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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''optimal patent val''' for a [[regular temperament]] is the unique [[patent val]] that [[support]]s the temperament with the lowest [[error]].  
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-14 15:30:41 UTC</tt>.<br>
: The original revision id was <tt>201700784</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Given any collection of p-limit commas, there is a finite list of p-limit [[Patent val|patent vals]] tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest [[Tenney-Euclidean temperament measures|TE error]]; this is the //optimal (TE) patent val// for the temperament defined by the commas. Note that other defintions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.


Given N-edo, and the odd primes up to p, let us set e = max_q |round(Nlog2(q))/N - log2(q)|; that is, e is the maximum absolute value of the error of the patent val for N-edo, measured in octaves, for all of the odd primes q up to p. Then e &lt; 1/2N, since the error cannot be more than half the size of a step of N-edo. From this it follows that N &lt; 1/2e, or if we measure e in cents, we can also say N &lt; 600/e. If e is the maximum absolute error in cents for the [[POTE tuning]] of the temperament defined by the collection of commas, then we need only search as far as 600/e for the optimal patent val.
Given any temperament, which is characterized by the [[comma]]s it [[tempering out|tempers out]], there is a finite list of [[patent val]]s that temper out all the commas of the temperament in the same [[subgroup]]. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the one which has the lowest [[TE error]]; this is the (TE) optimal patent val for the temperament. Note that other definitions of error lead to different results.


Below are tabulated some values.
On this wiki, the optimal patent val for each temperament is given as the last patent val in the [[optimal ET sequence]], or stated explicitly in case it is not a member of the sequence.  


==5-limit rank two==
== Instructions ==
27/25: [[14edo]]
By tempering a JI scale using the ''N''-edo found on the list below we automatically temper it to the corresponding temperament. This can be done in [http://www.huygens-fokker.org/scala/ Scala] using the Quantize command: either type in "Quantize/consistent N" on the bottom, or use the pull-down menu under "Modify", check the box saying "Consistent" and type N (without a decimal point) into "Resolution".
16/15: [[8edo]]
135/128: [[23edo]]
25/24: [[17edo]]
648/625: [[12edo]]
250/243: [[22edo]]
128/125: [[39edo]]
3125/3072: [[60edo]]
81/80: [[81edo]]
2048/2025: [[80edo]]
78732/78125: [[539edo]]
393216/390625: [[164edo]]
2109375/2097152: [[296edo]]
15625/15552: [[458edo]]
1600000/1594323: [[873edo]]
1224440064/1220703125: [[1496edo]]
6115295232/6103515625: [[1400edo]]
32805/32768: [[749edo]]
274877906944/274658203125: [[1559edo]]
7629394531250/7625597484987: [[3501edo]]


==7-limit rank two==
To limit the search range when finding the optimal patent val a useful observation is this: given ''N''-edo, and an odd prime ''q'' ≤ ''p'', if ''d'' is the absolute value in cents of the difference between the tuning of ''q'' given by the [[POTE tuning]] and the POTE tuning rounded to the nearest ''N''-edo value, then d &lt; 600/''N'', from which it follows that N &lt; 600/d. Likewise, if ''e'' is the absolute value of the error of ''q'' in the patent val tuning, then ''e'' &lt; 600/''N'' and so ''N'' &lt; 600/''e''. If ''N''-edo defines an optimal patent val, then the patent val will be identical to the val obtained by rounding the POTE tuning to the nearest N-edo value. We have two distances from the patent val, one to the POTE tuning and one to the the JI tuning, both bounded by 600/''N'', and so by the triangle inequality the distance from the JI tuning to the POTE tuning, which is the error of the prime ''q'' in the POTE tuning, is bounded by 1200/''N''. Hence, ''N'' &lt; 1200/error(''q''). If now we take the minimum value for 1200/error(prime) for all the odd primes up to ''p'', we obtain an upper bound for ''N''.
[[Ennealimmal]]: [[612edo]]
[[Supermajor]]: [[6214edo]]
[[Enneadecal]]: [[2185edo]]
[[Sesquiquartififths]]: [[1498edo]]
[[Tertiaseptal]]: [[171edo]]
[[Meantone]]: [[81edo]]
[[Pontiac]]: [[171edo]]
[[Miracle]]: [[72edo]]
[[Beep]]: [[9edo]]
[[Magic]]: [[41edo]]
[[Dicot]]: [[7edo]]
[[Term]]: [[1722edo]]
[[Pajara]]: [[22edo]]
[[Hemiwuerschmidt]]: [[328edo]]
[[Dominant]]: [[12edo]]
[[Orwell]]: [[137edo]]
[[Father]]: [[5edo]]
[[Catakleismic]]: [[197edo]]
[[Garibaldi]]: [[94edo]]
[[Hemififths]]: [[338edo]]
[[Diminished]]: [[12edo]]
[[Neptune]]: [[1778edo]]
[[Amity]]: [[350edo]]
[[Mother]]: [[5edo]]
[[Augene]]: [[27edo]]


== Examples ==
Below are tabulated some values. In each case an identifier which uniquely identifies the temperament in question is given. In the codimension one case, where the temperament is defined by a single comma, the comma is given and used as a name. In other cases, for a temperament of rank ''n'', ''n'' independent vals are given. Normally this is by way of integers conjoined by ampersands, such as 2&10 for 7-limit pajara. This tells us we can use the 7-limit patent vals for 2 and 10 to define the temperament. In case ''n'' independent patent vals cannot be found, vals using the [[wart notation]] are given; this adjusts the nth prime mapping to its second-best value by appending the ''n''-th lower-case letter in alphabetical order. Thus, "12f" adjusts a patent val for 12 in the 13-limit or above, for instance {{val| 12 19 28 34 42 44 }}, to {{val| 12 19 28 34 42 45 }} (which is actually a better mapping, and hence more useful for this purpose.)


</pre></div>
=== 5-limit rank two ===
<h4>Original HTML content:</h4>
Comma: ET w/ optimal patent val: 1000 * badness
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Optimal patent val&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Given any collection of p-limit commas, there is a finite list of p-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures"&gt;TE error&lt;/a&gt;; this is the &lt;em&gt;optimal (TE) patent val&lt;/em&gt; for the temperament defined by the commas. Note that other defintions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.&lt;br /&gt;
 
&lt;br /&gt;
16/15: [[8edo|8et]] 14.884
Given N-edo, and the odd primes up to p, let us set e = max_q |round(Nlog2(q))/N - log2(q)|; that is, e is the maximum absolute value of the error of the patent val for N-edo, measured in octaves, for all of the odd primes q up to p. Then e &amp;lt; 1/2N, since the error cannot be more than half the size of a step of N-edo. From this it follows that N &amp;lt; 1/2e, or if we measure e in cents, we can also say N &amp;lt; 600/e. If e is the maximum absolute error in cents for the &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE tuning&lt;/a&gt; of the temperament defined by the collection of commas, then we need only search as far as 600/e for the optimal patent val.&lt;br /&gt;
 
&lt;br /&gt;
648/625: [[12edo|12et]] 47.231
Below are tabulated some values.&lt;br /&gt;
 
&lt;br /&gt;
27/25: [[14edo|14et]] 32.801
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-5-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit rank two&lt;/h2&gt;
 
27/25: &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;&lt;br /&gt;
25/24: [[17edo|17et]] 13.028
16/15: &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt;&lt;br /&gt;
 
135/128: &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
250/243: [[22edo|22et]] 30.778
25/24: &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;&lt;br /&gt;
 
648/625: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
135/128: [[23edo|23et]] 39.556
250/243: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;br /&gt;
 
128/125: &lt;a class="wiki_link" href="/39edo"&gt;39edo&lt;/a&gt;&lt;br /&gt;
128/125: [[39edo|39et]] 22.315
3125/3072: &lt;a class="wiki_link" href="/60edo"&gt;60edo&lt;/a&gt;&lt;br /&gt;
 
81/80: &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt;&lt;br /&gt;
3125/3072: [[60edo|60et]] 39.163
2048/2025: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt;&lt;br /&gt;
 
78732/78125: &lt;a class="wiki_link" href="/539edo"&gt;539edo&lt;/a&gt;&lt;br /&gt;
2048/2025: [[80edo|80et]] 19.915
393216/390625: &lt;a class="wiki_link" href="/164edo"&gt;164edo&lt;/a&gt;&lt;br /&gt;
 
2109375/2097152: &lt;a class="wiki_link" href="/296edo"&gt;296edo&lt;/a&gt;&lt;br /&gt;
81/80: [[81edo|81et]] 7.381
15625/15552: &lt;a class="wiki_link" href="/458edo"&gt;458edo&lt;/a&gt;&lt;br /&gt;
 
1600000/1594323: &lt;a class="wiki_link" href="/873edo"&gt;873edo&lt;/a&gt;&lt;br /&gt;
20000/19683: [[109edo|109et]] 48.518
1224440064/1220703125: &lt;a class="wiki_link" href="/1496edo"&gt;1496edo&lt;/a&gt;&lt;br /&gt;
 
6115295232/6103515625: &lt;a class="wiki_link" href="/1400edo"&gt;1400edo&lt;/a&gt;&lt;br /&gt;
393216/390625: [[164edo|164et]] 40.603
32805/32768: &lt;a class="wiki_link" href="/749edo"&gt;749edo&lt;/a&gt;&lt;br /&gt;
 
274877906944/274658203125: &lt;a class="wiki_link" href="/1559edo"&gt;1559edo&lt;/a&gt;&lt;br /&gt;
2109375/2097152: [[296edo|296et]] 40.807
7629394531250/7625597484987: &lt;a class="wiki_link" href="/3501edo"&gt;3501edo&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
15625/15552: [[458edo|458et]] 13.234
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-7-limit rank two"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit rank two&lt;/h2&gt;
 
&lt;a class="wiki_link" href="/Ennealimmal"&gt;Ennealimmal&lt;/a&gt;: &lt;a class="wiki_link" href="/612edo"&gt;612edo&lt;/a&gt;&lt;br /&gt;
78732/78125: [[539edo|539et]] 35.220
&lt;a class="wiki_link" href="/Supermajor"&gt;Supermajor&lt;/a&gt;: &lt;a class="wiki_link" href="/6214edo"&gt;6214edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Enneadecal"&gt;Enneadecal&lt;/a&gt;: &lt;a class="wiki_link" href="/2185edo"&gt;2185edo&lt;/a&gt;&lt;br /&gt;
32805/32768: [[749edo|749et]] 4.259
&lt;a class="wiki_link" href="/Sesquiquartififths"&gt;Sesquiquartififths&lt;/a&gt;: &lt;a class="wiki_link" href="/1498edo"&gt;1498edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Tertiaseptal"&gt;Tertiaseptal&lt;/a&gt;: &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;&lt;br /&gt;
1600000/1594323: [[873edo|873et]] 21.960
&lt;a class="wiki_link" href="/Meantone"&gt;Meantone&lt;/a&gt;: &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Pontiac"&gt;Pontiac&lt;/a&gt;: &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;&lt;br /&gt;
6115295232/6103515625: [[1400edo|1400et]] 31.181
&lt;a class="wiki_link" href="/Miracle"&gt;Miracle&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Beep"&gt;Beep&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;&lt;br /&gt;
1224440064/1220703125: [[1496edo|1496et]] 43.729
&lt;a class="wiki_link" href="/Magic"&gt;Magic&lt;/a&gt;: &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Dicot"&gt;Dicot&lt;/a&gt;: &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
274877906944/274658203125: [[1559edo|1559et]] 20.576
&lt;a class="wiki_link" href="/Term"&gt;Term&lt;/a&gt;: &lt;a class="wiki_link" href="/1722edo"&gt;1722edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Pajara"&gt;Pajara&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;br /&gt;
31381059609/31250000000: [[2760edo|2760et]] 82.423
&lt;a class="wiki_link" href="/Hemiwuerschmidt"&gt;Hemiwuerschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/328edo"&gt;328edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Dominant"&gt;Dominant&lt;/a&gt;: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
7629394531250/7625597484987: [[3501edo|3501et]] 17.191
&lt;a class="wiki_link" href="/Orwell"&gt;Orwell&lt;/a&gt;: &lt;a class="wiki_link" href="/137edo"&gt;137edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Father"&gt;Father&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;&lt;br /&gt;
=== 7-limit rank two ===
&lt;a class="wiki_link" href="/Catakleismic"&gt;Catakleismic&lt;/a&gt;: &lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;&lt;br /&gt;
Name: ET w/ optimal patent val: Val name: 1000*badness
&lt;a class="wiki_link" href="/Garibaldi"&gt;Garibaldi&lt;/a&gt;: &lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Hemififths"&gt;Hemififths&lt;/a&gt;: &lt;a class="wiki_link" href="/338edo"&gt;338edo&lt;/a&gt;&lt;br /&gt;
[[Father family#Pater|Pater]]: [[3edo|3et]] 3&11b 53.001
&lt;a class="wiki_link" href="/Diminished"&gt;Diminished&lt;/a&gt;: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Neptune"&gt;Neptune&lt;/a&gt;: &lt;a class="wiki_link" href="/1778edo"&gt;1778edo&lt;/a&gt;&lt;br /&gt;
[[Dicot family#Flat|Flat]]: [[4edo|4et]] 3&4 25.381
&lt;a class="wiki_link" href="/Amity"&gt;Amity&lt;/a&gt;: &lt;a class="wiki_link" href="/350edo"&gt;350edo&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Mother"&gt;Mother&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;&lt;br /&gt;
[[Trienstonic clan|Father]]: [[5edo|5et]] 3d&5 21.312
&lt;a class="wiki_link" href="/Augene"&gt;Augene&lt;/a&gt;: &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Archytas clan|Mother]]: [[5edo|5et]] 2&3 24.152
 
[[Meantone family|Sharptone]]: [[5edo|5et]] 5&7d 24.848
 
[[Father family#Baba|Baba]]: [[5edo|5et]] 1&5 44.321
 
[[Father family#Quint|Quint]]: [[5edo|5et]] 5&15cd 48.312
 
[[Bug family#Mite|Mite]]: [[5edo|5et]] 1cdd&5 54.770
 
[[Father family#Walid|Walid]]: [[6edo|6et]] 2&6 48.978
 
[[Dicot family|Dicot]]: [[7edo|7et]] 4&7 19.935
 
[[Dicot family#Jamesbond|Jamesbond]]: [[7edo|7et]] 7&14c 41.714
 
[[Septisemi temperaments#Oxygen|Oxygen]]: [[8edo|8et]] 7d&8 59.866
 
[[Bug family|Beep]]: [[9edo|9et]] 4&5 18.638
 
[[Mint temperaments#Progression|Progression]]: [[9edo|9et]] 9&17c 48.356
 
[[Augmented family#Deflated|Deflated]]: [[9edo|9et]] 3&9 59.079
 
[[Septisemi temperaments#Fluorine|Fluorine]]: [[9edo|9et]] 9&20bd 55.623
 
[[Dicot family|Sharp]]: [[10edo|10et]] 3d&7d 28.942
 
[[Dicot family|Decimal]]: [[10edo|10et]] 4&10 28.334
 
[[Septisemi temperaments#Sodium|Sodium]]: [[11edo|11et]] 4&11 55.814
 
[[Meantone family|Dominant]]: [[12edo|12et]] 5&7 20.690
 
[[Diminished family #Septimal diminished|Diminished]]: [[12edo|12et]] 4&12 22.401
 
