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Middle Path table of 5-limit rank-2 temperaments

Revision as of 22:44, 6 December 2013 by Wikispaces>spt3125 (**Imported revision 475396102 - Original comment: **)

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This table is an an updated version of Table 1 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.

The "main sequence" of this table comprises all possible five-limit 2-D cases where complexity/7.65 + damage/10 < 1. The 'exotemperaments' have larger damage and lend themselves to special measures such as custom inharmonic timbres in order to aid harmoniousness. The 'bonus temperaments' are more complex but have exceedingly small damage and sound like JI.

See also [[Middle Path table of seven-limit rank two temperaments]], [[Middle Path table of eleven-limit rank two temperaments]].

|| Vanishing Interval's Ratio || V.I. Vector || V.I. cents || Temperament
name || TOP
period || TOP
generator || Mapp.
of 2 || Mapp.
of 3 || Mapp.
of 5 || Cmplx. || TOP
Dmg. || ETs ||
|||||||||||||||||||||||| TWO EXOTEMPERAMENTS: ||
|| 16/15 || [4, -1, -1> || 111.7 || [[Father]] || 1185.9 || 447.4 || 1, 0 || 2, -1 || 2, 1 || 1.37 || 14.13 ||   ||
|| 27/25 || [0, 3, -2> || 133.2 || [[Bug]] || 1200.0 || 260.3 || 1, 0 || 2, -2 || 3, -3 || 1.63 || 14.18 ||   ||
|||||||||||||||||||||||| MAIN SEQUENCE: ||
|| 25/24 || [-3, -1, 2> || 70.7 || [[Dicot]] || 1207.66 || 353.22 || 1, 0 || 1, 2 || 2, 1 || 1.60 || 7.66 || [[24edo|24c]], 41cc, (48cc), 65ccc... ||
|| 81/80 || [-4, 4, -1> || 21.5 || [[Meantone]] || 1201.70 || 504.13 || 1, 0 || 2, -1 || 4, -4 || 2.19 || 1.70 || [[12edo|12]], [[19edo|19]], (24), 26, 29c, 31, 33c, (36)... ||
|| 128/125 || [7, 0, -3> || 41.1 || [[Augmented]] || 399.02 || 93.15 || 3, 0 || 5, -1 || 7, 0 || 2.42 || 2.94 || [[12edo|12]], [[15edo|15]], (24), 27, (30), 33, (36), 39... ||
|| 135/128 || [-7, 3, 1> || 92.2 || [[Mavila]] || 1206.55 || 685.03 || 1, 0 || 1, 1 || 4, -3 || 2.44 || 6.55 || [[37edo|37bc]], 67bbccc, (74bbccc), 81bbcccc... ||
|| 250/243 || [1, -5, 3> || 49.2 || [[Porcupine]] || 1196.91 || 1034.59 || 1, 0 || -1, 3 || -2, 5 || 2.75 || 3.09 || [[15edo|15]], [[22edo|22]], [[29edo|29]], (30), 36c, 37, 43c, (44)... ||
|| 256/243 || [8, -5, 0> || 90.2 || [[Blackwood]] || 238.87 || 158.78 || 5, 0 || 8, 0 || 11, 1 || 2.76 || 5.67 || [[15edo|15]], [[25edo|25]], (30), 35bc, 40b, (45bc)... ||
