26edt
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The 26 equal division of 3 (the tritave), divides it into 26 equal parts of 73.152 cents each, corresponding to 16.404 edo. It is contorted in the 7-limit, tempering out the same commas, 245/243 and 3125/3087, as [[13edt]]. In the 11-limit it tempers out 125/121 and 3087/3025, in the 13-limit 175/169, 147/143, and 847/845, and in the 17-limit 119/117. It is the seventh [[The Riemann Zeta Function and Tuning#Removing%20prime|zeta peak tritave division]]. A reason to double 13edt to 26edt is to approximate the 8th, 13th, 17th, 20th, and 22nd harmonics particularly well. Moreover, it has an exaggerated diatonic scale with 11:16:21 supermajor triads, though only the 16:11 is particularly just due to its best 16 still being 28.04 cents sharp, or just about as bad as the 25 of 12edo (which is 27.373 cents sharp, an essentially just 100:63). ==Intervals== ||~ Steps ||~ Cents ||~ BP nonatonic degree ||~ Diatonic degree ||~ Corresponding JI intervals ||~ Comments ||~ Generator for... || || 1 || 73.15 || Sa1/sd2 || A1/dd2 || 25/24 || || || || 2 || 146.3 || A1/m2 || AA1/sm2 || 27/25~49/45 || || || || 3 || 219.5 || N2 || m2 || 9/8~312/275 || || || || 4 || 292.6 || M2/d3 || M2 || 25/21~13/11 || || || || 5 || 365.8 || Sa2/sd3 || SM2/dd3 || 5/4~243/196 || False 11/9 || || || 6 || 438.9 || A2/P3/d4 || AA2/sm3 || 9/7 || || || || 7 || 512.1 || Sa3/sd4 || m3 || 27/20 || False 21/16 || || || 8 || 585.2 || A3/m4/d5 || M3 || 7/5 || || || || 9 || 658.4 || N4/sd5 || SM3/dd4 || 16/11 || False 13/9 || || || 10 || 731.5 || M4/m5 || AA3/d4 || 75/49 || False 3/2 || || || 11 || 804.7 || Sa4/N5 || P4 || 8/5 || False 11/7 || || || 12 || 877.8 || A4/M5/d6 || A4 || 5/3 || False 27/16 || || || 13 || 951.0 || Sa5/sd6 || AA4/dd5 || 125/72 || || || || 14 || 1024.1 || A5/m6/d7 || d5 || 9/5 || False 16/9 || || || 15 || 1097.3 || N6/sd7 || P5 || 15/8 || False 21/11 || || || 16 || 1170.4 || M6/m7 || A5/dd6 || 49/25 || False 2/1 || || || 17 || 1243.6 || Sa6/N7 || AA5/sm6 || 33/16 || False 27/13 || || || 18 || 1316.7 || A6/M7/d8 || m6 || 15/7 || || || || 19 || 1389.9 || Sa7/sd8 || M6 || 20/9 || False 16/7 || || || 20 || 1463.0 || A7/P8/d9 || SM6/dd7 || 7/3 || || || || 21 || 1536.2 || Sa8/sd9 || AA6/sm7 || 12/5~196/81 || False 27/11 || || || 22 || 1609.3 || A8/m9 || m7 || 63/25 || || || || 23 || 1682.5 || N9 || M7 || 8/3~275/104 || || || || 24 || 1755.65 || M9/d10 || SM7/dd8 || 25/9~135/49 || || || || 25 || 1828.8 || Sa9/sd10 || A7/d8 || 72/25 || || || || 26 || 1902.0 || A9/P10 || P8 || 3/1 || Tritave || || It is a weird coincidence how 26edt intones any [[26edo]] intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning: ||~ 26edt ||~ 26edo ||~ Discrepancy || || 365.761 || 369.231 || -3.47 || || 512.065 || 507.692 || +4.373 || || 877.825 || 876.923 || +0.902 || || 1243.586 || 1246.154 || -2.168 || || 1389.89 || 1384.615 || +5.275 || || 1755.651 || 1753.846 || +1.805 || || 2121.411 || 2123.077 || -1.666 || || 2633.476 || 2630.769 || +2.647 || …and so on [[https://www.youtube.com/watch?v=AhWJ2yJsODs|The Eel And Loach To Attack In Lasciviousness Are Insane]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20The%20Eel%20And%20Loach%20To%20Attack%20In%20Lasciviousness%20Are%20Insane.mp3|play]] by Omega9