[[Augmented family|August]]: [[12edo|12et]] 9&12 26.459
 
[[Augmented family#Hexe|Hexe]]: [[12edo|12et]] 6&12 57.730
 
[[Schismatic family#Schism|Schism]]: [[12edo|12et]] 12&29de 56.648
 
[[Mint temperaments#Ripple|Ripple]]: [[12edo|12et]] 12&23 59.735
 
[[Archytas clan|Blacksmith]]: [[15edo|15et]] 5&10 25.640
 
[[Trienstonic clan|Opossum]]: [[15edo|15et]] 7d&8d 40.650
 
[[Augmented family#Inflated|Inflated]]: [[15edo|15et]] 15&48bc 54.729
 
[[Pelogic family#Armodue|Armodue]]: [[16edo|16et]] 7&9 49.038
 
[[Dicot family#Dichotic|Dichotic]]: [[17edo|17et]] 3&7 37.565
 
[[Trienstonic clan|Octokaidecal]]: [[18edo|18et]] 10&18 36.747
 
[[Trienstonic clan|Uncle]]: [[18edo|18et]] 5&18 72.653
 
[[Marvel temperaments|Negri]]: [[19edo|19et]] 1&9 26.483
 
[[Meantone family|Godzilla]]: [[19edo|19et]] 5&19 26.747
 
[[Kleismic family|Keemun]]: [[19edo|19et]] 4&15 27.408
 
[[Trienstonic clan#Wallaby|Wallaby]]: [[19edo|19ccdd]] 2d&5c 58.468
 
[[Gamelismic clan|Gorgo]]: [[21edo|21et]] 5&16 46.385
 
[[Diaschismic family|Pajara]]: [[22edo|22et]] 2&10 20.033
 
[[Porcupine family#Hedgehog|Hedgehog]]: [[22edo|22et]] 14c&22 43.983
 
[[Jubilismic clan|Lemba]]: [[26edo|26et]] 10&16 62.208
 
[[Augmented family#Augene|Augene]]: [[27edo|27et]] 3&12 24.816
 
[[Augmented family#Niner|Niner]]: [[27edo|27et]] 9&18 67.157
 
[[Archytas clan|Beatles]]: [[27edo|27et]] 10&27 45.872
 
[[Porcupine family|Nautilus]]: [[29edo|29et]] 15&29 57.420
 
[[Meantone family|Mothra]]: [[31edo|31et]] 5&26 37.146
 
[[Meantone family|Squares]]: [[31edo|31et]] 31&45 45.993
 
[[Immunity family#Septimal immunity|Immunity]]: [[34edo|34et]] 5&29 77.631
 
[[Meantone family|Injera]]: [[38edo|38et]] 12&26 31.130
 
[[Augmented family|Triforce]]: [[39edo|39et]] 6&9 54.988
 
[[Magic family|Magic]]: [[41edo|41et]] 19&41 18.918
 
[[Gamelismic clan|Superkleismic]]: [[41edo|41et]] 15&26 47.932
 
[[Keemic temperaments#Quasitemp|Quasitemp]]: [[41edo|41et]] 4&37 60.269
 
[[Meantone family|Flattone]]: [[45edo|45et]] 7&19 38.553
 
[[Starling temperaments|Sensi]]: [[46edo|46et]] 19&27 25.622
 
[[Starling temperaments#Vines|Vines]]: [[46edo|46et]] 4&42 78.049
 
[[Jubilismic clan|Doublewide]]: [[48edo|48et]] 4&18 43.462
 
[[Archytas clan|Superpyth]]: [[49edo|49et]] 5&17 32.318
 
[[Archytas clan|Passion]]: [[49edo|49et]] 12&37 62.327
 
[[Porcupine family#Porky|Porky]]: [[51edo|51et]] 22&51 54.389
 
[[Marvel temperaments#Submajor-7-limit|Submajor]]: [[53edo|53et]] 10&33 60.533
 
[[Meantone family|Liese]]: [[55edo|55et]] 19&55 46.706
 
[[Sycamore family#Sycamore|Sycamore]]: [[56edo|56et]] 18&19 62.018
 
[[Diaschismic family|Diaschismic]]: [[58edo|58et]] 12&34 37.914
 
[[Porcupine family#Porcupine|Porcupine]]: [[59edo|59et]] 7&15 41.057
 
[[Starling temperaments#Kumonga|Kumonga]]: [[70edo|70et]] 16&27 87.500
 
[[Gamelismic clan|Miracle]]: [[72edo|72et]] 10&21 16.742
 
[[Marvel temperaments|Wizard]]: [[72edo|72et]] 22&50 40.846
 
[[Unicorn family|Unicorn]] [[77edo|77et]] 19&58 40.913
 
[[Diaschismic family|Bidia]]: [[80edo|80et]] 12&56 56.474
 
[[Orwellismic temperaments#Quartonic|Quartonic]]: [[80edo|80et]] 26&27 42.632
 
[[Meantone family|Meantone]]: [[81edo|81et]] 12&19 13.707
 
[[Starling temperaments|Myna]]: [[89edo|89et]] 4&27 27.044
 
[[Marvel temperaments|Septimin]]: [[91edo|91et]] 9&32 54.502
 
[[Ragismic microtemperaments|Sfourth]]: [[91edo|91et]] 45&46 123.291
 
[[Schismatic family|Garibaldi]]: [[94edo|94et]] 12&29 21.644
 
[[Hemimean clan|Misty]]: [[99edo|99et]] 12&87 36.802
 
[[Starling temperaments|Nusecond]]: [[101edo|101et]] 31&101 50.389
 
[[Tetracot family|Octacot]]: [[109edo|109et]] 27&41 33.845
 
[[Hemimean clan|Semisept]]: [[111edo|111et]] 18&31 50.472
 
[[Hemifamity temperaments|Buzzard]]: [[111edo|111et]] 5&48 47.963
 
[[Schismatic family#Guiron|Guiron]]: [[118edo|118et]] 36&41 47.544
 
[[Gamelismic clan|Hemithirds]]: [[118edo|118et]] 25&31 44.284
 
[[Kleismic family#Hemikleismic|Hemikleismic]]: [[121edo|121et]] 15&38 52.054
 
[[Mirkwai clan#Pluto|Pluto]]: [[121edo|121et]] 41&80 57.514
 
[[Marvel temperaments|Tritonic]]: [[122edo|122et]] 2&29 47.578
 
[[Gravity family#Gravid|Gravid]]: [[123edo|123et]] 58&123 47.283
 
[[Marvel temperaments|Slender]]: [[125edo|125et]] 1&31 56.934
 
[[Marvel temperaments#Merman|Merman]]: [[125edo|125et]] 2&41 55.078
 
[[Gamelismic clan|Rodan]]: [[128edo|128et]] 5&41 37.112
 
[[Hemimean clan#Subpental|Subpental]]: [[130edo|130et]] 19&111 54.303
 
[[Sensipent family#Bison|Bison]]: [[130edo|130et]] 8&38 70.375
 
[[Semicomma family|Orwell]]: [[137edo|137et]] 9&22 20.375
 
[[Breedsmic temperaments#Tertiaseptal|Tertiaseptal]]: [[171edo|171et]] 31&109 12.995
 
[[Breedsmic temperaments#Septidiasemi|Septidiasemi]]: [[171edo|171et]] 10&151 44.115
 
[[Schismatic family|Pontiac]]: [[171edo|171et]] 53&118 14.133
 
[[Schismatic family|Tsaharuk]]: [[171edo|171et]] 17&77 30.697
 
[[Ragismic microtemperaments|Mitonic]]: [[171edo|171et]] 46&125 25.184
 
[[Horwell temperaments#Mutt|Mutt]]: [[171edo|171et]] 3&84 28.406
 
[[Horwell temperaments#Fifthplus|Fifthplus]]: [[171edo|171et]] 22&149 25.840
 
[[Landscape microtemperaments#Pnict|Pnict]]: [[171edo|171et]] 15&141 45.660
 
[[Wizmic microtemperaments#Tokko|Tokko]]: [[171edo|171et]] 5&166 44.417
 
[[Ragismic microtemperaments#Seniority|Seniority]]: [[171edo|171et]] 26&145 44.877
 
[[Starling temperaments|Valentine]]: [[185edo|185et]] 15&31 31.056
 
[[Sensipent family#Sensei|Sensei]]: [[187edo|187et]] 19&84 59.218
 
[[Gamelismic clan|Unidec]]: [[190edo|190et]] 26&46 38.393
 
[[Kleismic family|Catakleismic]]: [[197edo|197et]] 19&53 21.501
 
[[Kleismic family|Quadritikleismic]]: [[212edo|212et]] 4&68 39.231
 
[[Gamelismic clan#Hemiseven|Hemiseven]]: [[221edo|221et]] 5&72 56.557
 
[[Ragismic microtemperaments|Octoid]]: [[224edo|224et]] 72&152 42.670
 
[[Pythagorean family|Compton]]: [[228edo|228et]] 12&60 35.686
 
[[Kleismic family|Tritikleismic]]: [[231edo|231et]] 15&57 56.337
 
[[Mirkwai clan|Mirkat]]: [[255edo|255et]] 72&183 59.376
 
[[Breedsmic temperaments|Decoid]]: [[270edo|270et]] 10&120 33.902
 
[[Ragismic microtemperaments#Acrokleismic|Acrokleismic]] [[270edo|270et]] 19&251 56.184
 
[[Porwell temperaments#Septisuperfourth|Septisuperfourth]]: [[282edo|282et]] 22&86 59.241
 
[[Porwell temperaments|Hemischis]]: [[313edo|313et]] 24&53 45.817
 
[[Würschmidt family|Hemiwürschmidt]]: [[328edo|328et]] 6&31 20.307
 
[[Breedsmic temperaments|Hemififths]]: [[338edo|338et]] 41&58 22.243
 
[[Ragismic microtemperaments|Amity]]: [[350edo|350et]] 7&39 23.649
 
[[Schismatic family|Bischismic]]: [[378edo|378et]] 12&118 54.744
 
[[Porwell temperaments|Nessafof]]: [[381edo|381et]] 15&69 45.478
 
[[Hemifamity temperaments#Septiquarter|Septiquarter]]: [[391edo|391et]] 5&94 53.760
 
[[Ragismic microtemperaments|Parakleismic]]: [[415edo|415et]] 19&80 27.431
 
[[Ragismic microtemperaments|Gamera]]: [[422edo|422et]] 26&73 37.648
 
[[Hemimean clan#Sengagen|Sengagen]]: [[446edo|446et]] 49&50 57.978
 
[[Landscape microtemperaments|Chromat]]: [[456edo|456et]] 60&99 57.499
 
[[Kleismic family|Countercata]]: [[473edo|473et]] 34&53 52.128
 
[[Breedsmic temperaments|Harry]]: [[534edo|534et]] 58&72 34.077
 
[[Ragismic microtemperaments|Ennealimmal]]: [[612edo|612et]] 27&45 3.610
 
[[Breedsmic temperaments#Quinmite|Quinmite]]: [[701edo|701et]] 4&95 37.322
 
[[Ragismic microtemperaments#Semidimfourth|Semidimfourth]]: [[875edo|875et]] 91&99 55.245
 
[[Breedsmic temperaments|Quasiorwell]]: [[1111edo|1111et]] 31&177 35.832
 
[[Amicable]]: [[1131edo|1131et]] 99&212 45.473
 
[[Vulture family#Vulture|Vulture]]: [[1133edo|1133et]] 53&164 36.985
 
[[Breedsmic temperaments#Emmthird|Emmthird]] [[1255edo|1255et]] 58&113 16.736
 
[[Landscape microtemperaments#Septichrome|Septichrome]] [[1308edo|1308et]] 60&111 16.814
 
[[Schismatic family|Sesquiquartififths]]: [[1498edo|1498et]] 41&89 11.244
 
[[Ragismic microtemperaments|Brahmagupta]]: [[1547edo|1547et]] 7&217 29.122
 
[[Breedsmic temperaments#Maviloid|Maviloid]]: [[1614edo|1614et]] 76&99 57.632
 
[[Breedsmic temperaments#Osiris|Osiris]]: [[1696edo|1696et]] 157&171 28.307
 
[[Schismatic family|Term]]: [[1722edo|1722et]] 12&159 19.950
 
[[Gammic family|Neptune]]: [[1778edo|1778et]] 35&68 23.427
 
[[Ragismic microtemperaments|Abigail]]: [[1798edo|1798et]] 46&132 37.000
 
[[Wizmic microtemperaments#Qak|Qak]]: [[1831edo|1831et]] 50&121 29.267
 
[[Ragismic microtemperaments|Enneadecal]]: [[2185edo|2185et]] 19&152 10.954
 
[[Breedsmic temperaments#Newt|Newt]]: [[2201edo|2201et]] 41&188 41.878
 
[[Breedsmic temperaments#Subneutral|Subneutral]]: [[2236edo|2236et]] 31&348 45.792
 
[[Ragismic microtemperaments#Orga|Orga]]: [[2482edo|2482et]] 26&244 40.236
 
[[Tricot family|Trillium]]: [[4569edo|4569et]] 53&441 30.852
 
[[Ragismic microtemperaments|Supermajor]]: [[6214edo|6214et]] 80&171 10.836
 
[[Ragismic microtemperaments#Semidimi|Semidimi]]: [[8419edo|8419et]] 171&863 15.075
 
[[Minortonic family#Domain|Domain]]: [[22038edo|22038et]] 171&1164 13.979
 
=== 7-limit rank three ===
Comma: ET w/ optimal patent val: 10^6 * badness
 
36/35: [[12edo|12et]] 63.675
 
49/48: [[19edo|19et]] 115.514
 
875/864: [[41edo|41et]] 212.413
 
525/512: [[45edo|45et]] 476.454
 
686/675: [[46edo|46et]] 320.094
 
50/49: [[48edo|48et]] 127.208
 
64/63: [[49edo|49et]] 98.719
 
1029/1000: [[55edo|55et]] 678.164
 
3125/3087: [[94edo|94et]] 613.731
 
1728/1715: [[111edo|111et]] 187.341
 
2430/2401: [[137edo|137et]] 518.625
 
65625/65536: [[171edo|171et]] 172.601
 
126/125: [[185edo|185et]] 69.867
 
1029/1024: [[190edo|190et]] 176.105
 
225/224: [[197edo|197et]] 36.517
 
4000/3969: [[215edo|215et]] 215.550
 
16875/16807: [[224edo|224et]] 341.931
 
245/243: [[283edo|283et]] 121.191
 
6144/6125: [[381edo|381et]] 142.375
 
5120/5103: [[391edo|391et]] 153.052
 
3136/3125: [[446edo|446et]] 160.039
 
19683/19600: [[587edo|587et]] 300.987
 
10976/10935: [[695edo|695et]] 199.139
 
4802000/4782969: [[1131edo|1131et]] 1121.894
 
703125/702464: [[2185edo|2185et]] 149.828
 
2401/2400: [[2749edo|2749et]] 15.288
 
420175/419904: [[4306edo|4306et]] 86.449
 
4375/4374: [[8419edo|8419et]] 11.665
 
250047/250000: [[12555edo|12555et]] 21.301
 
78125000/78121827: [[101654edo|101654et]] 20.457
 
=== 11-limit rank two ===
Name: ET w/ optimal patent val: Val name: 1000*badness
 
[[Archytas clan#Fervor|Fervor]]: [[2edo|2et]] 2&27e 52.054
 
[[Dicot family#Decimal|Decimated]]: [[4edo|4et]] 4&10e 31.456
 
[[Starling temperaments#Myna temperament-Coleto|Coleto]]: [[4edo|4et]] 4&27e 48.687
 
[[Meantone family#Godzilla-Semafour|Semafour]]: [[5edo|5et]] 5&14c 28.510
 
[[Meantone family#Neutrominant|Neutrominant]]: [[7edo|7et]] 7&10c 40.240
 
[[Meantone family#Dominant-Arnold|Arnold]]: [[7edo|7et]] 5&7 26.141
 
[[Porcupine family#Hystrix|Hystrix]]: [[7edo|7et]] 7&15d 44.944
 
[[Dicot family#Dicot|Dicot]]: [[7edo|7et]] 4e&7 19.854
 
[[Dicot family#Jamesbond|Jamesbond]]: [[7edo|7et]] 7&14c 23.524
 
[[Tetracot family#Modus|Modus]]: [[7edo|7et]] 7&27e 35.149
 
[[Meantone family#Ptolemy|Ptolemy]]: [[7edo|7et]] 7&38d 58.785
 
[[Marvel temperaments|Negric]]: [[9edo|9et]] 1&9 30.617
 
[[Mint temperaments#Progression|Progression]]: [[9edo|9et]] 8d&9 26.050
 
[[Pelogic family#Superpelog-11-limit|Superpelog]]: [[9edo|9et]] 9&14c 28.535
 
[[Trienstonic clan#Octokaidecal|Octokaidecal]]: [[10edo|10et]] 10&18e 30.235
 
[[Dicot family#Decimal|Decimal]]: [[10edo|10et]] 10&14c 26.712
 
[[Dicot family#Sharp|Sharp]]: [[10edo|10et]] 10&17d 22.366
 
[[Archytas clan#Beatles|Ringo]]: [[10edo|10et]] 10&17c 32.863
 
[[Dicot family#Dichotic|Dichosis]]: [[10edo|10et]] 3&10 41.361
 
[[Dicot family#Decimal|Decibel]]: [[10edo|10et]] 4&6 32.385
 
[[Diminished family #Septimal diminished|Diminished]]: [[12edo|12et]] 4&12 22.132
 
