Middle Path table of seven-limit rank two temperaments
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This table is reproduced from Table 2 of [[Paul Erlich]]'s [[A Middle Path]], with small changes to update names and improve readability. This table "comprises all possible seven-limit 2-D cases where complexity/24 + damage/10 < 1." See also [[Catalog of five-limit rank two temperaments]], [[Catalog of eleven-limit rank two temperaments]]. || Vanishing Interval's Ratios || Temperament name || TOP period || TOP generator || Mapp. of 2 || Mapp. of 3 || Mapp. of 5 || Mapp. of 7 || Cmplx || TOP Dmg || || 28/27, 49/48, 64/63, 256/243, 343/324... || [[Blacksmith]] || 239.18 || 155.35 || 5,0 || 8,0 || 11,1 || 14,0 || 6.47 || 7.24 || || 36/35, 50/49, 126/125, 360/343, 648/625... || [[Diminished]] || || || || || || || 7.92 || 5.87 || || 36/35, 64/63, 81/80, 256/245, 729/700... || [[Dominant]] || || || || || || || 7.96 || 4.77 || || 36/35, 128/125, 225/224, 405/392, 729/686... || [[August]] || || || || || || || 8.30 || 5.87 || || 50/49, 64/63, 225/224, 2048/2025... || [[Pajara]] || || || || || || || 10.40 || 3.11 || || 49/48, 81/80, 245/243, 1323/1280... || [[Semaphore]] || || || || || || || 11.20 || 3.67 || || 81/80, 126/125, 225/224, 3136/3125... || [[Meantone]] || || || || || || || 11.77 || 1.70 || || 50/49, 81/80, 405/392, 4000/3969... || [[Injera]] || || || || || || || 11.92 || 3.58 || || 49/48, 225/224, 525/512, 686/675... || [[Negri]] || || || || || || || 12.12 || 3.19 || || 64/63, 126/125, 128/125, 4000/3969... || [[Augene]] || || || || || || || 12.13 || 2.94 || || 49/48, 126/125, 875/864, 1029/1000... || [[Keemun]] || || || || || || || 12.41 || 3.19 || || 81/80, 128/125, 648/625, 2048/2025... || [[Catler]] || || || || || || || 12.84 || 3.56 || || 50/49, 245/243, 250/243, 2430/2401... || [[Hedgehog]] || || || || || || || 13.19 || 3.11 || || 64/63, 245/243, 1728/1715, 2240/2187... || [[Superpyth]] || || || || || || || 14.43 || 2.40 || || 126/125, 245/243, 686/675, 4375/4374 || [[Sensi]] || || || || || || || 14.46 || 1.61 || || 50/49, 525/512, 1029/1024, 1875/1792... || [[Lemba]] || || || || || || || 14.63 || 3.74 || || 64/63, 250/243, 875/864, 6144/6125... || [[Porcupine]] || || || || || || || 14.80 || 3.09 || || 81/80, 525/512, 875/864, 4375/4374... || [[Flattone]] || || || || || || || 15.38 || 2.54 || || 225/224, 245/243, 875/864, 3125/3072... || [[Magic]] || || || || || || || 15.54 || 1.28 || || 50/49, 875/864, 1728/1715, 3125/3024... || [[Doublewide]] || || || || || || || 15.60 || 3.27 || || 49/48, 250/243, 4000/3969, 6125/5832... || [[Nautilus]] || || || || || || || 15.62 || 3.48 || || 64/63, 686/675, 2401/2400, 6272/6075... || [[Beatles]] || || || || || || || 16.88 || 2.90 || || 81/80, 686/675, 1029/1000, 10976/10935... || [[Liese]] || || || || || || || 17.49 || 2.62 || || 81/80, 1029/1024, 1728/1715, 8748/8575... || [[Cynder]] || || || || || || || 18.45 || 1.70 || || 225/224, 1728/1715, 2430/2401, 6144/6125... || [[Orwell]] || || || || || || || 19.98 || 0.95 || || 225/224, 3125/3087, 4000/3969, 5120/5103... || [[Garibaldi]] || || || || || || || 20.29 || 0.91 || || 126/125, 1728/1715, 2401/2400, 31104/30625... || [[Myna]] || || || || || || || 20.33 || 1.17 || || 225/224, 1029/1024, 2401/2400, 16875/16807... || [[Miracle]] || || || || || || || 21.10 || 0.63 || |||||||||||||||||||| A BONUS TEMPERAMENT: || || 2401/2400, 4375/4374, 250047/250000... || [[Ennealimmal]] || 133.337 || 84.313 || 9,0 || 13,2 || 19,3 || 24,2 || 39.83 || 0.04 ||
Original HTML content:
<html><head><title>Middle Path table of seven-limit rank two temperaments</title></head><body>This table is reproduced from Table 2 of <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a>'s <a class="wiki_link" href="/A%20Middle%20Path">A Middle Path</a>, with small changes to update names and improve readability.<br />
<br />
This table "comprises all possible seven-limit 2-D cases where complexity/24 + damage/10 < 1."<br />
<br />
See also <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">Catalog of five-limit rank two temperaments</a>, <a class="wiki_link" href="/Catalog%20of%20eleven-limit%20rank%20two%20temperaments">Catalog of eleven-limit rank two temperaments</a>.<br />
<br />
<table class="wiki_table">
<tr>
<td>Vanishing Interval's Ratios<br />
</td>
<td>Temperament<br />
name<br />
</td>
<td>TOP<br />
period<br />
</td>
<td>TOP<br />
generator<br />
</td>
<td>Mapp.<br />
of 2<br />
</td>
<td>Mapp.<br />
of 3<br />
</td>
<td>Mapp.<br />
of 5<br />
</td>
<td>Mapp.<br />
of 7<br />
</td>
<td>Cmplx<br />
</td>
<td>TOP<br />
Dmg<br />
</td>
</tr>
<tr>
<td>28/27, 49/48, 64/63, 256/243, 343/324...<br />
</td>
<td><a class="wiki_link" href="/Blacksmith">Blacksmith</a><br />
</td>
<td>239.18<br />
</td>
<td>155.35<br />
</td>
<td>5,0<br />
</td>
<td>8,0<br />
</td>
<td>11,1<br />
</td>
<td>14,0<br />
</td>
<td>6.47<br />
</td>
<td>7.24<br />
</td>
</tr>
<tr>
<td>36/35, 50/49, 126/125, 360/343, 648/625...<br />
</td>
<td><a class="wiki_link" href="/Diminished">Diminished</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7.92<br />
</td>
<td>5.87<br />
</td>
</tr>
<tr>
<td>36/35, 64/63, 81/80, 256/245, 729/700...<br />
</td>
<td><a class="wiki_link" href="/Dominant">Dominant</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7.96<br />
</td>
<td>4.77<br />
</td>
</tr>
<tr>
<td>36/35, 128/125, 225/224, 405/392, 729/686...<br />
</td>
<td><a class="wiki_link" href="/August">August</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>8.30<br />
</td>
<td>5.87<br />
</td>
</tr>
<tr>
<td>50/49, 64/63, 225/224, 2048/2025...<br />
</td>
<td><a class="wiki_link" href="/Pajara">Pajara</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>10.40<br />
</td>
<td>3.11<br />
</td>
</tr>
<tr>
<td>49/48, 81/80, 245/243, 1323/1280...<br />
</td>
<td><a class="wiki_link" href="/Semaphore">Semaphore</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11.20<br />
</td>
<td>3.67<br />
</td>
</tr>
<tr>
<td>81/80, 126/125, 225/224, 3136/3125...<br />
</td>
<td><a class="wiki_link" href="/Meantone">Meantone</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11.77<br />
</td>
<td>1.70<br />
</td>
</tr>
<tr>
<td>50/49, 81/80, 405/392, 4000/3969...<br />
</td>
<td><a class="wiki_link" href="/Injera">Injera</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>11.92<br />
</td>
<td>3.58<br />
</td>
</tr>
<tr>
<td>49/48, 225/224, 525/512, 686/675...<br />
</td>
<td><a class="wiki_link" href="/Negri">Negri</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12.12<br />
</td>
<td>3.19<br />
</td>
</tr>
<tr>
<td>64/63, 126/125, 128/125, 4000/3969...<br />
</td>
<td><a class="wiki_link" href="/Augene">Augene</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12.13<br />
</td>
<td>2.94<br />
</td>
</tr>
<tr>
<td>49/48, 126/125, 875/864, 1029/1000...<br />
</td>
<td><a class="wiki_link" href="/Keemun">Keemun</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12.41<br />
</td>
<td>3.19<br />
</td>
</tr>
<tr>
<td>81/80, 128/125, 648/625, 2048/2025...<br />
</td>
<td><a class="wiki_link" href="/Catler">Catler</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>12.84<br />
</td>
<td>3.56<br />
</td>
</tr>
<tr>
<td>50/49, 245/243, 250/243, 2430/2401...<br />
</td>