|| 648/625 || [3, 4, -4> || 62.6 || [[Diminished]] || 299.16 || 197.49 || 4, 0 || 7, -1 || 10, -1 || 3.23 || 3.36 || [[12edo|12]], (24), 28, 32c, (36), 40, 44c, (48c)... ||
|| 2048/2025 || [11, -4, -2> || 19.6 || [[Srutal]] || 599.56 || 494.86 || 2, 0 || 4, -1 || 3, 2 || 3.81 || 0.89 || [[12edo|12]], [[22edo|22]], (24), 34, (36), (44), 46, (48c), 54... ||
|| 3125/3072 || [-10, -1, 5> || 29.6 || [[Magic]] || 1201.28 || 380.80 || 1, 0 || 0, 5 || 2, 1 || 4.02 || 1.28 || [[19edo|19]], [[22edo|22]], (38), 41, (44), 54b, (57), 60... ||
|| 6561/6250 || [-1, 8, -5> || 84.1 || [[Ripple]] || 1203.32 || 101.99 || 1, 0 || 2, -5 || 3, -8 || 4.38 || 3.32 || [[12edo|12]], (24), (36), 47, (48c), 59b, (60c)... ||
|| 15625/15552 || [-6, -5, 6> || 8.11 || [[Hanson]] || 1200.29 || 317.07 || 1, 0 || 0, 6 || 1, 5 || 4.83 || 0.29 || [[19edo|19]], [[34edo|34]], (38), 49, 53, (57), 64b, (68)... ||
|| 16875/16384 || [-14, 3, 4> || 51.1 || [[Negri]] || 1201.82 || 1075.68 || 1, 0 || -2, 4 || 5, -3 || 4.86 || 1.82 || [[19edo|19]], [[29edo|29]], (38), 48, (57), (58c), 66b, 67c... ||
|| 20000/19683 || [5, -9, 4> || 27.7 || [[Tetracot]] || 1199.03 || 176.11 || 1, 0 || 1, 4 || 1, 9 || 4.95 || 0.97 || [[27edo|27]], [[34edo|34]], [[41edo|41]], 48, (54c), 55c, 61, (68), 75... ||
|| 20480/19683 || [12, -9, 1> || 68.7 || [[Superpyth]] || 1197.60 || 708.17 || 1, 0 || 1, 1 || -3, 9 || 4.95 || 2.40 || [[22edo|22]], [[27edo|27]], (44), 49, (54c), (66), 71, 76bc... ||
|| 32805/32768 || [-15, 8, 1> || 1.95 || [[Helmholtz]] || 1200.07 || 701.79 || 1, 0 || 1, 1 || 7, -8 || 5.20 || 0.07 || [[41edo|41]], [[53edo|53]], [[65edo|65]], 70c, 77, (82), 89, 94, 99c... ||
|| 78732/78125 || [2, 9, -7> || 13.4 || [[Sensi]] || 1199.59 || 756.60 || 1, 0 || 6, -7 || 8, -9 || 5.63 || 0.41 || [[19edo|19]], (38), [[46edo|46]], (57), 65, 73, (76), 84... ||
|| 262144/253125 || [18, -4, -5> || 60.6 || [[Passion]] || 1198.31 || 98.40 || 1, 0 || 2, -5 || 2, 4 || 6.23 || 1.69 || [[73edo|73]], 134bc, (146bc), 158bcc... ||
|| 393216/390625 || [17, 1, -8> || 11.4 || [[Würschmidt]] || 1199.69 || 812.05 || 1, 0 || 7, -8 || 3, -1 || 6.44 || 0.31 || [[34edo|34]], 65, (68), 96, 99, (102)... ||
|| 531441/524288 || [-19, 12, 0> || 23.5 || [[Compton]] || 100.05 || 15.13 || 12, 0 || 19, 0 || 28, -1 || 6.59 || 0.62 || [[60edo|60]], [[72edo|72]], 84, 96, 108, (120c), 132... ||