[[Diaschismic family#Pajara-Pajaric|Pajaric]]: [[12edo|12et]] 2&10 23.798
 
[[Meantone family#Dominant-11-limit|Dominant]]: [[12edo|12et]] 5&12 24.180
 
[[Meantone family#Dominant-Domineering|Domineering]]: [[12edo|12et]] 7&12 21.978
 
[[Meantone family#Injera-Lahoh|Lahoh]]: [[12edo|12et]] 12&14ce 43.062
 
[[Jubilismic clan#Duodecim|Duodecim]]: [[12edo|12et]] 12&24d 30.536
 
[[Schismatic family#Schism|Schism]]: [[12edo|12et]] 12&41d 37.482
 
[[Meantone family#Injera-Injerous|Injerous]]: [[12edo|12e]] 12e&14c 38.577
 
[[Augmented family#Hexe-11-limit|Hexe]]: [[12edo|12et]] 6&12 38.412
 
[[Mint temperaments#Ripple|Ripple]]: [[12edo|12et]] 1ce&12 38.811
 
[Diminished family #Hemidim|Hemidim]]: [[12edo|12et]] 12&20b 54.965
 
[[Mint temperaments#Smate|Smate]]: [[14edo|14et]] 14&17c 42.518
 
[[Trienstonic clan|Opossum]]: [[15edo|15et]] 7d&8d 22.325
 
[[Trienstonic clan#Kangaroo|Kangaroo]]: [[15edo|15et]] 2cde&15 43.195
 
[[Augmented family#x-Augene-11-limit|Augene]]: [[15edo|15et]] 3&12 19.613
 
[[Archytas clan#Progress|Progress]]: [[15edo|15et]] 2&13 31.036
 
[[Kleismic family#Keemun|Darjeeling]]: [[15edo|15et]] 15&19e 27.648
 
[[Archytas clan#Blacksmith|Ferrier]]: [[15edo|15et]] 5e&15 29.200
 
[[Augmented family#Inflated|Inflated]]: [[15edo|15et]] 15&48bce 31.171
 
[[Pelogic family#Armodue|Armodue]]: [[16edo|16et]] 7&9 27.211
 
[[Pelogic family#Bipelog-11-limit|Bipelog]]: [[16edo|16et]] 2&16 35.694
 
[[Dicot family#Dichotic|Dichotic]]: [[17edo|17et]] 7&10 30.680
 
[[Dicot family#Sidi|Sidi]]: [[17edo|17et]] 14c&17 32.957
 
[[Meantone family#Dominant-Domination|Domination]]: [[17edo|17c]] 5e&12e 36.562
 
[[Marvel temperaments|Negri]]: [[19edo|19et]] 9&10 26.190
 
[[Meantone family#Septimal meantone-Meanenneadecal|Meanenneadecal]]: [[19edo|19et]] 12&19 21.182
 
[[Meantone family#Flattone-11-limit|Flattone]] [[19edo|19et]] 7&19 33.839
 
[[Meantone family#Godzilla-11-limit|Godzilla]]: [[19edo|19et]] 14c&19 28.947
 
[[Meantone family#Undevigintone|Undevigintone]]: [[19edo|19et]] 19&38d 36.387
 
[[Meantone family#Septimal meantone-Meanundeci|Meanundeci]]: [[19edo|19e]] 12e&19e 31.539
 
[[Meantone family#Liese-Lisa|Lisa]]: [[19edo|19et]] 2cde&19 54.829
 
[[Magic family#Magic-Horcrux|Horcrux]]: [[19edo|19et]] 19&60e 39.282
 
[[Magic family#Spell-11-limit|Spell]]: [[19edo|19et]] 6&19 59.791
 
[[Unicorn family#Rhinoceros|Rhinoceros]]: [[19edo|19et]] 1ce&19 59.319
 
[[Marvel temperaments#Triton-11-limit|Triton]]: [[19edo|19et]] 2&19 45.675
 
[[Kleismic family#Keemun-Qeema|Qeema]]: [[19edo|19et]] 4e&19 40.056
 
[[Kleismic family#Cataleptic|Cataleptic]]: [[19edo|19et]] 19&34d 44.335
 
[[Augmented family#Oodako-11-limit|Oodako]]: [[21edo|21et]] 6&21 59.192
 
[[Diaschismic family#Pajara|Pajara]]: [[22edo|22et]] 12&22 20.343
 
[[Diaschismic family#Pajara|Pajarous]]: [[22edo|22et]] 10&22 28.349
 
[[Magic family#Magic-Telepathy|Telepathy]]: [[22edo|22et]] 19e&22 27.109
 
[[Porcupine family#Hedgehog|Hedgehog]]: [[22edo|22et]] 14c&22 23.095
 
[[Porcupine family#Ceratitid|Ceratitid]]: [[22edo|22et]] 1ce&22 51.319
 
[[Jubilismic clan#Vigintiduo|Vigintiduo]]: [[22edo|22et]] 22&66de 48.372
 
[[Magic family#Astrology-11-limit|Astrology]]: [[22edo|22et]] 22&60de 39.151
 
[[Magic family#Divination|Divination]]: [[22edo|22et]] 22&38d 35.864
 
[[Jubilismic clan#Doublewide-Fleetwood|Fleetwood]]: [[22edo|22et]] 22&26e 35.202
 
[[Archytas clan#Quasisuper|Quasisupra]]: [[22edo|22et]] 17c&22 32.203
 
[[Comic family#Comic-11-limit|Comic]]: [[22edo|22et]] 2cde&22 45.052
 
[[Diaschismic family#Pajara-Hemipaj|Hemipaj]]: [[22edo|22et]] 2&20 38.890
 
[[Meantone family#Mohamaq-11-limit|Mohamaq]]: [[24edo|24et]] 17c&24 36.207
 
[[Meantone family#Godzilla-Baragon|Baragon]]: [[24edo|24et]] 5&19 35.673
 
[[Meantone family#Godzilla-Varan|Varan]]: [[24edo|24et]] 19e&24 39.647
 
[[Augmented family#Hemiaug|Hemiaug]]: [[24edo|24et]] 24&27e 38.232
 
[[Diminished family #Hemidim|Hemidim]]: [[24edo|24et]] 4e&24 56.576
 
[[Diminished family #Octonion|Octonion]]: [[24edo|24et]] 24&32c 30.597
 
[[Meantone family#Injera-11-limit|Injera]]: [[26edo|26et]] 12&26 23.124
 
[[Jubilismic clan#Lemba-11-limit|Lemba]]: [[26edo|26et]] 10&16 41.563
 
[[Avicennmic temperaments#Secund|Secund]]: [[26edo|26et]] 9&17 42.562
 
[[Jubilismic clan#Crepuscular-11-limit|Crepuscular]]: [[26edo|26et]] 26&34d 40.758
 
[[Orwellismic temperaments#Quartonic-Quarto|Quarto]]: [[26edo|26et]] 26&27e 41.786
 
[[Meantone family#Mothra-Cynder|Cynder]]: [[26edo|26et]] 5e&26 55.706
 
[[Jubilismic clan#Doublewide-Cavalier|Cavalier]]: [[26edo|26et]] 4e&26 52.899
 
[[Sensipent family#Sensi-Sensa|Sensa]]: [[27edo|27et]] 19e&27 36.835
 
[[Diminished family #Demolished|Demolished]]: [[28edo|28et]] 12&28 26.574
 
[[Porcupine family|Nautilus]]: [[29edo|29et]] 15&29 26.023
 
[[Marvel temperaments|Negril]]: [[29edo|29et]] 19&29 38.679
 
[[Marvel temperaments#Negroni|Negroni]]: [[29edo|29et]] 10&29 35.296
 
[[Porcupine family#Coendou|Coendou]]: [[29edo|29et]] 7&29 49.669
 
[[Slendro clan#Wilsec|Wilsec]]: [[29edo|29et]] 9&20 41.886
 
[[Immunity family#Immunity-Impunity|Impunity]]: [[29edo|29et]] 5e&29 55.243
 
[[Immunity family#Immunity-11-limit|Immunity]]: [[29edo|29et]] 5&29 52.661
 
[[Meantone family|Mohajira]]: [[31edo|31et]] 7&24 26.064
 
[[Meantone family|Squares]]: [[31edo|31et]] 31&45e 21.636
 
[[Meantone family#Cuboctahedra|Cuboctahedra]]: [[31edo|31et]] 31&45 56.826
 
[[Meantone family#Migration|Migration]]: [[31edo|31et]] 31&100de 25.516
 
[[Marvel temperaments|Tritonic]]: [[31edo|31et]] 2&29 23.659
 
[[Starling temperaments|Casablanca]]: [[31edo|31et]] 31&42 67.291
 
[[Starling temperaments#Myna temperament-Myno|Myno]]: [[31edo|31et]] 4&27 33.434
 
[[Starling temperaments#Cypress-11-limit|Cypress]]: [[31edo|31et]] 20cde&31 42.719
 
[[Gamelismic clan#Miracle|Revelation]]: [[31edo|31et]] 21&31 32.946
 
[[Orwellismic temperaments#Diesic-11-limit|Diesic]]: [[31edo|31et]] 1ce&31 44.186
 
[[Mint temperaments#Slurpee|Slurpee]]: [[33edo|33et]] 16&33 50.514
 
[[Kleismic family|Keemun]]: [[34edo|34et]] 4&15 27.410
 
[[Tetracot family#Wollemia|Wollemia]]: [[34edo|34et]] 27e&34 37.551
 
[[Diaschismic family#Anguirus-11-limit|Anguirus]]: [[34edo|34et]] 10&24 49.253
 
[[Magic family#Muggles-11-limit|Muggles]]: [[35edo|35et]] 16&19 48.038
 
[[Greenwoodmic temperaments#Greenwood|Greenwood]]: [[35edo|35et]] 21&35 57.471
 
[[Meantone family#Liese-Liesel|Liesel]]: [[36edo|36et]] 19&36 40.721
 
[[Meantone family#Liese-Elisa|Elisa]]: [[36edo|36e]] 19e&36e 41.592
 
[[Compton family#Catnip|Catnip]]: [[36edo|36et]] 12&24 34.478
 
[[Augmented family#Niner|Niner]]: [[36edo|36et]] 9&36 34.861
 
[[Archytas clan#Beatles|Beatles]]: [[37edo|37et]] 27e&37 45.639
 
[[Augmented family|Triforce]]: [[39edo|39et]] 6&9 20.248
 
[[Schismatic family|Andromeda]]: [[41edo|41et]] 12&29 23.556
 
[[Gamelismic clan|Superkleismic]]: [[41edo|41et]] 15&26 25.659
 
[[Gamelismic clan#Miracle-Hemimiracle|Hemimiracle]]: [[41edo|41et]] 20&21 59.232
 
[[Tetracot family#Monkey|Monkey]]: [[41edo|41et]] 7&34 38.836
 
[[Tetracot family#Bunya|Bunya]]: [[41edo|41et]] 7d&41 31.332
 
[[Magic family#Hocus|Hocus]]: [[41edo|41et]] 38d&41 38.519
 
[[Magic family#Witchcraft|Witchcraft]]: [[41edo|41et]] 41&60e 30.706
 
[[Magic family#Trismegistus-11-limit|Trismegistus]]: [[41edo|41et]] 16&41 45.623
 
[[Sensamagic clan#Salsa|Salsa]]: [[41edo|41et]] 17&24 39.444
 
[[Gamelismic clan#Rodan|Varan]]: [[41edo|41et]] 41&46e 44.937
 
[[Sensamagic clan#Bohpier|Bohpier]]: [[41edo|41et]] 41&49 33.949
 
[[Tetracot family#Octacot|Octacot]]: [[41edo|41et]] 27e&41 24.078
 
[[Keemic temperaments#Quasitemp|Quato]]: [[41edo|41et]] 4e&41 41.170
 
[[Mirkwai clan#Pluto-Plutino|Plutino]]: [[41edo|41et]] 2cde&41 57.966
 
[[Augmented family#Augene|Eugene]]: [[42edo|42et]] 15&27 35.554
 
[[Marvel temperaments#Amavil|Amavil]]: [[43edo|43et]] 9&43 42.649
 
[[Starling temperaments#Kumonga-11-limit|Kumonga]]: [[43edo|43et]] 16&43 43.336
 
[[Meantone family#Flattone-11-limit|Flattone]]: [[45edo|45et]] 7&19 33.839
 
[[Starling temperaments|Sensor]]: [[46edo|46et]] 19&27 37.942
 
[[Starling temperaments|Sensus]]: [[46edo|46et]] 46&73 29.486
 
[[Hemifamity temperaments|Leapday]]: [[46edo|46et]] 29&46 38.624
 
[[Porwell temperaments|Twothirdtonic]]: [[46edo|46et]] 9&37 40.768
 
[[Gamelismic clan#Rodan-Aerodino|Aerodino]]: [[46edo|46et]] 5e&46 54.294
 
[[Amity family#Bamity|Bamity]]: [[46edo|46et]] 14c&46 35.504
 
[[Ragismic microtemperaments#Amity-Accord-11-limit|Accord]]: [[46edo|46et]] 7d&46 42.468
 
[[Starling temperaments#Vines-11-limit|Vines]]: [[46edo|46et]] 4&42 44.499
 
[[Jubilismic clan|Doublewide]]: [[48edo|48et]] 4&18 32.058
 
[[Archytas clan|Superpyth]]: [[49edo|49et]] 22&49 24.976
 
[[Archytas clan#Passion|Passion]]: [[49edo|49et]] 12&37 40.809
 
[[Kleismic family#Catalan-11-limit|Catalan]]: [[49edo|49et]] 15&49 36.894
 
[[Meantone family#Septimal meantone-Bimeantone|Bimeantone]]: [[50edo|50et]] 12&50 38.122
 
[[Porcupine family#Porky|Porky]]: [[51edo|51et]] 22&51 27.268
 
[[Semicomma family|Orwell]]: [[53edo|53et]] 9&22 15.231
 
[[Hemifamity temperaments#Tricot|Tricot]]: [[53edo|53et]] 53&70 56.134
 
[[Kleismic family#Cataclysmic|Cataclysmic]]: [[53edo|53et]] 53&140d 39.954
 
[[Amity family#Hamity|Hamity]]: [[53edo|53et]] 14c&53 42.947
 
[[Kleismic family#Kleiboh-11-limit|Kleiboh]]: [[53edo|53et]] 49&53 52.805
 
[[Maja family#Maja-11-limit|Maja]]: [[53edo|53et]] 45e&53 49.991
 
[[Schismatic family#Garibaldi-Helenus|Helenus]]: [[53edo|53et]] 12&53 35.637
 
[[Schismatic family#Hemigari|Hemigari]]: [[53edo|53et]] 29&53 50.681
 
[[Orwellismic temperaments#Quartonic-Quartz|Quartz]]: [[53edo|53et]] 26&53 53.285
 
[[Sycamore family#Sycamore|Sycamore]]: [[56edo|56et]] 18&19 55.940
 
[[Diaschismic family|Diaschismic]]: [[58edo|58et]] 12&46 25.034
 
[[Breedsmic temperaments|Hemififths]]: [[58edo|58et]] 41&58 23.498
 
[[Starling temperaments#Thuja-11-limit|Thuja]]: [[58edo|58et]] 15&43 33.078
 
[[Unicorn family#Alicorn|Alicorn]]: [[58edo|58et]] 19&58 39.156
 
[[Orwellismic temperaments#Secant-11-limit|Secant]]: [[58edo|58et]] 26&58 46.373
 
[[Orwellismic temperaments#Infraorwell-11-limit|Infraorwell]]: [[58edo|58et]] 9&49 40.721
 
[[Diaschismic family#Sruti|Sruti]]: [[58edo|58et]] 24&58 41.459
 
[[Unicorn family#Qilin|Qilin]]: [[58edo|58et]] 58&77 41.426
 
[[Breedsmic temperaments#Gorgik|Gorgik]]: [[58edo|58et]] 21&37 59.260
 
[[Porcupine family|Porcupine]]: [[59edo|59et]] 7&15 21.562
 
[[Würschmidt family#Worschmidt|Worschmidt]]: [[65edo|65et]] 31&65 33.436
 
[[Sensipent family#Hemisensi|Hemisensi]]: [[65edo|65et]] 27e&65 48.714
 
[[Porcupine family#Ammonite|Ammonite]]: [[66edo|66et]] 29&37 45.694
 
[[Kleismic family#Hemikleismic|Hemikleismic]]: [[68edo|68et]] 15&38 38.023
 
[[Gamelismic clan|Miracle]]: [[72edo|72et]] 10&31 10.684
 
[[Kleismic family|Catakleismic]]: [[72edo|72et]] 19&53 21.849
 
[[Pythagorean family|Compton]]: [[72edo|72et]] 12&72 22.235
 
[[Pythagorean family#Hours|Hours]]: [[72edo|72et]] 24&48 36.248
 
[[Kleismic family#Bikleismic|Bikleismic]]: [[72edo|72et]] 72&106 29.319
 
[[Ragismic microtemperaments#Ennealimmal-Ennealimnic|Ennealimnic]]: [[72edo|72et]] 27e&72 20.697
 
[[Ragismic microtemperaments#Ennealimmal-Ennealiminal|Ennealiminal]]: [[72edo|72et]] 27&45 31.123
 
[[Marvel temperaments#Marvolo|Marvolo]]: [[72edo|72et]] 29&43 28.965
 
[[Kleismic family#Catalytic|Catalytic]]: [[72edo|72et]] 53e&72 30.422
 
[[Marvel temperaments#Enneaportent|Enneaportent]]: [[72edo|72et]] 9&54 30.426
 
[[Starling temperaments#Casablanca temperament-Marrakesh|Marrakesh]]: [[73edo|73et]] 31&73 40.539
 
[[Starling temperaments|Valentine]]: [[77edo|77et]] 15&31 16.687
 
[[Unicorn family#Alicorn|Camahueto]] [[77edo|77et]] 19&77 65.940
 
[[Diaschismic family|Keen]]: [[78edo|78et]] 22&56 45.270
 
[[Orwellismic temperaments#Sentinel-11-limit|Sentinel]]: [[79edo|79et]] 14&17 39.595
 
[[Diaschismic family|Echidna]]: [[80edo|80et]] 22&58 25.987
 
[[Ragismic microtemperaments#Parakleismic-Paradigmic|Paradigmic]]: [[80edo|80et]] 19&80 41.720
 
