Middle Path table of seven-limit rank two temperaments
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This table is an updated version of Table 2 of [[Paul Erlich]]'s [[A Middle Path]]. The complexity is now measured a different way (which, however, is proportional to the original complexity for this table), and some temperament names have been updated. This table comprises all possible seven-limit 2-D cases where complexity/7.65 + damage/10 < 1. See also [[Middle Path table of five-limit rank two temperaments]], [[Middle Path table 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 || ETs || || 28/27, 49/48, 64/63, 256/243, 343/324... || [[Blacksmith]] || 239.18 || 155.35 || 5,0 || 8,0 || 11,1 || 14,0 || 2.01 || 7.24 || [[15edo|15]], [[25edo|25]], (30), 35bc, 40b, (45bc), 50bc, (50b)... || || 36/35, 50/49, 126/125, 360/343, 648/625... || [[Diminished]] || 298.53 || 197.08 || 4,0 || 7,-1 || 10,-1 || 12,-1 || 2.46 || 5.87 || [[12edo|12]], (24d), (36d), (48cdd), 56cddd, (60cddd)... || || 36/35, 64/63, 81/80, 256/245, 729/700... || [[Dominant]] || 1195.23 || 495.88 || 1,0 || 2,-1 || 4,-4 || 2,2 || 2.47 || 4.77 || [[12edo|12]], (24d), 29cd, (36d), 41cd, 46ccd, (48cdd)... || || 36/35, 128/125, 225/224, 405/392, 729/686... || [[August]] || 399.99 || 107.31 || 3,0 || 5,-1 || 7,0 || 9,-2 || 2.58 || 5.87 || [[12edo|12]], (24d), 33, (36d), 45cd, (48cdd), 57cd... || || 50/49, 64/63, 225/224, 2048/2025... || [[Pajara]] || 598.45 || 491.88 || 2,0 || 4,-1 || 3,2 || 4,2 || 3.23 || 3.11 || [[22edo|22]], [[32edo|32]], [[34edo|34d]], (44), 46d, 54, 56d, 58dd, (64bc)... || || 49/48, 81/80, 245/243, 1323/1280... || [[Semaphore]] || 1203.67 || 252.48 || 1,0 || 2,-2 || 4,-8 || 3,-1 || 3.48 || 3.67 || [[19edo|19]], [[33edo|33cd]], (38d), 43d, 52cd, (57dd), 62dd... || || 81/80, 126/125, 225/224, 3136/3125... || [[Meantone]] || 1201.70 || 504.13 || 1,0 || 2,-1 || 4,-4 || 7,-10 || 3.65 || 1.70 || [[19edo|19]], [[31edo|31]], (38d), 43, 50, 55d, (57dd), (62), 67d... || || 50/49, 81/80, 405/392, 4000/3969... || [[Injera]] || 600.89 || 507.28 || 2,0 || 4,-1 || 8,-4 || 9,-4 || 3.70 || 3.58 || [[26edo|26]], [[38edo|38]], [[50edo|50d]], (52c), 62d, 64c, 66bcc, 74dd... || || 49/48, 225/224, 525/512, 686/675... || [[Negri]] || 1203.19 || 1078.35 || 1,0 || -2,4 || 5,-3 || 1,2 || 3.76 || 3.19 || [[19edo|19]], [[29edo|29]], (38d), 47d, 48d, (57dd), (58cd)... || || 64/63, 126/125, 128/125, 4000/3969... || [[Augene]] || 399.02 || 90.59* || 3,0 || 5,-1 || 7,0 || 8,2 || 3.76 || 2.94 || [[27edo|27]], [[39edo|39d]], 42, 51cd, (54c), 57bc, 63cdd, 66cd... || || 49/48, 126/125, 875/864, 1029/1000... || [[Keemun]] || 1203.19 || 317.84 || 1,0 || 0,6 || 1,5 || 2,3 || 3.85 || 3.19 || [[19edo|19]], [[34edo|34]], (38d), 53d, (57dd), 61bcdd, (68d)... || || 81/80, 128/125, 648/625, 2048/2025... || [[Catler]] || 99.81 || 75.22 || 12,0 || 19,0 || 28,0 || 33,1 || 3.98 || 3.56 || [[36edo|36]], [[48edo|48c]], 60cd, 60c, 72cd, (72c), 84cdd, 84c... || || 50/49, 245/243, 250/243, 2430/2401... || [[Hedgehog]] || 598.45 || 436.13 || 2,0 || 1,3 || 1,5 || 2,5 || 4.09 || 3.11 || [[22edo|22]], [[36edo|36c]], (44), 52bdd, 58c, (66d), (72cc)... || || 64/63, 245/243, 1728/1715, 2240/2187... || [[Superpyth]] || 1197.60 || 708.17 || 1,0 || 1,1 || -3,9 || 4,-2 || 4.48 || 2.40 || [[22edo|22]], [[27edo|27]], (44), 49, (54c), (66d), 71d, 76bcd... || || 126/125, 245/243, 686/675, 4375/4374 || [[Sensi]] || 1198.39 || 755.23 || 1,0 || 6,-7 || 8,-9 || 11,-13 || 4.49 || 1.61 || [[19edo|19]], [[27edo|27]], (38d), 46, (54c), (57dd), 65, 73, 76dd... || || 50/49, 525/512, 1029/1024, 1875/1792... || [[Lemba]] || 601.70 || 230.87 || 2,0 || 2,3 || 5,-1 || 6,-1 || 4.54 || 3.74 || [[26edo|26]], (52c), 62c, (78bcc), 88cc, 104bcc... || || 64/63, 250/243, 