|| 1600000/1594323 || [9, -13, 5> || 6.15 || [[Amity]] || 1199.85 || 860.38 || 1, 0 || -2, 5 || -7, 13 || 7.14 || 0.15 || [[53edo|53]], [[99edo|99]], (106), 145, 152, (159)... ||
|| 2109375/2097152 || [-21, 3, 7> || 10.1 || [[Orson]] || 1200.24 || 271.65 || 1, 0 || 0, 7 || 3, -3 || 7.28 || 0.24 || [[53edo|53]], (106), 137, (159), 190... ||
|||||||||||||||||||||||| TWO BONUS TEMPS: ||
|| 6115295232/6103515625 || [23, 6, -14> || 3.34 || [[Vishnu]] || 599.97 || 71.15 || 2, 0 || 4, -7 || 5, -3 || 11.27 || 0.05 ||   ||
|| 274877906944/274658203125 || [38, -2, -15> || 1.38 || [[Luna]] || 1199.98 || 193.196 || 1, 0 || 4, -15 || 2, 2 || 13.17 || 0.02 ||   ||

|| ET || TOP damage || TOP octave || Rank-2 temperaments supported ||
|| 12 || 3.56 || 1197.67 || meantone, augmented, diminished, srutal, ripple ||
|| 15 || 5.67 || 1194.33 || augmented, porcupine, blackwood ||
|| 19 || 2.28 || 1202.28 || meantone, magic, hanson, negri, sensi ||
|| 22 || 3.22 || 1198.72 || porcupine, srutal, magic, superpyth ||
|| 24 (contorted) || 3.56 || 1197.67 || meantone, augmented, diminished, srutal, ripple ||
|| 24c || 7.87 || 1207.87 || dicot ||
|| 25 || 6.16 || 1194.83 || blackwood ||
|| 26 || 3.69 || 1203.69 || meantone ||
|| 27 || 2.94 || 1197.06 || augmented, tetracot, superpyth ||
|| 28 || 5.15 || 1205.15 || diminished ||
|| 29 || 3.47 || 1202.53 || porcupine, negri ||
|| 29c || 5.89 || 1194.11 || meantone ||
|| 30 (contorted) || 5.67 || 1194.33 || augmented, porcupine, blackwood ||
|| 31 || 1.81 || 1201.47 || meantone ||
|| 32c || 5.61 || 1194.39 || diminished ||
|| 33 || 6.43 || 1200.54 || augmented ||
|| 33c || 4.90 || 1204.90 || meantone ||
|| 34 || 1.24 || 1198.76 || srutal, hanson, tetracot, wuerschmidt ||
|| 35bc || 9.43 || 1209.43 || blackwood ||
|| 36 (contorted) || 3.56 || 1197.67 || meantone, augmented, diminished, srutal, ripple ||
|| 36c || 4.25 || 1204.25 || porcupine ||
|| 37 || 3.64 || 1196.36 || porcupine ||
|| 37bc || 6.62 || 1206.62 || mavila ||
|| 38 (contorted) || 2.28 || 1202.28 || meantone, magic, hanson, negri, sensi ||

[[media type="custom" key="24641486"]]
The bubble chart above ([[@https://docs.google.com/spreadsheet/ccc?key=0Avc-RUOiywQtdHVXQU9DM0ZKVkFZY3BBVEYzNlRJdlE&usp=sharing|source]]) arranges the temperaments by complexity (x-axis, log10 scale) vs. damage (y-axis, log10 scale). Colors are arbitrary. The size of the bubble is determined by ln(complexity*damage).