[[Diaschismic family|Bidia]]: [[80edo|80et]] 12&68 40.191
 
[[Orwellismic temperaments#Quartonic-11-limit|Quartonic]]: [[80edo|80et]] 53&80 34.031
 
[[Meantone family|Meanpop]]: [[81edo|81et]] 19&31 21.543
 
[[Semicomma family#Newspeak|Newspeak]]: [[81edo|81et]] 31&84 31.438
 
[[Marvel temperaments#Merman-11-limit|Merman]]: [[84edo|84et]] 2&41 36.383
 
[[Gamelismic clan|Rodan]]: [[87edo|87et]] 5&41 23.093
 
[[Kleismic family#Clyde|Clyde]]: [[87edo|87et]] 19&68 47.41686
 
[[Misty family#Misty|Misty]]: [[87edo|87et]] 12&87 35.932
 
[[Hemimean clan#Emka-11-limit|Emka]]: [[87edo|87et]] 37&50 54.744
 
[[Meantone family|Mothra]]: [[88edo|88et]] 5&26 25.642
 
[[Starling temperaments|Myna]]: [[89edo|89et]] 31&58 16.842
 
[[Starling temperaments#Amigo-11-limit|Amigo]]: [[89edo|89et]] 43&46 43.438
 
[[Marvel temperaments|Septimin]]: [[91edo|91et]] 9&32 31.309
 
[[31st-octave temperaments #Prajapati|Prajapati]]: [[93edo|93et]] 31&93 42.959
 
[[Schismatic family|Cassandra]]: [[94edo|94et]] 41&53 27.396
 
[[Schismatic family#Sanjaab|Sanjaab]]: [[94edo|94et]] 29&94 58.040
 
[[Sensamagic clan#Magus|Magus]]: [[95edo|95et]] 46&95 45.108
 
[[Marvel temperaments#Submajor-Interpental|Interpental]]: [[96edo|96et]] 43&53 51.806
 
[[Ragismic microtemperaments|Hitchcock]]: [[99edo|99et]] 7&39 35.187
 
[[Würschmidt family#Hemiwürschmidt|Hemiwur]]: [[99edo|99et]] 6&31 29.270
 
[[Porwell temperaments#Hendecatonic|Hendecatonic]]: [[99edo|99et]] 22&55 46.088
 
[[Starling temperaments|Nusecond]]: [[101edo|101et]] 31&101 25.621
 
[[Magic family|Magic]]: [[104edo|104et]] 19&22 25.621
 
[[Meantone family|Meantone]]: [[105edo|105et]] 12&31 17.027
 
[[Starling temperaments#Bisemidim-11-limit|Bisemidim]]: [[108edo|108et]] 50&58 41.190
 
[[Leapweek]]: [[109edo|109et]] 17&46 50.679
 
[[Hemifamity temperaments|Buzzard]]: [[111edo|111et]] 53&58 34.484
 
[[Diaschismic family|Shrutar]]: [[114edo|114et]] 22&46 26.489
 
[[Marvel temperaments#Submajor-11-limit|Submajor]]: [[116edo|116et]] 10&53 50.582
 
[[Gamelismic clan|Hemithirds]]: [[118edo|118et]] 31&87 19.003
 
[[Ragismic microtemperaments|Parakleismic]]: [[118edo|118et]] 19&99 49.711
 
[[Keemic temperaments#Quasitemp|Quasitemp]]: [[119edo|119et]] 4&37 43.209
 
[[Mirkwai clan#Pluto|Pluto]]: [[121edo|121et]] 41&80 29.844
 
[[Hemimage temperaments#Subfourth-11-limit|Subfourth]]: [[121edo|121et]] 58&121 45.323
 
[[Marvel temperaments|Tritoni]]: [[122edo|122et]] 31&91 45.456
 
[[Marvel temperaments|Slender]]: [[125edo|125et]] 31&63 25.342
 
[[Diaschismic family#Srutal-11-limit|Srutal]]: [[126edo|126et]] 46&80 35.315
 
[[Würschmidt family#Würschmidt|Würschmidt]]: [[127edo|127et]] 31&96 24.413
 
[[Meantone family#Mothra-Mosura|Mosura]]: [[129edo|129et]] 31&129 31.334
 
[[Würschmidt family|Hemiwürschmidt]]: [[130edo|130et]] 31&130 21.069
 
[[Schismatic family#Sesquiquartififths|Sesquart]]: [[130edo|130et]] 41&89 29.306
 
[[11-limit_comma temperaments#Bosonic|Bosonic]]: [[130edo|130et]] 26&130 65.219
 
[[Maquila family|Hemimaquila]]: [[130edo|130et]] 9&121 47.440
 
[[Semicomma family#Borwell|Borwell]]: [[137edo|137et]] 31&106 38.377
 
[[Breedsmic temperaments#Tertiaseptal|Tertia]]: [[140edo|140et]] 31&109 30.171
 
[[Breedsmic temperaments#Fibo|Fibo]]: [[140edo|140et]] 37&103 56.514
 
[[Hemifamity temperaments#Ketchup-11-limit|Ketchup]]: [[140edo|140et]] 46&94 39.555
 
[[Hemifamity temperaments|Mystery]]: [[145edo|145et]] 29&58 34.291
 
[[Diaschismic family|Echidnic]]: [[148edo|148et]] 10&46 45.127
 
[[Sensipent family|Heinz]]: [[149edo|149et]] 46&103 42.412
 
[[Gamelismic clan#Hemiseven|Hemiseven]]: [[149edo|149et]] 5&72 28.467
 
[[Mirkwai clan|Grendel]]: [[152edo|152et]] 31&121 19.845
 
[[Mirkwai clan|Kwai]]: [[152edo|152et]] 41&111 26.219
 
[[Hemifamity temperaments#Supers|Supers]]: [[152edo|152et]] 58&94 28.240
 
[[Ragismic microtemperaments#Amity-11-limit|Amity]]: [[152edo|152et]] 53&152 31.506
 
[[Porwell temperaments#Whoops|Whoops]]: [[152edo|152et]] 15&137 43.743
 
[[Unicorn family#Alicorn|Monocerus]]: [[154edo|154et]] 58&154 52.757
 
[[Schismatic family|Guiron]]: [[159edo|159et]] 41&77 26.648
 
[[Breedsmic temperaments#Mintone|Mintone]]: [[161edo|161et]] 58&103 39.962
 
[[Marvel temperaments|Wizard]]: [[166edo|166et]] 22&50 18.539
 
[[Porwell temperaments#Polypyth|Polypyth]]: [[167edo|167et]] 46&121 51.131
 
[[Ragismic microtemperaments#Parakleismic-Parkleismic|Parkleismic]]: [[179edo|179et]] 80&179 55.844
 
[[Gamelismic clan|Unidec]]: [[190edo|190et]] 26&46 15.479
 
[[Semicomma family#Triwell-11-limit|Triwell]]: [[190edo|190et]] 31&97 29.807
 
[[Gamelismic clan#Widefourth-11-limit|Widefourth]]: [[190edo|190et]] 16&71 40.785
 
[[Breedsmic temperaments#Semihemi|Semihemi]]: [[198edo|198et]] 58&140 42.487
 
[[Breedsmic temperaments|Harry]]: [[202edo|202et]] 58&72 15.867
 
[[Breedsmic temperaments|Tertiaseptal]]: [[202edo|202et]] 31&171 35.576
 
[[Cataharry temperaments#Swetneus|Swetneus]]: [[207edo|207et]] 58&149 55.163
 
[[Kleismic family#Metakleismic|Metakleismic]]: [[208edo|208et]] 87&121 48.570
 
[[Marvel temperaments#Marvo|Marvo]]: [[209edo|209et]] 72&137 26.882
 
[[Schismatic family#Kleischismic|Kleischismic]]: [[212edo|212et]] 24&94 36.749
 
[[Octagar temperaments#Slithy-11-limit|Slithy]]: [[215edo|215et]] 94&121 45.895
 
[[Hemimean clan#Arch|Arch]]: [[217edo|217et]] 43&87 36.541
 
[[Ragismic microtemperaments|Octoid]]: [[224edo|224et]] 72&152 14.097
 
[[Schismatic family#Quanharuk|Quanharuk]]: [[224edo|224et]] 41&142 31.549
 
[[Kleismic family|Countercata]]: [[227edo|227et]] 34&53 39.770
 
[[Kleismic family|Tritikleismic]]: [[231edo|231et]] 15&57 19.333
 
[[Hemimean clan#Subpental|Subpental]]: [[241edo|241et]] 19&111 45.352
 
[[Ragismic microtemperaments#Ennealimmal|Ennealimnic]]: [[243edo|243et]] 72&171 20.347
 
[[Schismatic family|Bischismic]]: [[248edo|248et]] 12&118 28.160
 
[[31st-octave temperaments #Birds|Birds]]: [[248edo|248et]] 31&217 39.921
 
[[Quince clan#Essence|Essence]]: [[248edo|248et]] 58&190 46.447
 
[[Mirkwai clan|Mirkat]]: [[255edo|255et]] 72&183 22.126
 
[[Kleismic family|Sqrtphi]]: [[265edo|265et]] 49&72 25.515
 
[[Breedsmic temperaments|Quasiorwell]]: [[270edo|270et]] 31&208 17.540
 
[[Ragismic microtemperaments#Acrokleismic-Counteracro|Counteracro]]: [[270edo|270et]] 270&1061e 42.572
 
[[Marvel temperaments|Marvo]]: [[281edo|281et]] 72&281 31.685
 
[[Porwell temperaments#Septisuperfourth|Septisuperfourth]]: [[282edo|282et]] 22&86 24.619
 
[[Sensamagic clan|Sensa]]: [[283edo|283et]] 22&65 35.844
 
[[Kleismic family|Quadritikleismic]]: [[284edo|284et]] 4&68 23.406
 
[[Ragismic microtemperaments#Quincy|Quincy]]: [[289edo|289et]] 72&217 30.875
 
[[Hemimage temperaments#Commatic|Commatic]]: [[294edo|294et]] 58&118 30.461
 
[[Breedsmic temperaments#Neominor|Neominor]]: [[305edo|305et]] 72&161 27.958
 
[[Sensipent family#Bison-11-limit|Bison]]: [[306edo|306et]] 46&84 37.132
 
[[Breedsmic temperaments#Unthirds|Unthirds]]: [[311edo|311et]] 72&167 22.926
 
[[Porwell temperaments|Hemischis]]: [[313edo|313et]] 53&130 36.289
 
[[Ragismic microtemperaments#Semiparakleismic|Semiparakleismic]]: [[316edo|316et]] 80&118 34.208
 
[[Werckismic temperaments#Octowerck|Octowerck]]: [[320edo|320et]] 72&176 30.159
 
[[Pental family|Decal]]: [[320edo|320et]] 130&190 40.633
 
[[Breedsmic temperaments#Hemitert|Hemitert]]: [[342edo|342et]] 31&280 15.633
 
[[Ragismic microtemperaments|Hemiamity]]: [[350edo|350et]] 46&106 31.307
 
[[Stearnsmic clan #Stearnscape|Stearnscape]]: [[354edo|354et]] 72&282 32.096
 
[[Hemimage temperaments#Degrees|Degrees]]: [[360edo|360et]] 80&140 46.770
 
[[Breedsmic temperaments#Catafourth|Catafourth]]: [[363edo|363et]] 103&130 36.785
 
[[Ragismic microtemperaments#Neusec-13-limit|Neusec]]: [[388edo|388et]] 190&388 59.127
 
[[Hemifamity temperaments#Alphaquarter|Alphaquarter]]: [[391edo|391et]] 87&152 29.638
 
[[Kleismic family#Novemkleismic|Novemkleismic]]: [[405edo|405et]] 72&261 51.730
 
[[Mirkwai clan#Subsemifourth|Subsemifourth]]: [[407edo|407et]] 49&103 34.276
 
[[Ragismic microtemperaments|Semiennealimmal]]: [[441edo|441et]] 72&441 34.196
 
[[Horwell temperaments#Emkay|Emkay]]: [[535edo|535et]] 87&137 35.586
 
[[Schismatic family#Pogo|Pogo]]: [[578edo|578et]] 36&94 31.857
 
[[Ragismic microtemperaments#Quatracot-11-limit|Quatracot]]: [[638edo|638et]] 190&224 41.043
 
[[Ragismic microtemperaments#Gamera-Hemigamera|Hemigamera]]: [[646edo|646et]] 26&198 40.955
 
[[Ragismic microtemperaments#Brahmagupta|Brahmagupta]]: [[665edo|665et]] 7&217 52.190
 
[[Mirkwai clan#Eris|Eris]]: [[703edo|703et]] 31&193 27.621
 
[[Ragismic microtemperaments|Abigail]]: [[764edo|764et]] 46&132 12.860
 
[[Landscape microtemperaments#Sextile|Sextile]]: [[1092edo|1092et]] 12&270 29.677
 
[[Ragismic microtemperaments#Orga-11-limit|Orga]]: [[1106edo|1106et]] 26&244 16.188
 
[[Schismatic family#Octant-11-limit|Octant]]: [[1168edo|1168et]] 24&224 44.778
 
[[Breedsmic temperaments|Decoid]]: [[1210edo|1210et]] 130&270 18.735
 
[[Ragismic microtemperaments|Deca]]: [[1270edo|1270et]] 80&190 24.329
 
[[Ragismic microtemperaments#Ennealimmal-Trinealimmal|Trinealimmal]]: [[1323edo|1323et]] 27&243 29.812
 
[[Tricot family#Trillium|Trillium]]: [[1429edo|1429et]] 53&441 46.758
 
[[Ragismic microtemperaments#Quasithird-11-limit|Quasithird]]: [[1448edo|1448et]] 164&224 21.125
 
[[Schismatic family#Sesquiquartififths-Bisesqui|Bisesqui]]: [[1498edo|1498et]] 130&212 16.968
 
[[Vishnuzmic family#Vishnu|Vishnu]]: [[1502edo|1502et]] 118&152 14.180
 
[[Ragismic microtemperaments|Hemiennealimmal]]: [[1566edo|1566et]] 72&198 6.283
 
[[Ragismic microtemperaments#Acrokleismic-11-limit|Acrokleismic]]: [[1639edo|1639et]] 19&251 36.878
 
[[Ragismic microtemperaments#Ennealimmal-Quadraennealimmal|Quadraennealimmal]]: [[1737edo|1737et]] 342&1053 21.320
 
[[Breedsmic temperaments#Newt|Newt]]: [[1972edo|1972et]] 41&188 19.461
 
[[Ragismic microtemperaments#Supermajor-Semisupermajor|Semisupermajor]]: [[2554edo|2554et]] 80&342 12.773
 
=== 11-limit rank three ===
Name: ET w/ optimal patent val: Val name: 10^5 * badness
 