Original HTML content:
<html><head><title>26edt</title></head><body>The 26 equal division of 3 (the tritave), divides it into 26 equal parts of 73.152 cents each, corresponding to 16.404 edo. It is contorted in the 7-limit, tempering out the same commas, 245/243 and 3125/3087, as <a class="wiki_link" href="/13edt">13edt</a>. In the 11-limit it tempers out 125/121 and 3087/3025, in the 13-limit 175/169, 147/143, and 847/845, and in the 17-limit 119/117. It is the seventh <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20prime">zeta peak tritave division</a>. A reason to double 13edt to 26edt is to approximate the 8th, 13th, 17th, 20th, and 22nd harmonics particularly well. Moreover, it has an exaggerated diatonic scale with 11:16:21 supermajor triads, though only the 16:11 is particularly just due to its best 16 still being 28.04 cents sharp, or just about as bad as the 25 of 12edo (which is 27.373 cents sharp, an essentially just 100:63).<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h2>
<table class="wiki_table">
<tr>
<th>Steps<br />
</th>
<th>Cents<br />
</th>
<th>BP nonatonic degree<br />
</th>
<th>Diatonic degree<br />
</th>
<th>Corresponding JI intervals<br />
</th>
<th>Comments<br />
</th>
<th>Generator for...<br />
</th>
</tr>
<tr>
<td>1<br />
</td>
<td>73.15<br />
</td>
<td>Sa1/sd2<br />
</td>
<td>A1/dd2<br />
</td>
<td>25/24<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>146.3<br />
</td>
<td>A1/m2<br />
</td>
<td>AA1/sm2<br />
</td>
<td>27/25~49/45<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>219.5<br />
</td>
<td>N2<br />
</td>
<td>m2<br />
</td>
<td>9/8~312/275<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>292.6<br />
</td>
<td>M2/d3<br />
</td>
<td>M2<br />
</td>
<td>25/21~13/11<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>365.8<br />
</td>
<td>Sa2/sd3<br />
</td>
<td>SM2/dd3<br />
</td>
<td>5/4~243/196<br />
</td>
<td>False 11/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>438.9<br />
</td>
<td>A2/P3/d4<br />
</td>
<td>AA2/sm3<br />
</td>
<td>9/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>512.1<br />
</td>
<td>Sa3/sd4<br />
</td>
<td>m3<br />
</td>
<td>27/20<br />
</td>
<td>False 21/16<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>585.2<br />
</td>
<td>A3/m4/d5<br />
</td>
<td>M3<br />
</td>
<td>7/5<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>658.4<br />
</td>
<td>N4/sd5<br />
</td>
<td>SM3/dd4<br />
</td>
<td>16/11<br />
</td>
<td>False 13/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>731.5<br />
</td>
<td>M4/m5<br />
</td>
<td>AA3/d4<br />
</td>
<td>75/49<br />
</td>
<td>False 3/2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>804.7<br />
</td>
<td>Sa4/N5<br />
</td>
<td>P4<br />
</td>
<td>8/5<br />
</td>
<td>False 11/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>877.8<br />
</td>
<td>A4/M5/d6<br />
</td>
<td>A4<br />
</td>
<td>5/3<br />
</td>
<td>False 27/16<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>951.0<br />
</td>
<td>Sa5/sd6<br />
</td>
<td>AA4/dd5<br />
</td>
<td>125/72<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>1024.1<br />