Original HTML content:

<html><head><title>Middle Path table of five-limit rank two temperaments</title></head><body>This table is an an updated version of Table 1 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 />
The &quot;main sequence&quot; of this table comprises all possible five-limit 2-D cases where complexity/7.65 + damage/10 &lt; 1. The 'exotemperaments' have larger damage and lend themselves to special measures such as custom inharmonic timbres in order to aid harmoniousness. The 'bonus temperaments' are more complex but have exceedingly small damage and sound like JI.<br />
<br />
See also <a class="wiki_link" href="/Middle%20Path%20table%20of%20seven-limit%20rank%20two%20temperaments">Middle Path table of seven-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 Ratio<br />
</td>
        <td>V.I. Vector<br />
</td>
        <td>V.I. cents<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>Cmplx.<br />
</td>
        <td>TOP<br />
Dmg.<br />
</td>
        <td>ETs<br />
</td>
    </tr>
    <tr>
        <td colspan="12">TWO EXOTEMPERAMENTS:<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>[4, -1, -1&gt;<br />
</td>
        <td>111.7<br />
</td>
        <td><a class="wiki_link" href="/Father">Father</a><br />
</td>
        <td>1185.9<br />
</td>
        <td>447.4<br />
</td>
        <td>1, 0<br />
</td>
        <td>2, -1<br />
</td>
        <td>2, 1<br />
</td>
        <td>1.37<br />
</td>
        <td>14.13<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>27/25<br />
</td>
        <td>[0, 3, -2&gt;<br />
</td>
        <td>133.2<br />
</td>
        <td><a class="wiki_link" href="/Bug">Bug</a><br />
</td>
        <td>1200.0<br />
</td>
        <td>260.3<br />
</td>
        <td>1, 0<br />
</td>
        <td>2, -2<br />
</td>
        <td>3, -3<br />
</td>
        <td>1.63<br />
</td>
        <td>14.18<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td colspan="12">MAIN SEQUENCE:<br />
</td>
    </tr>
    <tr>
        <td>25/24<br />
</td>
        <td>[-3, -1, 2&gt;<br />
</td>
        <td>70.7<br />
</td>
        <td><a class="wiki_link" href="/Dicot">Dicot</a><br />
</td>
        <td>1207.66<br />
</td>
        <td>353.22<br />
</td>
        <td>1, 0<br />
</td>
        <td>1, 2<br />
</td>
        <td>2, 1<br />
</td>
        <td>1.60<br />
</td>
        <td>7.66<br />
</td>
        <td><a class="wiki_link" href="/24edo">24c</a>, 41cc, (48cc), 65ccc...<br />
</td>
    </tr>
    <tr>
        <td>81/80<br />
</td>
        <td>[-4, 4, -1&gt;<br />
</td>
        <td>21.5<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>2.19<br />
</td>
        <td>1.70<br />
</td>
        <td><a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">19</a>, (24), 26, 29c, 31, 33c, (36)...<br />
</td>
    </tr>
    <tr>
        <td>128/125<br />
</td>
        <td>[7, 0, -3&gt;<br />
</td>
        <td>41.1<br />
</td>
        <td><a class="wiki_link" href="/Augmented">Augmented</a><br />
</td>
        <td>399.02<br />
</td>
        <td>93.15<br />
</td>
        <td>3, 0<br />
</td>
        <td>5, -1<br />
</td>
        <td>7, 0<br />
</td>
        <td>2.42<br />
</td>
        <td>2.94<br />
</td>
        <td><a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/15edo">15</a>, (24), 27, (30), 33, (36), 39...<br />
</td>
    </tr>
    <tr>
        <td>135/128<br />
</td>
        <td>[-7, 3, 1&gt;<br />
</td>
        <td>92.2<br />
</td>
        <td><a class="wiki_link" href="/Mavila">Mavila</a><br />
</td>