[[Archytas family #Vulcan|Vulcan]]: [[15edo|15et]] 2&3&10 57.7113
 
[[Marvel family #Potassium|Potassium]]: [[19edo|19et]] 2&9&10 46.3665
 
[[Jubilismic family #Festival|Festival]]: [[26edo|26et]] 2&10&26 68.8510
 
[[Mint family #Nickel|Nickel]]: [[28edo|28et]] 7&9&12 46.3463
 
[[Starling family #Thrasher|Thrasher]]: [[34edo|34et]] 3&4&12 48.0188
 
[[Semaphore family #Selenium|Selenium]]: [[34edo|34et]] 4&5&10 66.5377
 
[[Didymus rank three family #Calliope|Calliope]]: [[45edo|45et]] 7&12&19 52.9778
 
[[Jubilismic family #Jubilee|Jubilee]]: [[48edo|48et]] 4&12&22 55.9842
 
[[Archytas family #Ares|Ares]]: [[49edo|49et]] 3&7&12 46.8874
 
[[Porcupine rank three family #Sonic|Sonic]]: [[51edo|51et]] 7&15&51 52.3158
 
[[Nuwell family #Big Brother|Big Brother]]: [[53edo|53et]] 9&22&70 50.6556
 
[[Orwellismic family #Orwellian|Orwellian]]: [[53edo|53et]] 4&5&17 71.513
 
[[Marvel family #Prodigy|Prodigy]]: [[72edo|72et]] 2&10&29 33.4745
 
[[Rastmic temperaments #Mirwomo|Mirwomo]]: [[72edo|72et]] 7&10&24 64.0943
 
[[Gamelismic family #Gamel|Gamel]]: [[72edo|72et]] 5e&31&72 85.266
 
[[Starling family #Oxpecker|Oxpecker]]: [[77edo|77et]] 8d&15&31 69.945
 
[[Starling family #Undecimal starling|Starling]]: [[77edo|77et]] 4&15&27 67.680
 
[[Didymus rank three family #Erato|Erato]]: [[81edo|81et]] 12&19&31 55.7521
 
[[Sensamagic family #Sensawer|Sensawer]]: [[87edo|87et]] 41&46&73 79.632
 
[[Didymus rank three family #Euterpe|Euterpe]]: [[88edo|88et]] 5&12&26 53.5809
 
[[Starling family #Thrush|Thrush]]: [[89edo|89et]] 3&12&31 35.2591
 
[[Starling family #Aplonis|Aplonis]]: [[89edo|89et]] 19&31&58 64.7511
 
[[Valinorismic temperaments #Mandos|Mandos]]: [[89edo|89et]] 7&24&58 75.1090
 
[[Marvel family #Malcolm|Malcolm]]: [[94edo|94et]] 19e&41&53 124.957
 
[[Sensamagic family #Shrusus|Shrusus]]: [[95edo|95et]] 22&46&95 87.6795
 
[[Porwell family #Zeus|Zeus]]: [[99edo|99et]] 6&7&9 39.9882
 
[[Marvel family #Apollo|Apollo]]: [[104edo|104et]] 12&19&22 52.9766
 
[[Keemic family #Supermagic|Supermagic]]: [[104edo|104et]] 4&7&15 64.0789
 
[[Keemic family #Supernatural|Supernatural]]: [[104edo|104et]] 19&22&82e 88.8164
 
[[Sensamagic family #Octarod|Octarod]]: [[104edo|104et]] 19&22&49 58.0664
 
[[Orwellismic family #Guanyin|Guanyin]]: [[111edo|111et]] 9&22&58 41.1252
 
[[Valinorismic temperaments #Manwe|Manwe]]: [[111edo|111et]] 15&31&80 67.9150
 
[[Sensamagic family #Bisector|Bisector ]]: [[114edo|114et]] 14c&22&46 108.9026
 
[[Horwell family #Zelda|Zelda]]: [[118edo|118et]]: 9&22&87 64.1882
 
[[Rastmic temperaments #Parahemif|Parahemif]]: [[123edo|123et]] 17&24&58 134.547
 
[[Valinorismic temperaments #Varda|Varda]]: [[126edo|126et]] 12&22&46 72.8125
 
[[Marvel family #Minerva|Minerva]]: [[127edo|127et]] 1&9&12 38.1064
 
[[Didymus rank three family|Clio]]: [[129edo|129et]] 7&12&24 73.7590
 
[[Hemifamity family #Pele|Pele]]: [[145edo|145et]] 5&12&29 64.8199
 
[[Hemifamity family #Laka|Laka]]: [[152edo|152et]] 41&53&58 82.5317
 
[[Marvel family #Marvel|Marvel]]: [[166edo|166et]] 9&10&22 25.5033
 
[[Marvel family #Fantastic|Fantastic]]: [[166edo|166et]] 12&22&50 74.3439
 
[[Gamelismic family #Portent|Portent]]: [[190edo|190et]] 5&10&26 23.4092
 
[[Ragisma family #Beyla|Beyla]]: [[190edo|190et]] 7&19&46 72.097
 
[[Breed family #Jove|Jove]]: [[202edo|202et]] 10&31&58 24.1055
 
[[Pentacircle temperaments #Tolerant|Tolerant]]: [[208edo|208et]] 5&41&80 103.923
 
[[Hemimean family #Belobog|Belobog]]: [[248edo|248et]] 12&31&87 60.9402
 
[[Marvel family #Spectacle|Spectacle]]: [[281edo|281et]] 10&31&281 49.8669
 
[[Porwell family #Jupiter|Jupiter]]: [[282edo|282et]] 9&22&108 56.2368
 
[[Sensamagic family #Unidecimal sensamagic|Sensamagic]]: [[283edo|283et]] 5&17&19 72.231
 
[[Breed family #Agni|Agni]]: [[284edo|284et]] 4&6&27 49.3790
 
[[Kleismic rank three family #Enlil|Enlil]]: [[284edo|284et]] 4&15&38 79.8062
 
[[Werckismic temperaments #Trimyna|Trimyna]]: [[294edo|294et]] 2&29&58 81.4047
 
[[Hemimean family #Triglav|Triglav]]: [[316edo|316et]] 31&80&87 81.896
 
[[Werckismic temperaments #Varuna|Varuna]]: [[320edo|320et]] 12&26&46 41.8714
 
[[Porwell family #Hera|Hera]]: [[359edo|359et]] 46&53&84 223.1795
 
[[Canou family #Semicanou|Semicanou]]: [[410edo|410et]] 24&80&94 219.7478
 
[[Porwell family #Semiporwell|Semiporwell]]: [[480edo|480et]] 22&24&84 125.3053
 
[[Werckismic temperaments #History|History]]: [[491edo|491et]] 15&29&43 60.3636
 
[[Swetismic temperaments #Hades|Hades]]: [[578edo|578et]] 22&50&58 36.1398
 
[[Cataharry family #Albus|Albus]]: [[640edo|640et]] 19&53&58 62.1100
 
[[Mirkwai family #Indra|Indra]]: [[703edo|703et]] 10&31&152 26.6020
 
[[Lehmerismic temperaments #Hanuman|Hanuman]]: [[998edo|998et]] 15&57&152 49.965
 
[[Kalismic temperaments #Loki|Loki]]: [[1092edo|1092et]] 12&22&86 49.2550
 
[[Lehmerismic temperaments #Ganesha|Ganesha]]: [[1502edo|1502et]] 31&87&152 39.0462
 
[[Breed family #Freya|Freya]]: [[1566edo|1566et]] 10&31&167 16.9702
 
[[Lehmerismic temperaments #Tyr|Tyr]]: [[1566edo|1566et]] 15&57&183 25.8374
 
[[Breed family #Baldur|Baldur]]: [[1696edo|1696et]] 4&58&72 16.6115
 
[[Lehmerismic temperaments #Skadi|Skadi]]: [[2014edo|2014et]] 31&97&121 34.8944
 
[[Ragisma family #Thor|Thor]]: [[2554edo|2554et]] 26&46&152 8.8834
 
[[Lehmerismic temperaments #Lux|Lux]]: [[2603edo|2603et]] 41&46&137 50.834
 
[[Breed family #Ennealimmic|Ennealimmic]]: [[2619edo|2619et]] 27&45&171 27.4685
 
[[Lehmerismic temperaments #Galaxy|Galaxy]]: [[2665edo|2665et]] 46&103&121 84.057
 
[[Kalismic temperaments #Van Gogh|Van Gogh]]: [[6992edo|6992et]] 22&58&284 29.7565
 
[[Kalismic temperaments #Odin|Odin]]: [[7464edo|7464et]] 12&42&72 11.6151
 
=== 13-limit rank two ===
Name: ET w/ optimal patent val: Val name: 1000*badness
 
[[Diminished family #Septimal diminished|Diminished]]: [[4edo|4et]] 4&8d 19.509
 
[[Meantone family#Neutrominant-13-limit|Neutrominant]]: [[7edo|7et]] 7&10c 27.214
 
[[Tetracot family#Modus|Modus]]: [[7edo|7et]] 7&27e 23.806
 
[[Meantone family#Dominant-Arnold|Arnold]]: [[7edo|7et]] 5&7 23.300
 
[[Meantone family#Dominant-Dominatrix|Dominatrix]]: [[7edo|7et]] 7&12f 18.289
 
[[Dicot family#Jamesbond|Jamesbond]]: [[7edo|7et]] 7&14c 23.003
 
[[Dicot family#Jamesbond|Septimal]]: [[7edo|7et]] 7&14cf 22.569
 
[[Meantone family#Ptolemy-13-limit|Ptolemy]]: [[7edo|7et]] 7&38df 34.316
 
[[Mint temperaments|Progression]]: [[9edo|9et]] 8d&9 18.158
 
[[Marvel temperaments|Negric]]: [[9edo|9et]] 1&9 20.205
 
[[Bug family#Beep|Pentoid]]: [[9edo|9et]] 5&9 21.159
 
[[Archytas clan#Beatles|Ringo]]: [[10edo|10et]] 10&17c 22.619
 
[[Diaschismic family#Pajara-Pajaric-13-limit|Pajaric]]: [[10edo|10et]] 10&12f 20.461
 
[[Diaschismic family#Pajara-Pajaro|Pajaro]]: [[10edo|10et]] 10&22f 27.355
 
[[Augmented family#August|Augustus]]: [[12edo|12et]] 9&12 22.236
 
[[Meantone family#Dominant-Dominion|Dominion]]: [[12edo|12et]] 5&12 27.295
 
[[Augmented family#Hexe-13-limit|Hexe]]: [[12edo|12et]] 6f&12f 35.946
 
[[Mint temperaments#Ripple|Ripple]]: [[12edo|12f]] 1ce&12f 31.639
 
[[Mint temperaments#Smate|Smate]]: [[14edo|14et]] 14&17c 36.836
 
[[Trienstonic clan|Opossum]]: [[15edo|15et]] 7d&8d 19.389
 
[[Trienstonic clan#Kangaroo|Kangaroo]]: [[15edo|15et]] 2cde&15 32.653
 
[[Archytas clan#Blacksmith|Blacksmith]]: [[15edo|15et]] 5&10 20.498
 
[[Archytas clan#Blacksmith-Farrier-13-limit|Archytas clan]]: [[15edo|15et]] 5e&15 22.325
 
[[Archytas clan#Progress|Progress]]: [[15edo|15et]] 2&15 26.214
 
[[Porcupine family#Porcupine|Porcupine]]: [[15edo|15et]] 7&15 21.276
 
[[Porcupine family#Nautilus|Belauensis]]: [[15edo|15et]] 14c&15 29.816
 
[[Kleismic family#Keemun-13-limit-Kumbaya|Kumbaya]]: [[15edo|15et]] 4&15 31.633
 
[[Kleismic family#Keemun-Darjeeling-13-limit Darjeeling|Darjeeling]]: [[15edo|15et]] 15&19e 21.445
 
[[Augmented family#Augene-11-limit-13-limit|Augene]]: [[15edo|15et]] 3&15 20.785
 
[[Augmented family#Augene-11-limit-Ogene|Ogene]]: [[15edo|15et]] 12&15 22.890
 
[[Pelogic family#Armodue-13-limit Armodue|Armodue]]: [[16edo|16et]] 7&9 19.351
 
[[Meantone family#Dominant-Domination-13-limit|Domination]]: [[17edo|17c]] 5e&12e 27.435
 
[[Meantone family#Dominant-13-limit|Dominant]]: [[17edo|17c]] 12f&17c 24.108
 
[[Archytas clan#Progress|Progressive]]: [[17edo|17c]] 2f&15f 32.721
 
[[Marvel temperaments|Negri]]: [[19edo|19et]] 9&10 17.833
 
[[Starling temperaments|Sensis]]: [[19edo|19et]] 8d&19 20.017
 
[[Meantone family|Meanenneadecal]]: [[19edo|19et]] 12f&19 21.182
 
[[Meantone family#Septimal meantone-Meanpop-Meanplop|Meanplop]]: [[19edo|19et]] 12e&19 27.666
 
[[Meantone family#Godzilla-13-limit|Godzilla]]: [[19edo|19et]] 14cf&19 22.503
 
[[Meantone family#Undevigintone-13-limit|Undevigintone]]: [[19edo|19et]] 19&38df 22.933
 
[[Meantone family#Liese-Lisa|Lisa]]: [[19edo|19et]] 2cde&19 36.144
 
[[Kleismic family#Keemun-13-limit|Keemun]]: [[19edo|19et]] 4&19 29.749
 
[[Kleismic family#Keemun-Qeema-13-limit|Qeema]]: [[19edo|19et]] 4ef&19 29.419
 
[[Kleismic family#Cataleptic-13-limit|Cataleptic]]: [[19edo|19et]] 19&34d 27.343
 
[[Unicorn family#Rhinoceros|Rhinoceros]]: [[19edo|19et]] 1ce&19 39.343
 
[[Magic family#Spell-13-limit|Spell]]: [[19edo|19et]] 6&19 45.591
 
[[Magic family#Spell-Cantrip|Cantrip]]: [[19edo|19et]] 6f&19 41.603
 
[[Magic family#Muggles-13-limit|Muggles]]: [[19edo|19et]] 16&19 30.386
 
[[Augmented family|August]]: [[21edo|21et]] 9&21 18.448
 
[[Augmented family#Oodako-13-limit|Oodako]]: [[21edo|21et]] 6&21 42.323
 
[[Magic family#Magic-Telepathy-13-limit telepathy|Telepathy]]: [[22edo|22et]] 19e&22 25.522
 
[[Magic family#Magic-13-limit-Sorcery|Sorcery]]: [[22edo|22et]] 19&22 25.829
 
[[Magic family#Divination-13-limit|Divination]]: [[22edo|22et]] 22f&60e 34.551
 
[[Semicomma family#Blair|Blair]]: [[22edo|22et]] 9&22 23.086
 
[[Porcupine family#Hedgehog|Hedgehog]]: [[22edo|22et]] 14cf&22
 
[[Diaschismic family#Pajara-13-limit|Pajarous]]: [[22edo|22et]] 10&22 25.176
 
[[Diaschismic family#Pajara-13-limit|Pajara]]: [[22edo|22et]] 12&22 27.642
 
[[Porcupine family#Porcupine|Porkpie]]: [[22edo|22et]] 7&22 26.043
 
[[Porcupine family#Ceratitid|Ceratitid]]: [[22edo|22et]] 1ce&22 44.739
 
[[Porcupine family#Hedgehog|Urchin]]: [[22edo|22et]] 14c&22f 25.233
 
[[Jubilismic clan#Doublewide-Fleetwood-13-limit|Fleetwood]]: [[22edo|22et]] 22&84bdf 31.835
 
[[Archytas clan#Superpyth|Suprapyth]]: [[22edo|22et]] 17&22 36.336
 
[[Comic family#Comic-13-limit|Comic]]: [[22edo|22et]] 2cde&22 41.470
 
[[Magic family#Astrology-13-limit|Astrology]]: [[22edo|22et]] 6&16 34.376
 
[[Archytas clan#Quasisuper-Quasisupra-13-limit|Quasisupra]]: [[22edo|22et]] 17c&22 30.219
 
[[Compton family#Catnip|Catnip]]: [[24edo|24et]] 12f&24 28.363
 
[[Augmented family|Triforce]]: [[24edo|24et]] 9&15 20.248
 
[[Augmented family#Hemiaug-13-limit|Hemiaug]]: [[24edo|24et]] 3de&24 30.159
 
[[Diminished family #Hemidim|Hemidim]]: [[24edo|24et]] 4ef&24 39.030
 
[[Diminished family #Octonion|Octonion]]: [[24edo|24et]] 24&32c 30.597
 
[[Meantone family#Mohamaq-13-limit|Mohamaq]]: [[24edo|24et]] 17c&24 28.738
 
[[Meantone family#Godzilla-Varan-13-limit|Varan]]: [[24edo|24et]] 19e&24 25.676
 
[[Meantone family#Injera-13-limit|Injera]]: [[26edo|26et]] 26&104bcf 21.565
 
[[Meantone family#Flattone-13-limit|Flattone]]: [[26edo|26et]] 7&19 22.260
 
[[Jubilismic clan#Lemba-13-limit|Lemba]]: [[26edo|26et]] 10&16 25.477
 
[[Jubilismic clan#Crepuscular-13-limit|Crepuscular]]: [[26edo|26et]] 26&34d 24.368
 
[[Orwellismic temperaments#Quartonic-Quarto-13-limit|Quarto]]: [[26edo|26et]] 26&27e 27.692
 
[[Meantone family#Mothra-Cynder-13-limit|Cynder]]: [[26edo|26et]] 5e&26 34.124
 
[[Avicennmic temperaments#Secund|Secundly]]: [[26edo|26et]] 9&17 26.212
 
[[Jubilismic clan#Doublewide-Cavalier-13-limit|Cavalier]]: [[26edo|26et]] 4ef&26 35.040
 
[[Sensipent family#Sensi-Sensa|Sensa]]: [[27edo|27et]] 19e&27 23.258
 
[[Tetracot family#Ponens|Ponens]]: [[27edo|27et]] 7&27 39.043
 
[[Archytas clan#Fervor|Fervor]]: [[27edo|27e]] 2f&27e 39.705
 
[[Tetracot family#Octacot|Octocat]]: [[27edo|27e]] 14cf&27e 27.601
 
[[Starling temperaments#Myna temperament-Minah|Minah]]: [[27edo|27e]] 4ef&27e 27.568
 
[[Avicennmic temperaments|Roman]]: [[29edo|29et]] 3&23 30.043
 
[[Porcupine family#Porky|Porky]]: [[29edo|29et]] 22&29 26.543
 
[[Porcupine family#Coendou|Coendou]]: [[29edo|29et]] 7&29 30.233
 
[[Porcupine family|Nautilus]]: [[29edo|29et]] 15&29 22.285
 
[[Marvel temperaments|Negril]]: [[29edo|29et]] 19&29 24.383
 
[[Marvel temperaments#Negroni-13-limit|Negroni]]: [[29edo|29et]] 10&29 21.559
 
[[Slendro clan#Wilsec|Wilsec]]: [[29edo|29et]] 9&20 25.192
 
[[Immunity family#Immunity-Impunity-13-limit|Impunity]]: [[29edo|29et]] 5e&29 33.196
 