<td><a class="wiki_link" href="/Hedgehog">Hedgehog</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13.19<br />
</td>
<td>3.11<br />
</td>
</tr>
<tr>
<td>64/63, 245/243, 1728/1715, 2240/2187...<br />
</td>
<td><a class="wiki_link" href="/Superpyth">Superpyth</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>14.43<br />
</td>
<td>2.40<br />
</td>
</tr>
<tr>
<td>126/125, 245/243, 686/675, 4375/4374<br />
</td>
<td><a class="wiki_link" href="/Sensi">Sensi</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>14.46<br />
</td>
<td>1.61<br />
</td>
</tr>
<tr>
<td>50/49, 525/512, 1029/1024, 1875/1792...<br />
</td>
<td><a class="wiki_link" href="/Lemba">Lemba</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>14.63<br />
</td>
<td>3.74<br />
</td>
</tr>
<tr>
<td>64/63, 250/243, 875/864, 6144/6125...<br />
</td>
<td><a class="wiki_link" href="/Porcupine">Porcupine</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>14.80<br />
</td>
<td>3.09<br />
</td>
</tr>
<tr>
<td>81/80, 525/512, 875/864, 4375/4374...<br />
</td>
<td><a class="wiki_link" href="/Flattone">Flattone</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>15.38<br />
</td>
<td>2.54<br />
</td>
</tr>
<tr>
<td>225/224, 245/243, 875/864, 3125/3072...<br />
</td>
<td><a class="wiki_link" href="/Magic">Magic</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>15.54<br />
</td>
<td>1.28<br />
</td>
</tr>
<tr>
<td>50/49, 875/864, 1728/1715, 3125/3024...<br />
</td>
<td><a class="wiki_link" href="/Doublewide">Doublewide</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>15.60<br />
</td>
<td>3.27<br />
</td>
</tr>
<tr>
<td>49/48, 250/243, 4000/3969, 6125/5832...<br />
</td>
<td><a class="wiki_link" href="/Nautilus">Nautilus</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>15.62<br />
</td>
<td>3.48<br />
</td>
</tr>
<tr>
<td>64/63, 686/675, 2401/2400, 6272/6075...<br />
</td>
<td><a class="wiki_link" href="/Beatles">Beatles</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>16.88<br />
</td>
<td>2.90<br />
</td>
</tr>
<tr>
<td>81/80, 686/675, 1029/1000, 10976/10935...<br />
</td>
<td><a class="wiki_link" href="/Liese">Liese</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>17.49<br />
</td>
<td>2.62<br />
</td>
</tr>
<tr>
<td>81/80, 1029/1024, 1728/1715, 8748/8575...<br />
</td>
<td><a class="wiki_link" href="/Cynder">Cynder</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>18.45<br />
</td>
<td>1.70<br />
</td>
</tr>
<tr>
<td>225/224, 1728/1715, 2430/2401, 6144/6125...<br />
</td>
<td><a class="wiki_link" href="/Orwell">Orwell</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>19.98<br />
</td>
<td>0.95<br />
</td>
</tr>
<tr>
<td>225/224, 3125/3087, 4000/3969, 5120/5103...<br />
</td>
<td><a class="wiki_link" href="/Garibaldi">Garibaldi</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>20.29<br />
</td>
<td>0.91<br />
</td>
</tr>
<tr>
<td>126/125, 1728/1715, 2401/2400, 31104/30625...<br />
</td>
<td><a class="wiki_link" href="/Myna">Myna</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>20.33<br />
</td>
<td>1.17<br />
</td>
</tr>
<tr>
<td>225/224, 1029/1024, 2401/2400, 16875/16807...<br />
</td>
<td><a class="wiki_link" href="/Miracle">Miracle</a><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>21.10<br />
</td>
<td>0.63<br />
</td>
</tr>
<tr>
<td colspan="10">A BONUS TEMPERAMENT:<br />
</td>
</tr>
<tr>
<td>2401/2400, 4375/4374, 250047/250000...<br />
</td>
<td><a class="wiki_link" href="/Ennealimmal">Ennealimmal</a><br />
</td>
<td>133.337<br />
</td>
<td>84.313<br />
</td>
<td>9,0<br />
</td>
<td>13,2<br />
</td>
<td>19,3<br />
</td>
<td>24,2<br />
</td>
<td>39.83<br />
</td>
<td>0.04<br />
</td>
</tr>
</table>
</body></html>