        <td>1206.55<br />
</td>
        <td>685.03<br />
</td>
        <td>1, 0<br />
</td>
        <td>1, 1<br />
</td>
        <td>4, -3<br />
</td>
        <td>2.44<br />
</td>
        <td>6.55<br />
</td>
        <td><a class="wiki_link" href="/37edo">37bc</a>, 67bbccc, (74bbccc), 81bbcccc...<br />
</td>
    </tr>
    <tr>
        <td>250/243<br />
</td>
        <td>[1, -5, 3&gt;<br />
</td>
        <td>49.2<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>2.75<br />
</td>
        <td>3.09<br />
</td>
        <td><a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/29edo">29</a>, (30), 36c, 37, 43c, (44)...<br />
</td>
    </tr>
    <tr>
        <td>256/243<br />
</td>
        <td>[8, -5, 0&gt;<br />
</td>
        <td>90.2<br />
</td>
        <td><a class="wiki_link" href="/Blackwood">Blackwood</a><br />
</td>
        <td>238.87<br />
</td>
        <td>158.78<br />
</td>
        <td>5, 0<br />
</td>
        <td>8, 0<br />
</td>
        <td>11, 1<br />
</td>
        <td>2.76<br />
</td>
        <td>5.67<br />
</td>
        <td><a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/25edo">25</a>, (30), 35bc, 40b, (45bc)...<br />
</td>
    </tr>
    <tr>
        <td>648/625<br />
</td>
        <td>[3, 4, -4&gt;<br />
</td>
        <td>62.6<br />
</td>
        <td><a class="wiki_link" href="/Diminished">Diminished</a><br />
</td>
        <td>299.16<br />
</td>
        <td>197.49<br />
</td>
        <td>4, 0<br />
</td>
        <td>7, -1<br />
</td>
        <td>10, -1<br />
</td>
        <td>3.23<br />
</td>
        <td>3.36<br />
</td>
        <td><a class="wiki_link" href="/12edo">12</a>, (24), 28, 32c, (36), 40, 44c, (48c)...<br />
</td>
    </tr>
    <tr>
        <td>2048/2025<br />
</td>
        <td>[11, -4, -2&gt;<br />
</td>
        <td>19.6<br />
</td>
        <td><a class="wiki_link" href="/Srutal">Srutal</a><br />
</td>
        <td>599.56<br />
</td>
        <td>494.86<br />
</td>
        <td>2, 0<br />
</td>
        <td>4, -1<br />
</td>
        <td>3, 2<br />
</td>
        <td>3.81<br />
</td>
        <td>0.89<br />
</td>
        <td><a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/22edo">22</a>, (24), 34, (36), (44), 46, (48c), 54...<br />
</td>
    </tr>
    <tr>
        <td>3125/3072<br />
</td>
        <td>[-10, -1, 5&gt;<br />
</td>
        <td>29.6<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>4.02<br />
</td>
        <td>1.28<br />
</td>
        <td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/22edo">22</a>, (38), 41, (44), 54b, (57), 60...<br />
</td>
    </tr>
    <tr>
        <td>6561/6250<br />
</td>
        <td>[-1, 8, -5&gt;<br />
</td>
        <td>84.1<br />
</td>
        <td><a class="wiki_link" href="/Ripple">Ripple</a><br />
</td>
        <td>1203.32<br />
</td>
        <td>101.99<br />
</td>
        <td>1, 0<br />
</td>
        <td>2, -5<br />
</td>
        <td>3, -8<br />
</td>
        <td>4.38<br />
</td>
        <td>3.32<br />
</td>
        <td><a class="wiki_link" href="/12edo">12</a>, (24), (36), 47, (48c), 59b, (60c)...<br />
</td>
    </tr>
    <tr>
        <td>15625/15552<br />
</td>
        <td>[-6, -5, 6&gt;<br />
</td>
        <td>8.11<br />
</td>
        <td><a class="wiki_link" href="/Hanson">Hanson</a><br />
</td>
        <td>1200.29<br />
</td>
        <td>317.07<br />
</td>
        <td>1, 0<br />
</td>
        <td>0, 6<br />
</td>
        <td>1, 5<br />
</td>
        <td>4.83<br />
</td>
        <td>0.29<br />
</td>