[[Immunity family#Immunity-13-limit|Immunity]]: [[29edo|29et]] 5&29 37.078
 
[[Trienstonic clan#Quindecic|Quindecic]]: [[30edo|30et]] 15&30 28.944
 
[[Meantone family|Meantone]]: [[31edo|31et]] 12f&31 18.048
 
[[Meantone family|Squares]]: [[31edo|31et]] 17c&31 25.514
 
[[Meantone family#Squares-Agora|Agora]]: [[31edo|31et]] 31&76e 24.522
 
[[Meantone family#Mohajira-13-limit|Mohajira]]: [[31edo|31et]] 7&24 23.388
 
[[Semicomma family|Winston]]: [[31edo|31et]] 9&31 19.931
 
[[Gamelismic clan#Miracle-Revelation-13-limit|Revelation]]: [[31edo|31et]] 21&31 29.452
 
[[Marvel temperaments#Tritonic|Tritonic]]: [[31edo|31et]] 29&31 22.993
 
[[Starling temperaments|Lupercalia]]: [[31edo|31et]] 15&31 21.328
 
[[Starling temperaments#Casablanca|Murakuc]]: [[31edo|31et]] 31&73f 41.394
 
[[Starling temperaments#Nusecond|Nusecond]]: [[31edo|31et]] 31&70f 23.323
 
[[Starling temperaments#Cypress-13-limit|Cypress]]: [[31edo|31et]] 11cdeef&31 37.849
 
[[Starling temperaments#Maneh|Maneh]]: [[31edo|31et]] 4ef&31 29.868
 
[[31st-octave temperaments #Prajapati|Prajapati]]: [[31edo|31et]] 31&93f 37.885
 
[[Würschmidt family#Würschmidt-13-limit|Würschmidt]]: [[31edo|31et]] 31&65d 23.593
 
[[Würschmidt family#Würschmidt-Worseschmidt|Worseschmidt]]: [[31edo|31et]] 3def&31 34.382
 
[[Würschmidt family#Hemiwürschmidt-11-limit-Hemithir|Hemithir]]: [[31edo|31et]] 31&68e 31.199
 
[[Würschmidt family#Hemiwürschmidt-Hemiwur-Hemiwar|Hemiwar]]: [[31edo|31et]] 6f&31 44.886
 
[[Orwellismic temperaments#Sentinel-13-limit|Sentinel]]: [[31edo|31et]] 14&17 37.408
 
[[Orwellismic temperaments#Diesic-13-limit|Diesic]]: [[31edo|31et]] 1ce&31 38.116
 
[[Hemimean clan#Semisept-11-limit-Semishly|Semishly]]: [[31edo|31et]] 31&49f 28.408
 
[[Mint temperaments#Slurpee|Slurpee]]: [[33edo|33et]] 16&33 33.102
 
[[Kleismic family#Keemun-13-limit-Kema|Kema]]: [[34edo|34et]] 15&19 22.749
 
[[Tetracot family#Wollemia|Wollemia]]: [[34edo|34et]] 27e&34 31.219
 
[[Diaschismic family#Anguirus-13-limit|Anguirus]]: [[34edo|34et]] 10&24 30.829
 
[[Avicennmic temperaments#Secund|Secund]]: [[35edo|35et]] 9&35 49.684
 
[[Greenwoodmic temperaments#Greenwood|Greenwood]]: [[35edo|35et]] 21&35 54.009
 
[[Meantone family#Liese-13-limit|Liesel]]: [[36edo|36et]] 19&36 27.304
 
[[Augmented family#Niner-13-limit|Niner]]: [[36edo|36et]] 9&36 24.143
 
[[Archytas clan#Beatles|Beatles]]: [[37edo|37et]] 27e&37 30.161
 
[[Meantone family#Injera-Enjera|Enjera]]: [[38edo|38et]] 12f&26f 26.542
 
[[Magic family#Astrology-Horoscope|Horoscope]]: [[38edo|38et]] 16&38 35.284
 
[[Gamelismic clan|Miraculous]]: [[41edo|41et]] 10&31 18.669
 
[[Gamelismic clan|Superkleismic]]: [[41edo|41et]] 15&26 21.478
 
[[Gamelismic clan#Rodan-Varan-13-limit|Varan]]: [[41edo|41et]] 5e&41 32.284
 
[[Gamelismic clan#Miracle-Hemimiracle|Hemimiracle]]: [[41edo|41et]] 20&21 43.151
 
[[Schismatic family|Andromeda]]: [[41edo|41et]] 29&41 20.749
 
[[Tetracot family|Octacot]]: [[41edo|41et]] 27e&41 23.276
 
[[Tetracot family#Octacot|Octopod]]: [[41edo|41et]] 14cf&41 28.326
 
[[Tetracot family#Monkey|Monkey]]: [[41edo|41et]] 7&34 28.410
 
[[Tetracot family#Bunya|Bunya]]: [[41edo|41et]] 7d&41 24.886
 
[[Magic family|Magic]]: [[41edo|41et]] 19&41 21.509
 
[[Magic family#Hocus-13-limit|Hocus]]: [[41edo|41et]] 41&79d 30.280
 
[[Magic family#Witchcraft-13-limit|Witchcraft]]: [[41edo|41et]] 41&60e 23.547
 
[[Magic family#Trismegistus-13-limit|Trismegistus]]: [[41edo|41et]] 16&41 33.081
 
[[Sensamagic clan#Bohpier|Bohpier]]: [[41edo|41et]] 41&90ef 24.864
 
[[Sensamagic clan#Salsa|Salsa]]: [[41edo|41et]] 17&24 30.793
 
[[Mirkwai clan#Pluto-Plutino-13-limit|Plutino]]: [[41edo|41et]] 2cde&41 40.182
 
[[Keemic temperaments#Quasitemp-Quato-13-limit|Quato]]: [[41edo|41et]] 4ef&41 30.081
 
[[Octagar temperaments#Slendi|Slendi]]: [[41edo|41et]] 41&124ef 43.644
 
[[Meantone family#Jerome|Jerome]]: [[43edo|43et]] 26&43 29.285
 
[[Marvel temperaments#Amavil|Amavil]]: [[43edo|43et]] 9&43 25.791
 
[[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone|Meridetone]]: [[43edo|43et]] 43&117df 26.421
 
[[Starling temperaments#Kumonga-13-limit|Kumonga]]: [[43edo|43et]] 16&43 28.920
 
[[Jubilismic clan#Vigin|Vigin]]: [[44edo|44et]] 22&44 29.849
 
[[Starling temperaments|Sensor]]: [[46edo|46et]] 19&27 25.474
 
[[Starling temperaments|Sensus]]: [[46edo|46et]] 46&73 20.789
 
[[Starling temperaments|Dwynwen]]: [[46edo|46et]] 15&46 23.461
 
[[Hemifamity temperaments|Leapday]]: [[46edo|46et]] 29&46 24.732
 
[[Porwell temperaments|Twothirdtonic]]: [[46edo|46et]] 9&37 25.941
 
[[Amity family#Bamity|Bamity]]: [[46edo|46et]] 14cf&46 30.885
 
[[Sensamagic clan#Magus|Magus]]: [[46edo|46et]] 3de&46 43.024
 
[[Gamelismic clan#Rodan|Aerodactyl]]: [[46edo|46et]] 5&46 33.986
 
[[Gamelismic clan#Rodan-Aerodino-13-limit|Aerodino]]: [[46edo|46et]] 5e&46 35.836
 
[[Starling temperaments#Vines-13-limit|Vines]]: [[46edo|46et]] 4&42 29.693
 
[[Archytas clan|Superpyth]]: [[49edo|49et]] 22&49 24.673
 
[[Meantone family#Septimal meantone-Bimeantone-13-limit|Bimeantone]]: [[50edo|50et]] 12f&50 28.817
 
[[Kleismic family#Cataclysmic|Cataclysmic]]: [[53edo|53et]] 53&140d 22.554
 
[[Kleismic family#Hemikleismic|Hemikleismic]]: [[53edo|53et]] 15&53 26.005
 
[[Semicomma family#Orwell-13-limit|Orwell]]: [[53edo|53et]] 22&31 19.718
 
[[Semicomma family#Doublethink|Doublethink]]: [[53edo|53et]] 9&44 27.120
 
[[Hemifamity temperaments#Tricot|Tricot]]: [[53edo|53et]] 53&70 32.102
 
[[Amity family#Hamity|Hamity]]: [[53edo|53et]] 14cf&53 29.753
 
[[Kleismic family#Kleiboh-13-limit|Kleiboh]]: [[53edo|53et]] 4ef&53 31.074
 
[[Maja family#Maja-13-limit|Maja]]: [[53edo|53et]] 45ef&53 27.532
 
[[Schismatic family#Garibaldi-Helenus-13-limit Helenus|Helenus]]: [[53edo|53et]] 53&118d 26.284
 
[[Schismatic family#Hemigari-13-limit|Hemigari]]: [[53edo|53et]] 29&53 27.464
 
[[Orwellismic temperaments#Quartonic-Quartz-13-limit|Quartz]]: [[53edo|53et]] 26&53 28.818
 
[[Sycamore family#Sycamore|Sycamore]]: [[56edo|56et]] 18&19 34.295
 
[[Diaschismic family|Diaschismic]]: [[58edo|58et]] 46&58 18.926
 
[[Starling temperaments|Myna]]: [[58edo|58et]] 31&58 17.125
 
[[Breedsmic temperaments|Hemififths]]: [[58edo|58et]] 41&58 19.090
 
[[Orwellismic temperaments#Infraorwell-13-limit|Infraorwell]]: [[58edo|58et]] 9&58 23.683
 
[[Starling temperaments#Thuja-13-limit|Thuja]]: [[58edo|58et]] 15&43 22.838
 
[[Unicorn family#Alicorn|Alicorn]]: [[58edo|58et]] 19&58 23.667
 
[[Starling temperaments#Bisemidim-13-limit|Bisemidim]]: [[58edo|58et]] 50&58 23.877
 
[[Diaschismic family#Sruti|Sruti]]: [[58edo|58et]] 24&58 23.791
 
[[Unicorn family#Qilin|Qilin]]: [[58edo|58et]] 58&77 22.842
 
[[Breedsmic temperaments#Gorgik|Gorgik]]: [[58edo|58et]] 21&37 32.205
 
[[31st-octave temperaments #Gallium|Gallium]]: [[62edo|62et]] 31&62 25.484
 
[[Starling temperaments#Valentine temperament-Semivalentine|Semivalentine]]: [[62edo|62et]] 16&30 32.749
 
[[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone|Hemimeantone]]: [[62edo|62et]] 43&62 31.433
 
[[Porcupine family|Ammonite]]: [[66edo|66et]] 29&37 27.168
 
[[Würschmidt family#Hemiwürschmidt-Hemiwur-13-limit|Hemiwur]]: [[68edo|68et]] 6&31 28.432
 
[[Gamelismic clan|Manna]]: [[72edo|72et]] 41&72 17.012
 
[[Gamelismic clan|Hendec]]: [[72edo|72et]] 26&46 17.707
 
[[Kleismic family|Catakleismic]]: [[72edo|72et]] 19&53 16.883
 
[[Marvel temperaments|Lizard]]: [[72edo|72et]] 22&50 21.781
 
[[Breedsmic temperaments#Neominor|Neominor]]: [[72edo|72et]] 72&161f 26.942
 
[[Pythagorean family#Compton temperament|Compton]]: [[72edo|72et]] 72&228f 21.852
 
[[Pythagorean family#Compton temperament|Comptone]]: [[72edo|72et]] 12&72 25.144
 
[[Pythagorean family#Hours|Hours]]: [[72edo|72et]] 24&72 26.931
 
[[Kleismic family#Bikleismic|Bikleismic]]: [[72edo|72et]] 72&106 21.814
 
[[Marvel temperaments#Marvolo|Marvolo]]: [[72edo|72et]] 29&43 21.470
 
[[Gamelismic clan#Miracle-Semimiracle|Semimiracle]]: [[72edo|72et]] 10&62 24.622
 
[[Kleismic family#Catalytic-13-limit|Catalytic]]: [[72edo|72et]] 19e&72 22.337
 
[[Marvel temperaments#Enneaportent-13-limit|Enneaportent]]: [[72edo|72et]] 9&54 22.322
 
[[Ragismic microtemperaments#Ennealimmal-Ennealimmic-Ennealim|Ennealim]]: [[72edo|72et]] 27e&72 20.697
 
[[Ragismic microtemperaments#Ennealimmal-Ennealiminal-13-limit|Ennealiminal]]: [[72edo|72et]]  27&72 30.325
 
[[Starling temperaments#Casablanca|Marrakesh]]: [[73edo|73et]] 31&73 40.774
 
[[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone|Grosstone]]: [[74edo|74et]] 12&31 25.899
 
[[Starling temperaments|Valentino]]: [[77edo|77et]] 31&46 20.665
 
[[Unicorn family#Alicorn|Camahueto]] [[77edo|77et]] 19&77 36.155
 
[[Diaschismic family|Echidna]]: [[80edo|80et]] 22&58 23.679
 
[[Diaschismic family|Bidia]]: [[80edo|80et]] 12&68 41.137
 
[[Ragismic microtemperaments#Parakleismic|Paradigmic]]: [[80edo|80et]] 19&80 35.781
 
[[Orwellismic temperaments#Quartonic-13-limit|Quartonic]]: [[80edo|80et]] 53&80 23.875
 
[[Meantone family|Meanpop]]: [[81edo|81et]] 19&31 20.883
 
[[Magic family#Soothsaying|Soothsaying]]: [[82edo|82et]] 22&60 55.443
 
[[Orwellismic temperaments#Secant-13-limit|Secant]]: [[84edo|84et]] 26&58 46.373
 
[[Gamelismic clan|Rodan]]: [[87edo|87et]] 41&46 18.448
 
[[Kleismic family#Clyde|Clyde]]: [[87edo|87et]] 19&68 26.842
 
[[Misty family#Misty|Misty]]: [[87edo|87et]] 12f&87 27.820
 
[[Hemimean clan#Emka-13-limit|Emka]]: [[87edo|87et]] 37&50 29.741
 
[[Meantone family#Mothra|Mothra]]: [[88edo|88et]] 5&26 23.954
 
[[Starling temperaments#Amigo-13-limit|Amigo]]: [[89edo|89et]] 43&46 30.666
 
[[Marvel temperaments#Septimin-13-limit|Septimin]]: [[91edo|91et]] 9&41 23.117
 
[[31st-octave temperaments #Prajapati|Kumhar]]: [[93edo|93et]] 31&93 48.582
 
[[Marvel temperaments|Slender]]: [[94edo|94et]] 31&63 25.913
 
[[Schismatic family#Sanjaab-13-limit|Sanjaab]]: [[94edo|94et]] 29&94 33.849
 
[[Hemifamity temperaments#Supers|Supers]]: [[94edo|94et]] 58&94 21.644
 
[[Marvel temperaments#Submajor-Interpental-13-limit|Interpental]]: [[96edo|96et]] 43&53 29.680
 
[[Meantone family#Mothra|Mosura]]: [[98edo|98et]] 31&67 36.857
 
[[Ragismic microtemperaments#Amity-Hitchcock-13-limit|Hitchcock]]: [[99edo|99et]] 7&39 22.448
 
[[Diaschismic family|Echidnic]]: [[102edo|102et]] 10&46 28.874
 
[[Gamelismic clan|Benediction]]: [[103edo|103et]] 31&72 15.715
 
[[Gamelismic clan#Miracle-Phicordial|Phicordial]]: [[103edo|103et]] 10&103 33.198
 
[[Gamelismic clan#Miracle-Hemisecordite|Hemisecordite]]: [[103edo|103et]] 41&62 25.589
 
[[Magic family#Magic-13-limit-Necromancy|Necromancy]]: [[104edo|104et]] 22&41 25.275
 
[[Sensamagic clan#Leapweek|Leapweek]]: [[109edo|109et]] 17&46 32.727
 
[[Hemifamity temperaments|Buzzard]]: [[111edo|111et]] 53&58 18.842
 
[[Hemimean clan#Semisept-13-limit|Semisept]]: [[111edo|111et]]  31&80 25.204
 
[[Mirkwai clan#Kwai-13-limit|Kwai]]: [[111edo|111et]] 41&111 24.555
 
[[Diaschismic family|Shrutar]]: [[114edo|114et]] 46&68 28.057
 
[[Marvel temperaments#Submajor-13-limit|Submajor]]: [[116edo|116et]] 10&53 27.689
 
[[Schismatic family|Guiron]]: [[118edo|118et]] 41&77 28.444
 
[[Gamelismic clan#Hemithirds-13-limit|Hemithirds]]: [[118edo|118et]] 31&56 21.738
 
[[Schismatic family#Kleischismic|Kleischismic]]: [[118edo|118et]] 24&94 37.640
 
[[Mirkwai clan|Grendel]]: [[121edo|121et]] 31&121 24.839
 
[[Mirkwai clan#Pluto|Pluto]]: [[121edo|121et]] 41&80 25.717
 
[[Hemimage temperaments#Subfourth-13-limit|Subfourth]]: [[121edo|121et]] 58&121 23.800
 
[[Breedsmic temperaments|Harry]]: [[130edo|130et]] 58&72 13.046
 
[[26th-octave temperaments#Bosonic|Bosonic]]: [[130edo|130et]] 26&130 32.946
 
[[Sensipent family#Bison-13-limit|Bison]]: [[130edo|130et]] 46&84 23.504
 
[[Schismatic family#Sesquiquartififths-Sesquart-13-limit|Sesquart]]: [[130edo|130et]] 41&89 22.396
 
