
</td>
<td>617.4878<br />
</td>
<td>-2.1032<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>6t<br />
</td>
<td>646.1538<br />
</td>
<td>16/11<br />
</td>
<td>648.6821<br />
</td>
<td>-2.5283<br />
</td>
</tr>
<tr>
<td><strong>22·</strong><br />
</td>
<td><strong>6</strong><br />
</td>
<td><strong>676.9231</strong><br />
</td>
<td><strong>34/23</strong><br />
</td>
<td><strong>676.6811</strong><br />
</td>
<td><strong>+0.242</strong><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>6|<br />
</td>
<td>707.6923<br />
</td>
<td>128/85<br />
</td>
<td>708.7309<br />
</td>
<td>-1.0386<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>6#<br />
</td>
<td>738.4615<br />
</td>
<td>66/43<br />
</td>
<td>741.7552<br />
</td>
<td>-3.2937<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>7b<br />
</td>
<td>769.2308<br />
</td>
<td>64/41<br />
</td>
<td>770.9376<br />
</td>
<td>-1.7068<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>7t<br />
</td>
<td>800<br />
</td>
<td>27/17<br />
</td>
<td>800.9096<br />
</td>
<td>-0.9096<br />
</td>
</tr>
<tr>
<td><strong>27·</strong><br />
</td>
<td><strong>7</strong><br />
</td>
<td><strong>830.7692</strong><br />
</td>
<td><strong>21/13</strong><br />
</td>
<td><strong>830.2532</strong><br />
</td>
<td><strong>+0.516</strong><br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>7|<br />
</td>
<td>861.5385<br />
</td>
<td>51/31<br />
</td>
<td>861.8748<br />
</td>
<td>-0.3363<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>7# (A)<br />
</td>
<td>892.3077<br />
</td>
<td>82/49<br />
</td>
<td>891.4106<br />
</td>
<td>+0.8971<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>8b<br />
</td>
<td>923.0769<br />
</td>
<td>46/27<br />
</td>
<td>922.4093<br />
</td>
<td>+0.6676<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>8t<br />
</td>
<td>953.8462<br />
</td>
<td>26/15<br />
</td>
<td>952.2589<br />
</td>
<td>+1.5873<br />
</td>
</tr>
<tr>
<td><strong>32·</strong><br />
</td>
<td><strong>8</strong><br />
</td>
<td><strong>984.6154</strong><br />
</td>
<td><strong>30/17</strong><br />
</td>
<td><strong>983.3133</strong><br />
</td>
<td><strong>+1.3021</strong><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>8|<br />
</td>
<td>1015.3846<br />
</td>
<td>9/5<br />
</td>
<td>1017.5963<br />
</td>
<td>-2.2117<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>8#<br />
</td>
<td>1046.1538<br />
</td>
<td>75/41<br />
</td>
<td>1045.52<br />
</td>
<td>+0.6338<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>9b<br />
</td>
<td>1076.9231<br />
</td>
<td>54/29<br />
</td>
<td>1076.2878<br />
</td>
<td>+0.6353<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>9t<br />
</td>
<td>1107.6923<br />
</td>
<td>55/29<br />
</td>
<td>1108.0545<br />
</td>
<td>-0.3622<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>9<br />
</td>
<td>1138.4615<br />
</td>
<td>27/14<br />
</td>
<td>1137.0391<br />
</td>
<td>+1.4224<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>9| (1t)<br />
</td>
<td>1169.2308<br />
</td>
<td>57/29<br />
</td>
<td>1169.8908<br />
</td>
<td>-0.66<br />
</td>
</tr>
<tr>
<td><strong>39··(or 0)</strong><br />
</td>
<td><strong>1</strong><br />
</td>
<td><strong>1200</strong><br />
</td>
<td><strong>2/1</strong><br />
</td>
<td><strong>1200</strong><br />
</td>
<td><strong>None</strong><br />
</td>
</tr>
</table>
<br />
<br />
<strong>39 tone equal modes:</strong><br />
<br />
15 15 9<br />
14 14 11<br />
13 13 13<br />
11 11 11 6<br />
10 10 10 9<br />
9 9 9 9 3<br />
8 8 8 8 7<br />
7 7 7 7 7 4<br />
5 5 7 5 5 5 7<br />
5 5 5 7 5 5 7<br />
5 5 5 7 5 7 5<br />
5 5 5 5 5 5 5 4<br />
<strong>5 5 5 2 5 5 5 5 2</strong><br />
5 5 2 5 5 5 5 2 5<br />
5 5 3 5 5 3 5 5 3<br />
5 4 4 5 4 4 5 4 4<br />
4 4 4 4 4 4 4 4 4 3<br />
3 3 3 3 3 3 3 3 3 3 3 3 3<br />
<strong>3 3 3 2 3 3 3 3 2 3 3 3 3 2</strong><br />
2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2<br />
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1<br />
2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1</body></html>