875/864, 6144/6125... || [[Porcupine]] || 1196.91 || 1034.59 || 1,0 || -1,3 || -2,5 || 8,-6 || 4.59 || 3.09 || [[22edo|22]], [[37edo|37]], (44), 59, (66d), (74b), 81bd, (88bd)... || || 81/80, 525/512, 875/864, 4375/4374... || [[Flattone]] || 1202.54 || 507.14 || 1,0 || 2,-1 || 4,-4 || -1,9 || 4.77 || 2.54 || [[26edo|26]], [[45edo|45]], (52c), 64cd, 71bc, (78bcc), 83bcdd... || || 225/224, 245/243, 875/864, 3125/3072... || [[Magic]] || 1201.28 || 380.80 || 1,0 || 0,5 || 2,1 || -1,12 || 4.82 || 1.28 || [[22edo|22]], [[41edo|41]], (44), 60, 63, (66d), 79d, (82), 85... || || 50/49, 875/864, 1728/1715, 3125/3024... || [[Doublewide]] || 599.28 || 326.96 || 2,0 || 1,4 || 3,3 || 4,3 || 4.84 || 3.27 || [[22edo|22]], (44), 48, (66d), 70c, 74c, (88bd), 92cd... || || 49/48, 250/243, 4000/3969, 6125/5832... || [[Nautilus]] || 1202.99 || 1119.69 || 1,0 || -4,6 || -7,10 || 0,3 || 4.85 || 3.48 || [[29edo|29]], (58cd), (87ccdd), (116ccddd)... || || 64/63, 686/675, 2401/2400, 6272/6075... || [[Beatles]] || 1197.10 || 842.38 || 1,0 || 3,-2 || -4,9 || 0,4 || 5.24 || 2.90 || [[27edo|27]], (54c), (81bcd), (108bccd), 118bccd... || || 81/80, 686/675, 1029/1000, 10976/10935... || [[Liese]] || 1202.62 || 569.05 || 1,0 || 3,-3 || 8,-12 || 8,-11 || 5.43 || 2.62 || [almost [[19edo|19]]], 74d, 93dd, 112bdd, 129dd... || || 81/80, 1029/1024, 1728/1715, 8748/8575... || [[Cynder]] || 1201.7 || 969.18 || 1,0 || 4,-3 || 12,-12 || 2,1 || 5.72 || 1.70 || [[31edo|31]], [[57edo|57]], (62), 88, (93), 98, (114bc), 119b... || || 225/224, 1728/1715, 2430/2401, 6144/6125... || [[Orwell]] || 1199.53 || 271.49 || 1,0 || 0,7 || 3,-3 || 1,8 || 6.20 || 0.95 || [[31edo|31]], [[53edo|53]], (62), 75, 84, (93), (106), 115, (124b)... || || 225/224, 3125/3087, 4000/3969, 5120/5103... || [[Garibaldi]] || 1200.76 || 702.64 || 1,0 || 1,1 || 7,-8 || 11,-14 || 6.30 || 0.91 || [[41edo|41]], [[53edo|53]], (82), 94, (106), 118d, (123c), 135, 147... || || 126/125, 1728/1715, 2401/2400, 31104/30625... || [[Myna]] || 1198.83 || 888.94 || 1,0 || 9,-10 || 9,-9 || 8,-7 || 6.31 || 1.17 || [[58edo|58]], [[89edo|89]], (116c), 120, 143cd, 147c, 151, 174cd... || || 225/224, 1029/1024, 2401/2400, 16875/16807... || [[Miracle]] || 1200.63 || 116.72 || 1,0 || 1,6 || 3,-7 || 3,-2 || 6.55 || 0.63 || [[41edo|41]], [[72edo|72]], (82), 103, 113, (123c), 134, (144)... || |||||||||||||||||||| A BONUS TEMPERAMENT: || || || 2401/2400, 4375/4374, 250047/250000... || [[Ennealimmal]] || 133.337 || 84.313 || 9,0 || 13,2 || 19,3 || 24,2 || 12.36 || 0.04 || || * Correction from the Xenharmonikon version, which gives the corner case generator 92.46 erroneously. || ET (* = contorted) || TOP damage || TOP octave || Rank-2 temperaments supported || || 12 || || || diminished, dominant, august || || 15 || || || blacksmith || || 19 || || || semaphore, meantone, negri, keemun, sensi || || 22 || || || pajara, hedgehog, superpyth, porcupine, magic, doublewide || || 24d* || || || diminished, dominant, august || || 25 || || || blacksmith || || 26 || || || injera, lemba, flattone || || 27 || || || augene, superpyth, sensi, beatles || || 29 || || || negri, nautilus || || 29cd || || || dominant || || 30* || || || blacksmith || || 31 || || || meantone, cynder, orwell || || 32 || || || pajara || || 33 || || || august || || 33cd || || || semaphore || || 34 || || || keemun || || 34d || || || pajara || || 35bc || || || blacksmith || || 36 || || || catler || || 36c || || || hedgehog || || 36d* || || || diminished, dominant, august || || 37 || || || porcupine || || 38 || || || injera || || 38d* || || || semaphore, meantone, negri, keemun, sensi || || 39d || || || augene || || 40b || || || blacksmith || || 41 || || || magic, garibaldi, miracle || || 41cd || || || dominant || || 42 || || || augene || || 43 || || || meantone || || 43d || || || semaphore || || 44* || || || pajara, hedgehog, superpyth, porcupine, magic, doublewide || || 45 || || || flattone || || 45bc || || || blacksmith || || 45cd || || || august || || 46 || || || sensi || || 46ccd || || || dominant || || 46d || || || pajara || || 47d || || || negri || || 48 || || || doublewide || || 48c || || || catler || || 48cdd* || || || diminished, dominant, august || || 48d || || || negri || || 49 || || || superpyth || || 50 || || || meantone || || 50b* || || || blacksmith || || 50bc || || || blacksmith || || 50d || || || injera || || 51cd || || || augene || || 52bdd || || || hedgehog || || 52c* || || || injera, lemba, flattone || || 52cd || || || semaphore || || 53 || || || orwell, garibaldi || || 53cdd || || || dominant || || 53d || || || keemun || || 54 || || || pajara || || 54c* || || || augene, superpyth, sensi, beatles || || 55b || || || blacksmith || || 55d || || || meantone || || 56cddd || || || diminished || || 56d || || || pajara || || 57 || || || cynder || || 57bc || || || augene || || 57cd || || || august || || 57dd* || || || semaphore, meantone, negri, keemun, sensi || || 58 || || || myna || || 58c || || || hedgehog || || 58ccdd* || || || dominant || || 58cd* || || || negri, nautilus || || 58dd || || || pajara || || 59 || || || porcupine || || 60 || || || magic || || 60b || || || blacksmith || || 60bc* || || || blacksmith || || 60c || || || catler || || 60cd || || || catler || || 60cddd* || || || diminished, dominant, august || [[media type="custom" key="24724368"]] The bubble chart above ([[@https://docs.google.com/spreadsheet/ccc?key=0Avc-RUOiywQtdFRvdHhUTl9Ib2p6Tm1qVWVtZGRtMUE&usp=sharing|source]]) arranges the temperaments by complexity (x-axis) vs. damage (y-axis). Colors are arbitrary. The size of the bubble is proportional to the size of the first two commas listed. Note that the "bonus temperament" Ennealimmal is not shown (a much larger range is needed to make it visible). [[media type="custom" key="24724394"]]
Original HTML content:
<html><head><title>Middle Path table of seven-limit rank two temperaments</title></head><body>This table is an updated version of 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>. The complexity is now measured a different way (which, however, is proportional to the original complexity for this table), and some temperament names have been updated.<br />
<br />
This table comprises all possible seven-limit 2-D cases where complexity/7.65 + damage/10 < 1.<br />
<br />
See also <a class="wiki_link" href="/Middle%20Path%20table%20of%20five-limit%20rank%20two%20temperaments">Middle Path table of five-limit rank two temperaments</a>, <a class="wiki_link" href="/Middle%20Path%20table%20of%20eleven-limit%20rank%20two%20temperaments">Middle Path table 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>
<td>ETs<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>2.01<br />
</td>
<td>7.24<br />
</td>
<td><a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/25edo">25</a>, (30), 35bc, 40b, (45bc), 50bc, (50b)...<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>298.53<br />
</td>
<td>197.08<br />
</td>
<td>4,0<br />
</td>
<td>7,-1<br />
</td>
<td>10,-1<br />
</td>
<td>12,-1<br />
</td>
<td>2.46<br />
</td>
<td>5.87<br />
</td>
<td><a class="wiki_link" href="/12edo">12</a>, (24d), (36d), (48cdd), 56cddd, (60cddd)...<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>1195.23<br />
</td>
<td>495.88<br />
</td>
<td>1,0<br />
</td>
<td>2,-1<br />
</td>
<td>4,-4<br />
</td>
<td>2,2<br />
</td>
<td>2.47<br />
</td>
<td>4.77<br />
</td>
<td><a class="wiki_link" href="/12edo">12</a>, (24d), 29cd, (36d), 41cd, 46ccd, (48cdd)...<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>399.99<br />