[[Porwell temperaments#Septisuperfourth|Septisuperquad]]: [[130edo|130et]] 22&108 33.038
 
[[Maquila family|Hemimaquila]]: [[130edo|130et]] 9&121 24.445
 
[[Kleismic family|Countercata]]: [[140edo|140et]] 34&53 20.156
 
[[Hemimage temperaments#Degrees|Degrees]]: [[140edo|140et]] 80&140 32.718
 
[[Hemifamity temperaments#Ketchup-13-limit|Ketchup]]: [[140edo|140et]] 46&94 24.824
 
[[Breedsmic temperaments#Fibo|Fibo]]: [[140edo|140et]] 37&103 27.429
 
[[Pythagorean family#Omicronbeta temperament|Omicronbeta]]: [[144edo|144et]] 72&144 29.956
 
[[Sensipent family|Heinz]]: [[149edo|149et]] 46&103 25.779
 
[[Gamelismic clan#Hemiseven-13-limit|Hemiseven]]: [[149edo|149et]] 5&72 21.900
 
[[Ragismic microtemperaments#Octoid-Octopus|Octopus]]: [[152edo|152et]] 72&152 21.679
 
[[Unicorn family#Alicorn|Monocerus]]: [[154edo|154et]] 58&154 28.795
 
[[Kleismic family|Tritikleismic]]: [[159edo|159et]] 15&72 15.652
 
[[Breedsmic temperaments#Mintone|Mintone]]: [[161edo|161et]] 58&103 21.849
 
[[Marvel temperaments|Gizzard]]: [[166edo|166et]] 72&166 20.252
 
[[Porwell temperaments#Polypyth|Polypyth]]: [[167edo|167et]] 46&121 30.292
 
[[Breedsmic temperaments#Tertiaseptal|Tertiaseptal]]: [[171edo|171et]] 31&171 36.876
 
[[Ragismic microtemperaments#Parakleismic-Parkleismic-13-limit|Parkleismic]]: [[179edo|179et]] 80&179 36.559
 
[[Mirkwai clan|Mirkat]]: [[183edo|183et]] 72&111 18.632
 
[[Gamelismic clan|Ekadash]]: [[190edo|190et]] 72&118 20.381
 
[[Gamelismic clan#Widefourth-13-limit|Widefourth]]: [[190edo|190et]] 16&71 21.636
 
[[Kleismic family|Sqrtphi]]: [[193edo|193et]] 72&121 20.040
 
[[Misty family#Hemimist|Hemimist]]: [[198edo|198et]] 87&111 22.923
 
[[Breedsmic temperaments#Semihemi|Semihemi]]: [[198edo|198et]] 58&140 21.188
 
[[Ragismic microtemperaments#Amity-13-limit|Amity]]: [[205edo|205et]] 53&205 28.008
 
[[Hemifamity temperaments|Quanic]]: [[205edo|205et]] 94&111 32.481
 
[[Cataharry temperaments#Swetneus|Swetneus]]: [[207edo|207et]] 58&149 28.876
 
[[Kleismic family|Metakleismic]]: [[208edo|208et]] 87&121 24.371
 
[[Kleismic family|Quadritikleismic]]: [[212edo|212et]] 68&72 18.731
 
[[Octagar temperaments#Slithy-13-limit|Slithy]]: [[215edo|215et]] 94&121 28.492
 
[[Hemimean clan#Arch|Arch]]: [[217edo|217et]] 43&87 19.504
 
[[Ragismic microtemperaments|Octoid]]: [[224edo|224et]] 72&224 15.274
 
[[Schismatic family#Quanharuk-13-limit|Quanharuk]]: [[224edo|224et]] 41&142 21.392
 
[[Hemifamity temperaments|Mystery]]: [[232edo|232et]] 29&58 18.591
 
[[Hemimean clan#Subpental|Subpental]]: [[241edo|241et]] 19&111 23.940
 
[[Ragismic microtemperaments#Ennealimmal|Ennealimnic]]: [[243edo|243et]] 72&171 20.250
 
[[Quince clan#Essence|Essence]]: [[248edo|248et]] 58&190 26.107
 
[[Mirkwai clan#Subsemifourth|Subsemifourth]]: [[255edo|255et]] 103&255 28.387
 
[[Ragismic microtemperaments|Hemiennealimmal]]: [[270edo|270et]] 72&198 12.505
 
[[Ragismic microtemperaments#Acrokleismic-13-limit|Acrokleismic]]: [[270edo|270et]] 19&251 26.818
 
[[Ragismic microtemperaments#Acrokleismic-Counteracro-13-limit|Counteracro]]: [[270edo|270et]] 270&1331c 26.028
 
[[Porwell temperaments#Septisuperfourth|Septisuperfourth]]: [[282edo|282et]] 130&282 22.887
 
[[Escapade family#Escaped|Escaped]]: [[283edo|283et]] 22&65 31.366
 
[[Schismatic family#Sextilifourths|Sextilifourths]]: [[289edo|289et]] 29&130 25.276
 
[[Ragismic microtemperaments#Quincy|Quincy]]: [[289edo|289et]] 72&145 23.862
 
[[Würschmidt family#Hemiwürschmidt-11-limit-13-limit|Hemiwürschmidt]]: [[291edo|291et]] 31&130 23.074
 
[[Schismatic family#Hemischis|Hemischis]]: [[313edo|313et]] 53&130 20.816
 
[[Werckismic temperaments#Octowerck|Octowerck]]: [[320edo|320et]] 72&248 27.632
 
[[Quintile family#Decile|Decile]]: [[320edo|320et]] 130&190 23.948
 
[[Kleismic family#Novemkleismic|Novemkleismic]]: [[333edo|333et]] 72&261 39.072
 
[[Breedsmic temperaments#Catafourth|Catafourth]]: [[363edo|363et]] 103&130 21.694
 
[[Schismatic family|Bischismic]]: [[378edo|378et]] 12&118 28.722
 
[[Ragismic microtemperaments#Neusec|Neusec]]: [[388edo|388et]] 190&198 30.941
 
[[Ragismic microtemperaments#Gamera-Hemigamera-13-limit|Hemigamera]]: [[422edo|422et]] 26&198 20.416
 
[[Ragismic microtemperaments|Semiennealimmal]]: [[441edo|441et]] 72&441 26.122
 
[[31st-octave temperaments #Birds|Birds]]: [[465edo|465et]] 31&217 35.680
 
[[Horwell temperaments#Emkay|Emkay]]: [[535edo|535et]] 87&137 17.853
 
[[26th-octave temperaments#Fermionic|Fermionic]]: [[546edo|546et]] 130&286 43.581
 
[[Schismatic family#Pogo-13-limit|Pogo]]: [[578edo|578et]] 36&94 17.514
 
[[Ragismic microtemperaments#Quatracot-13-limit|Quatracot]]: [[638edo|638et]] 190&224 22.643
 
[[Breedsmic temperaments#Unthirds|Unthirds]]: [[694edo|694et]] 72&311 20.888
 
[[Schismatic family#Octant-13-limit|Octant]]: [[696edo|696et]] 24&224 30.425
 
[[Ragismic microtemperaments#Quasithird-13-limit|Quasithird]]: [[836edo|836et]] 164&224 29.501
 
[[Breedsmic temperaments#Newt|Newt]]: [[851edo|851et]] 41&229 13.830
 
[[Breedsmic temperaments|Decoid]]: [[940edo|940et]] 130&270 13.475
 
[[Ragismic microtemperaments#Ennealimmal|Semihemiennealimmal]] [[954edo|954et]] 126&144 13.104
 
[[Vishnuzmic family#Vishnu-Acyuta|Acyuta]]: [[962edo|962et]] 270&692 15.805
 
[[Ragismic microtemperaments|Deca]]: [[1000edo|1000et]] 80&190 16.810
 
[[Breedsmic temperaments|Quasiorwell]]: [[1111edo|1111et]] 31&239 17.921
 
[[Ragismic microtemperaments|Abigail]]: [[1258edo|1258et]] 46&178 8.856
 
[[Tricot family#Trillium|Trillium]]: [[1429edo|1429et]] 53&441 19.393
 
[[Vishnuzmic family#Vishnu-Ananta|Ananta]]: [[1468edo|1468et]] 118&152 23.678
 
=== 13-limit rank three ===
Name: ET w/ optimal patent val: Val name: 10^5 * badness
 
[[Starling family #Mockingbird|Mockingbird]]: [[15edo|15et]] 3&4&15 85.942
 
[[Starling family #Catbird|Catbird]]: [[19edo|19et]] 4&12f&19 90.475
 
[[Marvel family #Potassium|Potassium]]: [[19edo|19et]] 9&10&11 73.346
 
[[Mint family #Nickel|Nickel]]: [[28edo|28et]] 7&9&21 64.705
 
[[Semaphore family #Negric|Negric]]: [[29edo|29et]] 1&9&10 80.756
 
[[Starling family #Nightingale|Nightingale]]: [[31edo|31et]] 3&15&28 83.714
 
[[Starling family #Thrasher|Thrasher]]: [[34edo|34et]] 12&15&19 87.636
 
[[Semaphore family #Selenium|Selenium]]: [[34edo|34et]] 5&9&10 78.368
 
[[Sengic family #Krypton|Krypton]]: [[36edo|36et]] 9&10&36 72.673
 
[[Gamelismic family #Foreboding|Foreboding]]: [[41edo|41et]] 5&10&26 87.267
 
[[Marvel family #Prodigy|Prodigy]]: [[41edo|41et]] 10&29&31 73.639
 
[[Starling family #Veery|Veery]]: [[46edo|46et]] 12&15&46 99.122
 
[[Marvel family #Athene|Athene]]: [[53edo|53et]] 12f&22&53 81.781
 
[[Starling family #Thrush|Thrush]]: [[58edo|58et]] 31&46&58 67.663
 
[[Starling family #Bluebird|Bluebird]]: [[58edo|58et]] 12&15&31 91.548
 
[[Starling family #Aplonis|Aplonis]]: [[58edo|58et]] 19&31&58 82.078
 
[[Breed family #Jofur|Jofur]]: [[58edo|58et]] 10&31&58 74.932
 
[[Rastmic temperaments #Parahemif|Parahemif]]: [[58edo|58et]] 17&24&58 119.366
 
[[Marvel family #Deecee|Deecee]]: [[72edo|72et]] 9&22&41 92.048
 
[[Marvel family #Prodigy|Prodigious]]: [[72edo|72et]] 2&29&41 89.974
 
[[Marvel family #Marvelcat|Marvelcat]]: [[72edo|72et]] 9&10&44 99.966
 
[[Ragisma family #Beyla|Beyla]]: [[72edo|72et]] 7&19&46 83.962
 
[[Valinorismic temperaments #Varda|Varda]]: [[80edo|80et]] 22&46&58 97.041
 
[[Sensamagic family #Sensawer|Sensawer]]: [[87edo|87et]] 41&46&73 92.807
 
[[Marvel family #Tripod|Tripod]]: [[91edo|91et]] 9&10&31 74.546
 
[[Marvel family #Isis|Isis]]: [[94edo|94et]] 10&22&31 86.583
 
[[Marvel family #Malcolm|Malcolm]]: [[94edo|94et]] 19e&41&53 107.452
 
[[Marvel family #Undecimal marvel|Marvel]]: [[103edo|103et]] 19&22&31 68.977
 
[[Marvel family #Prodigy|Prodigal]]: [[103edo|103et]] 31&72&84 88.910
 
[[Marvel family #Mirage|Mirage]]: [[103edo|103et]] 10&31&62 73.850
 
[[Marvel family #Apollo|Apollo]]: [[104edo|104et]] 22&29&41 103.106
 
[[Swetismic temperaments #Cerberus|Cerberus]]: [[130edo|130et]] 22&50&58 76.512
 
[[Gamelismic family #Ominous|Ominous]]: [[149edo|149et]] 5&26&46 75.055
 
[[Gamelismic family #Portending|Portending]]: [[159edo|159et]] 15&26&46 62.715
 
[[Gamelismic family #Momentous|Momentous]]: [[164edo|164et]] 10&31&46 83.202
 
[[Marvel family #Hecate|Hecate]]: [[166edo|166et]] 19&41&53 72.113
 
[[Marvel family #Marvell|Marvell]]: [[166edo|166et]] 9&31&63 86.160
 
[[Valinorismic temperaments #Ulmo|Ulmo]]: [[179edo|179et]] 7&39&80 93.162
 
[[Mirkwai family #Vibhu|Vibhu]]: [[183edo|183et]] 31&72&111 82.598
 
[[Gamelismic family #Portentous|Portentous]]: [[190edo|190et]] 15&31&56 66.119
 
[[Mirkwai family #Vish|Vish]]: [[193edo|193et]] 41&72&121 92.976
 
[[Swetismic temperaments #Minos|Minos]]: [[193edo|193et]] 9&54&58 72.381
 
[[Hemifamity family #Namaka|Namaka]]: [[198edo|198et]] 29&53&58 78.124
 
[[Hemifamity family #Laka|Laka]]: [[205edo|205et]] 41&53&58 82.186
 
[[The Archipelago #Kujuku|Kujuku]] [[208edo|208et]] 24&29&58 105.976
 
[[Pentacircle temperaments #Tolerant|Tolerant]]: [[208edo|208et]] 41&46&80 102.099
 
[[Marvel family #Spectacle|Spectacle]]: [[209edo|209et]] 31&72&209 100.924
 
[[Breed family #Agni|Agni]]: [[212edo|212et]] 6&31&72 92.251
 
[[Mirkwai family #Yajna|Yajna]]: [[224edo|224et]] 31&72&121 69.986
 
[[Hemifamity family #Pele|Pele]]: [[232edo|232et]] 29&41&46 70.328
 
[[Werckismic temperaments #Trimyna|Trimyna]]: [[232edo|232et]] 29&31&56 81.405
 
[[Breed family #Jovial|Jovial]]: [[243edo|243et]] 41&58&72 62.380
 
[[Lehmerismic temperaments #Borneo|Borneo]]: [[270edo|270et]] 15&72&111 54.937
 
[[Werckismic temperaments #History|History]]: [[289edo|289et]] 15&29&43 53.955
 
[[Kleismic rank three family #Enlil|Enlil]]: [[299edo|299et]] 15&19&53 68.005
 
[[Cataharry family #Madagascar|Madagascar]]: [[313edo|313et]] 19&53&58 56.006
 
[[Porwell family #Hera|Hera]]: [[313edo|313et]] 46&53&84 129.736
 
[[Hemifamity family #Akea|Akea]]: [[321edo|321et]] 7&34&46 82.191
 
[[Porwell family #Semiporwell|Semiporwell]]: [[328edo|328et]] 46&68&84 122.026
 
[[Breed family #Jovis|Jovis]]: [[363edo|363et]] 31&58&72 54.221
 
[[Canou family #Semicanou|Semicanou]]: [[410edo|410et]] 94&198&212 297.443
 
[[Lehmerismic temperaments #Hanuman|Hanuman]]: [[535edo|535et]] 15&72&137 65.278
 
[[Swetismic temperaments #Hades|Hades]]: [[578edo|578et]] 36&58&72 53.531
 
[[Breed family #Vili|Vili]]: [[643edo|643et]] 37&93&103 73.821
 
[[Mirkwai family #Shibi|Shibi]]: [[703edo|703et]] 41&72&111 72.094
 
[[Breed family #Greenland|Greenland]]: [[940edo|940et]] 58&72&198 44.343
 
[[The Archipelago #Baffin|Baffin]]: [[940edo|940et]] 34&43&53 60.443
 
[[Breed family #Ennealimmic|Ennealimmic]]: [[981edo|981et]] 27&72&171 75.488
 
[[Breed family #Zisa|Zisa]]: [[1241edo|1241et]] 21&31&109 82.974
 
[[Ragisma family #Thunor|Thunor]]: [[1258edo|1258et]] 26&46&178 34.135
 
[[Breed family #Frigg|Frigg]]: [[1344edo|1344et]] 6&58&103 93.387
 
[[Ragisma family #Donar|Donar]]: [[1448edo|1448et]] 46&80&144 32.154
 
[[Ragisma family #Rym|Rym]]: [[1870edo|1870et]] 46&106&118 54.933
 
[[Lehmerismic temperaments #Galaxy|Galaxy]]: [[2125edo|2125et]] 46&103&121 46.311
 
[[Lehmerismic temperaments #Lux|Lux]]: [[2333edo|2333et]] 41&46&137 36.015
 
[[Breed family #Freya|Freya]]: [[2615edo|2615et]] 10&31&229 85.515
 
== See also ==
* [[Associated temperament]]
 
{{todo
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[[Category:Regular temperament theory]]
[[Category:Val]]
[[Category:Lists]]

Latest revision as of 12:34, 21 August 2025

The optimal patent val for a regular temperament is the unique patent val that supports the temperament with the lowest error.