        <td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, (38), 49, 53, (57), 64b, (68)...<br />
</td>
    </tr>
    <tr>
        <td>16875/16384<br />
</td>
        <td>[-14, 3, 4&gt;<br />
</td>
        <td>51.1<br />
</td>
        <td><a class="wiki_link" href="/Negri">Negri</a><br />
</td>
        <td>1201.82<br />
</td>
        <td>1075.68<br />
</td>
        <td>1, 0<br />
</td>
        <td>-2, 4<br />
</td>
        <td>5, -3<br />
</td>
        <td>4.86<br />
</td>
        <td>1.82<br />
</td>
        <td><a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/29edo">29</a>, (38), 48, (57), (58c), 66b, 67c...<br />
</td>
    </tr>
    <tr>
        <td>20000/19683<br />
</td>
        <td>[5, -9, 4&gt;<br />
</td>
        <td>27.7<br />
</td>
        <td><a class="wiki_link" href="/Tetracot">Tetracot</a><br />
</td>
        <td>1199.03<br />
</td>
        <td>176.11<br />
</td>
        <td>1, 0<br />
</td>
        <td>1, 4<br />
</td>
        <td>1, 9<br />
</td>
        <td>4.95<br />
</td>
        <td>0.97<br />
</td>
        <td><a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/41edo">41</a>, 48, (54c), 55c, 61, (68), 75...<br />
</td>
    </tr>
    <tr>
        <td>20480/19683<br />
</td>
        <td>[12, -9, 1&gt;<br />
</td>
        <td>68.7<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>4.95<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), (66), 71, 76bc...<br />
</td>
    </tr>
    <tr>
        <td>32805/32768<br />
</td>
        <td>[-15, 8, 1&gt;<br />
</td>
        <td>1.95<br />
</td>
        <td><a class="wiki_link" href="/Helmholtz">Helmholtz</a><br />
</td>
        <td>1200.07<br />
</td>
        <td>701.79<br />
</td>
        <td>1, 0<br />
</td>
        <td>1, 1<br />
</td>
        <td>7, -8<br />
</td>
        <td>5.20<br />
</td>
        <td>0.07<br />
</td>
        <td><a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/65edo">65</a>, 70c, 77, (82), 89, 94, 99c...<br />
</td>
    </tr>
    <tr>
        <td>78732/78125<br />
</td>
        <td>[2, 9, -7&gt;<br />
</td>
        <td>13.4<br />
</td>
        <td><a class="wiki_link" href="/Sensi">Sensi</a><br />
</td>
        <td>1199.59<br />
</td>
        <td>756.60<br />
</td>
        <td>1, 0<br />
</td>
        <td>6, -7<br />
</td>
        <td>8, -9<br />
</td>
        <td>5.63<br />
</td>
        <td>0.41<br />
</td>
        <td><a class="wiki_link" href="/19edo">19</a>, (38), <a class="wiki_link" href="/46edo">46</a>, (57), 65, 73, (76), 84...<br />
</td>
    </tr>
    <tr>
        <td>262144/253125<br />
</td>
        <td>[18, -4, -5&gt;<br />
</td>
        <td>60.6<br />
</td>
        <td><a class="wiki_link" href="/Passion">Passion</a><br />
</td>
        <td>1198.31<br />
</td>
        <td>98.40<br />
</td>
        <td>1, 0<br />
</td>
        <td>2, -5<br />
</td>
        <td>2, 4<br />
</td>
        <td>6.23<br />
</td>
        <td>1.69<br />
</td>
        <td><a class="wiki_link" href="/73edo">73</a>, 134bc, (146bc), 158bcc...<br />
</td>
    </tr>
    <tr>
        <td>393216/390625<br />
</td>
        <td>[17, 1, -8&gt;<br />
</td>
        <td>11.4<br />
</td>
        <td><a class="wiki_link" href="/W%C3%BCrschmidt">Würschmidt</a><br />
</td>
        <td>1199.69<br />
</td>
        <td>812.05<br />
</td>
        <td>1, 0<br />
</td>
        <td>7, -8<br />
</td>
        <td>3, -1<br />
</td>
        <td>6.44<br />
</td>
        <td>0.31<br />
</td>
        <td><a class="wiki_link" href="/34edo">34</a>, 65, (68), 96, 99, (102)...<br />
</td>