</td>
<td>107.31<br />
</td>
<td>3,0<br />
</td>
<td>5,-1<br />
</td>
<td>7,0<br />
</td>
<td>9,-2<br />
</td>
<td>2.58<br />
</td>
<td>5.87<br />
</td>
<td><a class="wiki_link" href="/12edo">12</a>, (24d), 33, (36d), 45cd, (48cdd), 57cd...<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>598.45<br />
</td>
<td>491.88<br />
</td>
<td>2,0<br />
</td>
<td>4,-1<br />
</td>
<td>3,2<br />
</td>
<td>4,2<br />
</td>
<td>3.23<br />
</td>
<td>3.11<br />
</td>
<td><a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/32edo">32</a>, <a class="wiki_link" href="/34edo">34d</a>, (44), 46d, 54, 56d, 58dd, (64bc)...<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>1203.67<br />
</td>
<td>252.48<br />
</td>
<td>1,0<br />
</td>
<td>2,-2<br />
</td>
<td>4,-8<br />
</td>
<td>3,-1<br />
</td>
<td>3.48<br />
</td>
<td>3.67<br />
</td>
<td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/33edo">33cd</a>, (38d), 43d, 52cd, (57dd), 62dd...<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>1201.70<br />
</td>
<td>504.13<br />
</td>
<td>1,0<br />
</td>
<td>2,-1<br />
</td>
<td>4,-4<br />
</td>
<td>7,-10<br />
</td>
<td>3.65<br />
</td>
<td>1.70<br />
</td>
<td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31</a>, (38d), 43, 50, 55d, (57dd), (62), 67d...<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>600.89<br />
</td>
<td>507.28<br />
</td>
<td>2,0<br />
</td>
<td>4,-1<br />
</td>
<td>8,-4<br />
</td>
<td>9,-4<br />
</td>
<td>3.70<br />
</td>
<td>3.58<br />
</td>
<td><a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/38edo">38</a>, <a class="wiki_link" href="/50edo">50d</a>, (52c), 62d, 64c, 66bcc, 74dd...<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>1203.19<br />
</td>
<td>1078.35<br />
</td>
<td>1,0<br />
</td>
<td>-2,4<br />
</td>
<td>5,-3<br />
</td>
<td>1,2<br />
</td>
<td>3.76<br />
</td>
<td>3.19<br />
</td>
<td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/29edo">29</a>, (38d), 47d, 48d, (57dd), (58cd)...<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>399.02<br />
</td>
<td>90.59*<br />
</td>
<td>3,0<br />
</td>
<td>5,-1<br />
</td>
<td>7,0<br />
</td>
<td>8,2<br />
</td>
<td>3.76<br />
</td>
<td>2.94<br />
</td>
<td><a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/39edo">39d</a>, 42, 51cd, (54c), 57bc, 63cdd, 66cd...<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>1203.19<br />
</td>
<td>317.84<br />
</td>
<td>1,0<br />
</td>
<td>0,6<br />
</td>
<td>1,5<br />
</td>
<td>2,3<br />
</td>
<td>3.85<br />
</td>
<td>3.19<br />
</td>
<td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, (38d), 53d, (57dd), 61bcdd, (68d)...<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>99.81<br />
</td>
<td>75.22<br />
</td>
<td>12,0<br />
</td>
<td>19,0<br />
</td>
<td>28,0<br />
</td>
<td>33,1<br />
</td>
<td>3.98<br />
</td>
<td>3.56<br />
</td>
<td><a class="wiki_link" href="/36edo">36</a>, <a class="wiki_link" href="/48edo">48c</a>, 60cd, 60c, 72cd, (72c), 84cdd, 84c...<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>598.45<br />
</td>
<td>436.13<br />
</td>
<td>2,0<br />
</td>
<td>1,3<br />
</td>
<td>1,5<br />
</td>
<td>2,5<br />
</td>
<td>4.09<br />
</td>
<td>3.11<br />
</td>
<td><a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/36edo">36c</a>, (44), 52bdd, 58c, (66d), (72cc)...<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>1197.60<br />
</td>
<td>708.17<br />
</td>
<td>1,0<br />
</td>
<td>1,1<br />
</td>
<td>-3,9<br />
</td>
<td>4,-2<br />
</td>
<td>4.48<br />
</td>
<td>2.40<br />
</td>
<td><a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/27edo">27</a>, (44), 49, (54c), (66d), 71d, 76bcd...<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>1198.39<br />