</td>
<td>A5/m6/d7<br />
</td>
<td>d5<br />
</td>
<td>9/5<br />
</td>
<td>False 16/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>1097.3<br />
</td>
<td>N6/sd7<br />
</td>
<td>P5<br />
</td>
<td>15/8<br />
</td>
<td>False 21/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>1170.4<br />
</td>
<td>M6/m7<br />
</td>
<td>A5/dd6<br />
</td>
<td>49/25<br />
</td>
<td>False 2/1<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>1243.6<br />
</td>
<td>Sa6/N7<br />
</td>
<td>AA5/sm6<br />
</td>
<td>33/16<br />
</td>
<td>False 27/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>1316.7<br />
</td>
<td>A6/M7/d8<br />
</td>
<td>m6<br />
</td>
<td>15/7<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>1389.9<br />
</td>
<td>Sa7/sd8<br />
</td>
<td>M6<br />
</td>
<td>20/9<br />
</td>
<td>False 16/7<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>1463.0<br />
</td>
<td>A7/P8/d9<br />
</td>
<td>SM6/dd7<br />
</td>
<td>7/3<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>1536.2<br />
</td>
<td>Sa8/sd9<br />
</td>
<td>AA6/sm7<br />
</td>
<td>12/5~196/81<br />
</td>
<td>False 27/11<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>1609.3<br />
</td>
<td>A8/m9<br />
</td>
<td>m7<br />
</td>
<td>63/25<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>1682.5<br />
</td>
<td>N9<br />
</td>
<td>M7<br />
</td>
<td>8/3~275/104<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>1755.65<br />
</td>
<td>M9/d10<br />
</td>
<td>SM7/dd8<br />
</td>
<td>25/9~135/49<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1828.8<br />
</td>
<td>Sa9/sd10<br />
</td>
<td>A7/d8<br />
</td>
<td>72/25<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1902.0<br />
</td>
<td>A9/P10<br />
</td>
<td>P8<br />
</td>
<td>3/1<br />
</td>
<td>Tritave<br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
It is a weird coincidence how 26edt intones any <a class="wiki_link" href="/26edo">26edo</a> intervals within plus or minus 6.5 cents when it is supposed to have nothing to do with this other tuning:<br />
<br />
<table class="wiki_table">
<tr>
<th>26edt<br />
</th>
<th>26edo<br />
</th>
<th>Discrepancy<br />
</th>
</tr>
<tr>
<td>365.761<br />
</td>
<td>369.231<br />
</td>
<td>-3.47<br />
</td>
</tr>
<tr>
<td>512.065<br />
</td>
<td>507.692<br />
</td>
<td>+4.373<br />
</td>
</tr>
<tr>
<td>877.825<br />
</td>
<td>876.923<br />
</td>
<td>+0.902<br />
</td>
</tr>
<tr>
<td>1243.586<br />
</td>
<td>1246.154<br />
</td>
<td>-2.168<br />
</td>
</tr>
<tr>
<td>1389.89<br />
</td>
<td>1384.615<br />
</td>
<td>+5.275<br />
</td>
</tr>
<tr>
<td>1755.651<br />
</td>
<td>1753.846<br />
</td>
<td>+1.805<br />
</td>
</tr>
<tr>
<td>2121.411<br />
</td>
<td>2123.077<br />
</td>
<td>-1.666<br />
</td>
</tr>
<tr>
<td>2633.476<br />
</td>
<td>2630.769<br />
</td>
<td>+2.647<br />
</td>
</tr>
</table>
…and so on<br />
<br />
<a class="wiki_link_ext" href="https://www.youtube.com/watch?v=AhWJ2yJsODs" rel="nofollow">The Eel And Loach To Attack In Lasciviousness Are Insane</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20The%20Eel%20And%20Loach%20To%20Attack%20In%20Lasciviousness%20Are%20Insane.mp3" rel="nofollow">play</a> by Omega9</body></html>