    </tr>
    <tr>
        <td>531441/524288<br />
</td>
        <td>[-19, 12, 0&gt;<br />
</td>
        <td>23.5<br />
</td>
        <td><a class="wiki_link" href="/Compton">Compton</a><br />
</td>
        <td>100.05<br />
</td>
        <td>15.13<br />
</td>
        <td>12, 0<br />
</td>
        <td>19, 0<br />
</td>
        <td>28, -1<br />
</td>
        <td>6.59<br />
</td>
        <td>0.62<br />
</td>
        <td><a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/72edo">72</a>, 84, 96, 108, (120c), 132...<br />
</td>
    </tr>
    <tr>
        <td>1600000/1594323<br />
</td>
        <td>[9, -13, 5&gt;<br />
</td>
        <td>6.15<br />
</td>
        <td><a class="wiki_link" href="/Amity">Amity</a><br />
</td>
        <td>1199.85<br />
</td>
        <td>860.38<br />
</td>
        <td>1, 0<br />
</td>
        <td>-2, 5<br />
</td>
        <td>-7, 13<br />
</td>
        <td>7.14<br />
</td>
        <td>0.15<br />
</td>
        <td><a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/99edo">99</a>, (106), 145, 152, (159)...<br />
</td>
    </tr>
    <tr>
        <td>2109375/2097152<br />
</td>
        <td>[-21, 3, 7&gt;<br />
</td>
        <td>10.1<br />
</td>
        <td><a class="wiki_link" href="/Orson">Orson</a><br />
</td>
        <td>1200.24<br />
</td>
        <td>271.65<br />
</td>
        <td>1, 0<br />
</td>
        <td>0, 7<br />
</td>
        <td>3, -3<br />
</td>
        <td>7.28<br />
</td>
        <td>0.24<br />
</td>
        <td><a class="wiki_link" href="/53edo">53</a>, (106), 137, (159), 190...<br />
</td>
    </tr>
    <tr>
        <td colspan="12">TWO BONUS TEMPS:<br />
</td>
    </tr>
    <tr>
        <td>6115295232/6103515625<br />
</td>
        <td>[23, 6, -14&gt;<br />
</td>
        <td>3.34<br />
</td>
        <td><a class="wiki_link" href="/Vishnu">Vishnu</a><br />
</td>
        <td>599.97<br />
</td>
        <td>71.15<br />
</td>
        <td>2, 0<br />
</td>
        <td>4, -7<br />
</td>
        <td>5, -3<br />
</td>
        <td>11.27<br />
</td>
        <td>0.05<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>274877906944/274658203125<br />
</td>
        <td>[38, -2, -15&gt;<br />
</td>
        <td>1.38<br />
</td>
        <td><a class="wiki_link" href="/Luna">Luna</a><br />
</td>
        <td>1199.98<br />
</td>
        <td>193.196<br />
</td>
        <td>1, 0<br />
</td>
        <td>4, -15<br />
</td>
        <td>2, 2<br />
</td>
        <td>13.17<br />
</td>
        <td>0.02<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />


<table class="wiki_table">
    <tr>
        <td>ET<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>3.56<br />
</td>
        <td>1197.67<br />
</td>
        <td>meantone, augmented, diminished, srutal, ripple<br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td>5.67<br />
</td>
        <td>1194.33<br />
</td>
        <td>augmented, porcupine, blackwood<br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td>2.28<br />
</td>
        <td>1202.28<br />
</td>
        <td>meantone, magic, hanson, negri, sensi<br />
</td>
    </tr>
    <tr>
        <td>22<br />
</td>
        <td>3.22<br />
</td>
        <td>1198.72<br />
</td>
        <td>porcupine, srutal, magic, superpyth<br />
</td>
    </tr>
    <tr>
        <td>24 (contorted)<br />
</td>
        <td>3.56<br />
</td>
        <td>1197.67<br />
</td>
        <td>meantone, augmented, diminished, srutal, ripple<br />
</td>
    </tr>
    <tr>
        <td>24c<br />
</td>
        <td>7.87<br />
</td>