</td>
<td>755.23<br />
</td>
<td>1,0<br />
</td>
<td>6,-7<br />
</td>
<td>8,-9<br />
</td>
<td>11,-13<br />
</td>
<td>4.49<br />
</td>
<td>1.61<br />
</td>
<td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/27edo">27</a>, (38d), 46, (54c), (57dd), 65, 73, 76dd...<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>601.70<br />
</td>
<td>230.87<br />
</td>
<td>2,0<br />
</td>
<td>2,3<br />
</td>
<td>5,-1<br />
</td>
<td>6,-1<br />
</td>
<td>4.54<br />
</td>
<td>3.74<br />
</td>
<td><a class="wiki_link" href="/26edo">26</a>, (52c), 62c, (78bcc), 88cc, 104bcc...<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>1196.91<br />
</td>
<td>1034.59<br />
</td>
<td>1,0<br />
</td>
<td>-1,3<br />
</td>
<td>-2,5<br />
</td>
<td>8,-6<br />
</td>
<td>4.59<br />
</td>
<td>3.09<br />
</td>
<td><a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/37edo">37</a>, (44), 59, (66d), (74b), 81bd, (88bd)...<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>1202.54<br />
</td>
<td>507.14<br />
</td>
<td>1,0<br />
</td>
<td>2,-1<br />
</td>
<td>4,-4<br />
</td>
<td>-1,9<br />
</td>
<td>4.77<br />
</td>
<td>2.54<br />
</td>
<td><a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/45edo">45</a>, (52c), 64cd, 71bc, (78bcc), 83bcdd...<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>1201.28<br />
</td>
<td>380.80<br />
</td>
<td>1,0<br />
</td>
<td>0,5<br />
</td>
<td>2,1<br />
</td>
<td>-1,12<br />
</td>
<td>4.82<br />
</td>
<td>1.28<br />
</td>
<td><a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/41edo">41</a>, (44), 60, 63, (66d), 79d, (82), 85...<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>599.28<br />
</td>
<td>326.96<br />
</td>
<td>2,0<br />
</td>
<td>1,4<br />
</td>
<td>3,3<br />
</td>
<td>4,3<br />
</td>
<td>4.84<br />
</td>
<td>3.27<br />
</td>
<td><a class="wiki_link" href="/22edo">22</a>, (44), 48, (66d), 70c, 74c, (88bd), 92cd...<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>1202.99<br />
</td>
<td>1119.69<br />
</td>
<td>1,0<br />
</td>
<td>-4,6<br />
</td>
<td>-7,10<br />
</td>
<td>0,3<br />
</td>
<td>4.85<br />
</td>
<td>3.48<br />
</td>
<td><a class="wiki_link" href="/29edo">29</a>, (58cd), (87ccdd), (116ccddd)...<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>1197.10<br />
</td>
<td>842.38<br />
</td>
<td>1,0<br />
</td>
<td>3,-2<br />
</td>
<td>-4,9<br />
</td>
<td>0,4<br />
</td>
<td>5.24<br />
</td>
<td>2.90<br />
</td>
<td><a class="wiki_link" href="/27edo">27</a>, (54c), (81bcd), (108bccd), 118bccd...<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>1202.62<br />
</td>
<td>569.05<br />
</td>
<td>1,0<br />
</td>
<td>3,-3<br />
</td>
<td>8,-12<br />
</td>
<td>8,-11<br />
</td>
<td>5.43<br />
</td>
<td>2.62<br />
</td>
<td>[almost <a class="wiki_link" href="/19edo">19</a>], 74d, 93dd, 112bdd, 129dd...<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>1201.7<br />
</td>
<td>969.18<br />
</td>
<td>1,0<br />
</td>
<td>4,-3<br />
</td>
<td>12,-12<br />
</td>
<td>2,1<br />
</td>
<td>5.72<br />
</td>
<td>1.70<br />
</td>
<td><a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/57edo">57</a>, (62), 88, (93), 98, (114bc), 119b...<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>1199.53<br />
</td>
<td>271.49<br />
</td>
<td>1,0<br />
</td>
<td>0,7<br />
</td>
<td>3,-3<br />
</td>
<td>1,8<br />
</td>
<td>6.20<br />
</td>
<td>0.95<br />
</td>
<td><a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/53edo">53</a>, (62), 75, 84, (93), (106), 115, (124b)...<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>1200.76<br />
</td>
<td>702.64<br />
</td>
<td>1,0<br />
</td>
<td>1,1<br />
</td>
<td>7,-8<br />
</td>
<td>11,-14<br />
</td>
<td>6.30<br />
</td>
<td>0.91<br />
</td>