        <td>1207.87<br />
</td>
        <td>dicot<br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td>6.16<br />
</td>
        <td>1194.83<br />
</td>
        <td>blackwood<br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td>3.69<br />
</td>
        <td>1203.69<br />
</td>
        <td>meantone<br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td>2.94<br />
</td>
        <td>1197.06<br />
</td>
        <td>augmented, tetracot, superpyth<br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td>5.15<br />
</td>
        <td>1205.15<br />
</td>
        <td>diminished<br />
</td>
    </tr>
    <tr>
        <td>29<br />
</td>
        <td>3.47<br />
</td>
        <td>1202.53<br />
</td>
        <td>porcupine, negri<br />
</td>
    </tr>
    <tr>
        <td>29c<br />
</td>
        <td>5.89<br />
</td>
        <td>1194.11<br />
</td>
        <td>meantone<br />
</td>
    </tr>
    <tr>
        <td>30 (contorted)<br />
</td>
        <td>5.67<br />
</td>
        <td>1194.33<br />
</td>
        <td>augmented, porcupine, blackwood<br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td>1.81<br />
</td>
        <td>1201.47<br />
</td>
        <td>meantone<br />
</td>
    </tr>
    <tr>
        <td>32c<br />
</td>
        <td>5.61<br />
</td>
        <td>1194.39<br />
</td>
        <td>diminished<br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td>6.43<br />
</td>
        <td>1200.54<br />
</td>
        <td>augmented<br />
</td>
    </tr>
    <tr>
        <td>33c<br />
</td>
        <td>4.90<br />
</td>
        <td>1204.90<br />
</td>
        <td>meantone<br />
</td>
    </tr>
    <tr>
        <td>34<br />
</td>
        <td>1.24<br />
</td>
        <td>1198.76<br />
</td>
        <td>srutal, hanson, tetracot, wuerschmidt<br />
</td>
    </tr>
    <tr>
        <td>35bc<br />
</td>
        <td>9.43<br />
</td>
        <td>1209.43<br />
</td>
        <td>blackwood<br />
</td>
    </tr>
    <tr>
        <td>36 (contorted)<br />
</td>
        <td>3.56<br />
</td>
        <td>1197.67<br />
</td>
        <td>meantone, augmented, diminished, srutal, ripple<br />
</td>
    </tr>
    <tr>
        <td>36c<br />
</td>
        <td>4.25<br />
</td>
        <td>1204.25<br />
</td>
        <td>porcupine<br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td>3.64<br />
</td>
        <td>1196.36<br />
</td>
        <td>porcupine<br />
</td>
    </tr>
    <tr>
        <td>37bc<br />
</td>
        <td>6.62<br />
</td>
        <td>1206.62<br />
</td>
        <td>mavila<br />
</td>
    </tr>
    <tr>
        <td>38 (contorted)<br />
</td>
        <td>2.28<br />
</td>
        <td>1202.28<br />
</td>
        <td>meantone, magic, hanson, negri, sensi<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24641486?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24641486&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><img src="https://docs.google.com/spreadsheet/oimg?key=0Avc-RUOiywQtdHVXQU9DM0ZKVkFZY3BBVEYzNlRJdlE&amp;oid=2&amp;zx=yp91o8x0ucso" /><!-- ws:end:WikiTextMediaRule:0 --><br />
The bubble chart above (<a class="wiki_link_ext" href="https://docs.google.com/spreadsheet/ccc?key=0Avc-RUOiywQtdHVXQU9DM0ZKVkFZY3BBVEYzNlRJdlE&amp;usp=sharing" rel="nofollow" target="_blank">source</a>) arranges the temperaments by complexity (x-axis, log10 scale) vs. damage (y-axis, log10 scale). Colors are arbitrary. The size of the bubble is determined by ln(complexity*damage).</body></html>
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