<td><a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, (82), 94, (106), 118d, (123c), 135, 147...<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>1198.83<br />
</td>
<td>888.94<br />
</td>
<td>1,0<br />
</td>
<td>9,-10<br />
</td>
<td>9,-9<br />
</td>
<td>8,-7<br />
</td>
<td>6.31<br />
</td>
<td>1.17<br />
</td>
<td><a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/89edo">89</a>, (116c), 120, 143cd, 147c, 151, 174cd...<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>1200.63<br />
</td>
<td>116.72<br />
</td>
<td>1,0<br />
</td>
<td>1,6<br />
</td>
<td>3,-7<br />
</td>
<td>3,-2<br />
</td>
<td>6.55<br />
</td>
<td>0.63<br />
</td>
<td><a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/72edo">72</a>, (82), 103, 113, (123c), 134, (144)...<br />
</td>
</tr>
<tr>
<td colspan="10">A BONUS TEMPERAMENT:<br />
</td>
<td><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>12.36<br />
</td>
<td>0.04<br />
</td>
<td><br />
</td>
</tr>
</table>
<ul><li>Correction from the Xenharmonikon version, which gives the corner case generator 92.46 erroneously.</li></ul><br />
<table class="wiki_table">
<tr>
<td>ET (* =<br />
contorted)<br />
</td>
<td>TOP damage<br />
</td>
<td>TOP octave<br />
</td>
<td>Rank-2 temperaments supported<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>diminished, dominant, august<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>semaphore, meantone, negri, keemun, sensi<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara, hedgehog, superpyth, porcupine, magic, doublewide<br />
</td>
</tr>
<tr>
<td>24d*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>diminished, dominant, august<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>injera, lemba, flattone<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>augene, superpyth, sensi, beatles<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>negri, nautilus<br />
</td>
</tr>
<tr>
<td>29cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>dominant<br />
</td>
</tr>
<tr>
<td>30*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>meantone, cynder, orwell<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>august<br />
</td>
</tr>
<tr>
<td>33cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>semaphore<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>keemun<br />
</td>
</tr>
<tr>
<td>34d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara<br />
</td>
</tr>
<tr>
<td>35bc<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>catler<br />
</td>
</tr>
<tr>
<td>36c<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>hedgehog<br />
</td>
</tr>
<tr>
<td>36d*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>diminished, dominant, august<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>porcupine<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>injera<br />
</td>
</tr>
<tr>
<td>38d*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>semaphore, meantone, negri, keemun, sensi<br />
</td>
</tr>
<tr>
<td>39d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>augene<br />
</td>
</tr>
<tr>
<td>40b<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>magic, garibaldi, miracle<br />
</td>
</tr>
<tr>
<td>41cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>dominant<br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>augene<br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>meantone<br />
</td>
</tr>
<tr>
<td>43d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>semaphore<br />
</td>
</tr>
<tr>
<td>44*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara, hedgehog, superpyth, porcupine, magic, doublewide<br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>flattone<br />
</td>
</tr>
<tr>
<td>45bc<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>45cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>august<br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>sensi<br />
</td>
</tr>
<tr>
<td>46ccd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>dominant<br />
</td>
</tr>
<tr>
<td>46d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara<br />
</td>
</tr>
<tr>
<td>47d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>negri<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>doublewide<br />
</td>
</tr>
<tr>
<td>48c<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>catler<br />
</td>
</tr>
<tr>
<td>48cdd*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>diminished, dominant, august<br />
</td>
</tr>
<tr>
<td>48d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>negri<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>superpyth<br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>meantone<br />
</td>
</tr>
<tr>
<td>50b*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>50bc<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>50d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>injera<br />
</td>
</tr>
<tr>
<td>51cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>augene<br />
</td>
</tr>
<tr>
<td>52bdd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>hedgehog<br />
</td>
</tr>
<tr>
<td>52c*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>injera, lemba, flattone<br />
</td>
</tr>
<tr>
<td>52cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>semaphore<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>orwell, garibaldi<br />
</td>
</tr>
<tr>
<td>53cdd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>dominant<br />
</td>
</tr>
<tr>
<td>53d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>keemun<br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara<br />
</td>
</tr>
<tr>
<td>54c*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>augene, superpyth, sensi, beatles<br />
</td>
</tr>
<tr>
<td>55b<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>55d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>meantone<br />
</td>
</tr>
<tr>
<td>56cddd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>diminished<br />
</td>
</tr>
<tr>
<td>56d<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara<br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>cynder<br />
</td>
</tr>
<tr>
<td>57bc<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>augene<br />
</td>
</tr>
<tr>
<td>57cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>august<br />
</td>
</tr>
<tr>
<td>57dd*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>semaphore, meantone, negri, keemun, sensi<br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>myna<br />
</td>
</tr>
<tr>
<td>58c<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>hedgehog<br />
</td>
</tr>
<tr>
<td>58ccdd*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>dominant<br />
</td>
</tr>
<tr>
<td>58cd*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>negri, nautilus<br />
</td>
</tr>
<tr>
<td>58dd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>pajara<br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>porcupine<br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>magic<br />
</td>
</tr>
<tr>
<td>60b<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>60bc*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>blacksmith<br />
</td>
</tr>
<tr>
<td>60c<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>catler<br />
</td>
</tr>
<tr>
<td>60cd<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>catler<br />
</td>
</tr>
<tr>
<td>60cddd*<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>diminished, dominant, august<br />
</td>
</tr>
</table>
<br />
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