Given any temperament, which is characterized by the commas it tempers out, there is a finite list of patent vals that temper out all the commas of the temperament in the same subgroup. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the one which has the lowest TE error; this is the (TE) optimal patent val for the temperament. Note that other definitions of error lead to different results.

On this wiki, the optimal patent val for each temperament is given as the last patent val in the optimal ET sequence, or stated explicitly in case it is not a member of the sequence.

Instructions

By tempering a JI scale using the N-edo found on the list below we automatically temper it to the corresponding temperament. This can be done in Scala using the Quantize command: either type in "Quantize/consistent N" on the bottom, or use the pull-down menu under "Modify", check the box saying "Consistent" and type N (without a decimal point) into "Resolution".

To limit the search range when finding the optimal patent val a useful observation is this: given N-edo, and an odd prime q ≤ p, if d is the absolute value in cents of the difference between the tuning of q given by the POTE tuning and the POTE tuning rounded to the nearest N-edo value, then d < 600/N, from which it follows that N < 600/d. Likewise, if e is the absolute value of the error of q in the patent val tuning, then e < 600/N and so N < 600/e. If N-edo defines an optimal patent val, then the patent val will be identical to the val obtained by rounding the POTE tuning to the nearest N-edo value. We have two distances from the patent val, one to the POTE tuning and one to the the JI tuning, both bounded by 600/N, and so by the triangle inequality the distance from the JI tuning to the POTE tuning, which is the error of the prime q in the POTE tuning, is bounded by 1200/N. Hence, N < 1200/error(q). If now we take the minimum value for 1200/error(prime) for all the odd primes up to p, we obtain an upper bound for N.

Examples

Below are tabulated some values. In each case an identifier which uniquely identifies the temperament in question is given. In the codimension one case, where the temperament is defined by a single comma, the comma is given and used as a name. In other cases, for a temperament of rank n, n independent vals are given. Normally this is by way of integers conjoined by ampersands, such as 2&10 for 7-limit pajara. This tells us we can use the 7-limit patent vals for 2 and 10 to define the temperament. In case n independent patent vals cannot be found, vals using the wart notation are given; this adjusts the nth prime mapping to its second-best value by appending the n-th lower-case letter in alphabetical order. Thus, "12f" adjusts a patent val for 12 in the 13-limit or above, for instance ⟨12 19 28 34 42 44], to ⟨12 19 28 34 42 45] (which is actually a better mapping, and hence more useful for this purpose.)

5-limit rank two

Comma: ET w/ optimal patent val: 1000 * badness

16/15: 8et 14.884

648/625: 12et 47.231

27/25: 14et 32.801

25/24: 17et 13.028

250/243: 22et 30.778

135/128: 23et 39.556

128/125: 39et 22.315

3125/3072: 60et 39.163

2048/2025: 80et 19.915

81/80: 81et 7.381

20000/19683: 109et 48.518

393216/390625: 164et 40.603

2109375/2097152: 296et 40.807

15625/15552: 458et 13.234

78732/78125: 539et 35.220

32805/32768: 749et 4.259

1600000/1594323: 873et 21.960

6115295232/6103515625: 1400et 31.181

1224440064/1220703125: 1496et 43.729

274877906944/274658203125: 1559et 20.576

31381059609/31250000000: 2760et 82.423

7629394531250/7625597484987: 3501et 17.191

7-limit rank two

Name: ET w/ optimal patent val: Val name: 1000*badness

Pater: 3et 3&11b 53.001

Flat: 4et 3&4 25.381

Father: 5et 3d&5 21.312

Mother: 5et 2&3 24.152

Sharptone: 5et 5&7d 24.848

Baba: 5et 1&5 44.321

Quint: 5et 5&15cd 48.312

Mite: 5et 1cdd&5 54.770

Walid: 6et 2&6 48.978

Dicot: 7et 4&7 19.935

Jamesbond: 7et 7&14c 41.714

Oxygen: 8et 7d&8 59.866

Beep: 9et 4&5 18.638

Progression: 9et 9&17c 48.356

Deflated: 9et 3&9 59.079

Fluorine: 9et 9&20bd 55.623

Sharp: 10et 3d&7d 28.942

Decimal: 10et 4&10 28.334

Sodium: 11et 4&11 55.814

Dominant: 12et 5&7 20.690

Diminished: 12et 4&12 22.401

August: 12et 9&12 26.459

Hexe: 12et 6&12 57.730

Schism: 12et 12&29de 56.648

Ripple: 12et 12&23 59.735

Blacksmith: 15et 5&10 25.640

Opossum: 15et 7d&8d 40.650

Inflated: 15et 15&48bc 54.729

Armodue: 16et 7&9 49.038

Dichotic: 17et 3&7 37.565

Octokaidecal: 18et 10&18 36.747

Uncle: 18et 5&18 72.653

Negri: 19et 1&9 26.483

Godzilla: 19et 5&19 26.747

Keemun: 19et 4&15 27.408

Wallaby: 19ccdd 2d&5c 58.468

Gorgo: 21et 5&16 46.385

Pajara: 22et 2&10 20.033

Hedgehog: 22et 14c&22 43.983

Lemba: 26et 10&16 62.208

Augene: 27et 3&12 24.816

Niner: 27et 9&18 67.157

Beatles: 27et 10&27 45.872

Nautilus: 29et 15&29 57.420

Mothra: 31et 5&26 37.146

Squares: 31et 31&45 45.993

Immunity: 34et 5&29 77.631

Injera: 38et 12&26 31.130

Triforce: 39et 6&9 54.988

Magic: 41et 19&41 18.918

Superkleismic: 41et 15&26 47.932

Quasitemp: 41et 4&37 60.269

Flattone: 45et 7&19 38.553

Sensi: 46et 19&27 25.622

Vines: 46et 4&42 78.049

Doublewide: 48et 4&18 43.462

Superpyth: 49et 5&17 32.318

Passion: 49et 12&37 62.327

Porky: 51et 22&51 54.389

Submajor: 53et 10&33 60.533

Liese: 55et 19&55 46.706

Sycamore: 56et 18&19 62.018

Diaschismic: 58et 12&34 37.914

Porcupine: 59et 7&15 41.057

Kumonga: 70et 16&27 87.500

Miracle: 72et 10&21 16.742

Wizard: 72et 22&50 40.846

Unicorn 77et 19&58 40.913

Bidia: 80et 12&56 56.474

Quartonic: 80et 26&27 42.632

Meantone: 81et 12&19 13.707

Myna: 89et 4&27 27.044

Septimin: 91et 9&32 54.502

Sfourth: 91et 45&46 123.291

Garibaldi: 94et 12&29 21.644

Misty: 99et 12&87 36.802

Nusecond: 101et 31&101 50.389

Octacot: 109et 27&41 33.845

Semisept: 111et 18&31 50.472

Buzzard: 111et 5&48 47.963

Guiron: 118et 36&41 47.544

Hemithirds: 118et 25&31 44.284

Hemikleismic: 121et 15&38 52.054

Pluto: 121et 41&80 57.514

Tritonic: 122et 2&29 47.578

Gravid: 123et 58&123 47.283

Slender: 125et 1&31 56.934

Merman: 125et 2&41 55.078

Rodan: 128et 5&41 37.112

Subpental: 130et 19&111 54.303

Bison: 130et 8&38 70.375

Orwell: 137et 9&22 20.375

Tertiaseptal: 171et 31&109 12.995

Septidiasemi: 171et 10&151 44.115

Pontiac: 171et 53&118 14.133

Tsaharuk: 171et 17&77 30.697

Mitonic: 171et 46&125 25.184

Mutt: 171et 3&84 28.406

Fifthplus: 171et 22&149 25.840

Pnict: 171et 15&141 45.660

Tokko: 171et 5&166 44.417

Seniority: 171et 26&145 44.877

Valentine: 185et 15&31 31.056

Sensei: 187et 19&84 59.218

Unidec: 190et 26&46 38.393

Catakleismic: 197et 19&53 21.501

Quadritikleismic: 212et 4&68 39.231

Hemiseven: 221et 5&72 56.557

Octoid: 224et 72&152 42.670

Compton: 228et 12&60 35.686

Tritikleismic: 231et 15&57 56.337

Mirkat: 255et 72&183 59.376

Decoid: 270et 10&120 33.902

Acrokleismic 270et 19&251 56.184

Septisuperfourth: 282et 22&86 59.241

Hemischis: 313et 24&53 45.817

Hemiwürschmidt: 328et 6&31 20.307

Hemififths: 338et 41&58 22.243

Amity: 350et 7&39 23.649

Bischismic: 378et 12&118 54.744

Nessafof: 381et 15&69 45.478

Septiquarter: 391et 5&94 53.760

Parakleismic: 415et 19&80 27.431

Gamera: 422et 26&73 37.648

Sengagen: 446et 49&50 57.978

Chromat: 456et 60&99 57.499

Countercata: 473et 34&53 52.128

Harry: 534et 58&72 34.077

Ennealimmal: 612et 27&45 3.610

Quinmite: 701et 4&95 37.322

Semidimfourth: 875et 91&99 55.245

Quasiorwell: 1111et 31&177 35.832

Amicable: 1131et 99&212 45.473

Vulture: 1133et 53&164 36.985

Emmthird 1255et 58&113 16.736

Septichrome 1308et 60&111 16.814

Sesquiquartififths: 1498et 41&89 11.244

Brahmagupta: 1547et 7&217 29.122

Maviloid: 1614et 76&99 57.632

Osiris: 1696et 157&171 28.307

Term: 1722et 12&159 19.950

Neptune: 1778et 35&68 23.427

Abigail: 1798et 46&132 37.000

Qak: 1831et 50&121 29.267

Enneadecal: 2185et 19&152 10.954

Newt: 2201et 41&188 41.878

Subneutral: 2236et 31&348 45.792

Orga: 2482et 26&244 40.236

Trillium: 4569et 53&441 30.852

Supermajor: 6214et 80&171 10.836

Semidimi: 8419et 171&863 15.075

Domain: 22038et 171&1164 13.979

7-limit rank three

Comma: ET w/ optimal patent val: 10^6 * badness

36/35: 12et 63.675

49/48: 19et 115.514

875/864: 41et 212.413

525/512: 45et 476.454

686/675: 46et 320.094

50/49: 48et 127.208

64/63: 49et 98.719

1029/1000: 55et 678.164

3125/3087: 94et 613.731

1728/1715: 111et 187.341

2430/2401: 137et 518.625

65625/65536: 171et 172.601

126/125: 185et 69.867

1029/1024: 190et 176.105

225/224: 197et 36.517

4000/3969: 215et 215.550

16875/16807: 224et 341.931

245/243: 283et 121.191

6144/6125: 381et 142.375

5120/5103: 391et 153.052

3136/3125: 446et 160.039

19683/19600: 587et 300.987

10976/10935: 695et 199.139

4802000/4782969: 1131et 1121.894

703125/702464: 2185et 149.828

2401/2400: 2749et 15.288

420175/419904: 4306et 86.449

4375/4374: 8419et 11.665

250047/250000: 12555et 21.301

78125000/78121827: 101654et 20.457

11-limit rank two

Name: ET w/ optimal patent val: Val name: 1000*badness

Fervor: 2et 2&27e 52.054

Decimated: 4et 4&10e 31.456

Coleto: 4et 4&27e 48.687

Semafour: 5et 5&14c 28.510

Neutrominant: 7et 7&10c 40.240

Arnold: 7et 5&7 26.141

Hystrix: 7et 7&15d 44.944

Dicot: 7et 4e&7 19.854

Jamesbond: 7et 7&14c 23.524

Modus: 7et 7&27e 35.149

Ptolemy: 7et 7&38d 58.785

Negric: 9et 1&9 30.617

Progression: 9et 8d&9 26.050

Superpelog: 9et 9&14c 28.535

Octokaidecal: 10et 10&18e 30.235

Decimal: 10et 10&14c 26.712

Sharp: 10et 10&17d 22.366

Ringo: 10et 10&17c 32.863

Dichosis: 10et 3&10 41.361

Decibel: 10et 4&6 32.385

Diminished: 12et 4&12 22.132

Pajaric: 12et 2&10 23.798

Dominant: 12et 5&12 24.180

Domineering: 12et 7&12 21.978

Lahoh: 12et 12&14ce 43.062

Duodecim: 12et 12&24d 30.536

Schism: 12et 12&41d 37.482

Injerous: 12e 12e&14c 38.577

Hexe: 12et 6&12 38.412

Ripple: 12et 1ce&12 38.811

[Diminished family #Hemidim|Hemidim]]: 12et 12&20b 54.965

Smate: 14et 14&17c 42.518

Opossum: 15et 7d&8d 22.325

Kangaroo: 15et 2cde&15 43.195

Augene: 15et 3&12 19.613

Progress: 15et 2&13 31.036

Darjeeling: 15et 15&19e 27.648

Ferrier: 15et 5e&15 29.200

Inflated: 15et 15&48bce 31.171

Armodue: 16et 7&9 27.211

Bipelog: 16et 2&16 35.694

Dichotic: 17et 7&10 30.680

Sidi: 17et 14c&17 32.957

Domination: 17c 5e&12e 36.562

Negri: 19et 9&10 26.190

Meanenneadecal: 19et 12&19 21.182

Flattone 19et 7&19 33.839

Godzilla: 19et 14c&19 28.947

Undevigintone: 19et 19&38d 36.387

Meanundeci: 19e 12e&19e 31.539

Lisa: 19et 2cde&19 54.829

Horcrux: 19et 19&60e 39.282

Spell: 19et 6&19 59.791

Rhinoceros: 19et 1ce&19 59.319

Triton: 19et 2&19 45.675

Qeema: 19et 4e&19 40.056

Cataleptic: 19et 19&34d 44.335

Oodako: 21et 6&21 59.192

Pajara: 22et 12&22 20.343

Pajarous: 22et 10&22 28.349

Telepathy: 22et 19e&22 27.109

Hedgehog: 22et 14c&22 23.095

Ceratitid: 22et 1ce&22 51.319

Vigintiduo: 22et 22&66de 48.372

Astrology: 22et 22&60de 39.151

Divination: 22et 22&38d 35.864

Fleetwood: 22et 22&26e 35.202

Quasisupra: 22et 17c&22 32.203

Comic: 22et 2cde&22 45.052

Hemipaj: 22et 2&20 38.890

Mohamaq: 24et 17c&24 36.207

Baragon: 24et 5&19 35.673

Varan: 24et 19e&24 39.647

Hemiaug: 24et 24&27e 38.232

Hemidim: 24et 4e&24 56.576

Octonion: 24et 24&32c 30.597

Injera: 26et 12&26 23.124

Lemba: 26et 10&16 41.563

Secund: 26et 9&17 42.562

Crepuscular: 26et 26&34d 40.758

Quarto: 26et 26&27e 41.786

Cynder: 26et 5e&26 55.706

Cavalier: 26et 4e&26 52.899

Sensa: 27et 19e&27 36.835

Demolished: 28et 12&28 26.574

Nautilus: 29et 15&29 26.023

Negril: 29et 19&29 38.679

Negroni: 29et 10&29 35.296

Coendou: 29et 7&29 49.669

Wilsec: 29et 9&20 41.886

Impunity: 29et 5e&29 55.243

Immunity: 29et 5&29 52.661

Mohajira: 31et 7&24 26.064

Squares: 31et 31&45e 21.636

Cuboctahedra: 31et 31&45 56.826

Migration: 31et 31&100de 25.516

Tritonic: 31et 2&29 23.659

Casablanca: 31et 31&42 67.291

Myno: 31et 4&27 33.434

Cypress: 31et 20cde&31 42.719

Revelation: 31et 21&31 32.946

Diesic: 31et 1ce&31 44.186

Slurpee: 33et 16&33 50.514

Keemun: 34et 4&15 27.410

Wollemia: 34et 27e&34 37.551

Anguirus: 34et 10&24 49.253

Muggles: 35et 16&19 48.038

Greenwood: 35et 21&35 57.471

Liesel: 36et 19&36 40.721

Elisa: 36e 19e&36e 41.592

Catnip: 36et 12&24 34.478

Niner: 36et 9&36 34.861

Beatles: 37et 27e&37 45.639

Triforce: 39et 6&9 20.248

Andromeda: 41et 12&29 23.556

Superkleismic: 41et 15&26 25.659

Hemimiracle: 41et 20&21 59.232

Monkey: 41et 7&34 38.836

Bunya: 41et 7d&41 31.332

Hocus: 41et 38d&41 38.519

Witchcraft: 41et 41&60e 30.706

Trismegistus: 41et 16&41 45.623

Salsa: 41et 17&24 39.444

Varan: 41et 41&46e 44.937

Bohpier: 41et 41&49 33.949

Octacot: 41et 27e&41 24.078

Quato: 41et 4e&41 41.170

Plutino: 41et 2cde&41 57.966

Eugene: 42et 15&27 35.554

Amavil: 43et 9&43 42.649

Kumonga: 43et 16&43 43.336

Flattone: 45et 7&19 33.839

Sensor: 46et 19&27 37.942

Sensus: 46et 46&73 29.486

Leapday: 46et 29&46 38.624

Twothirdtonic: 46et 9&37 40.768

Aerodino: 46et 5e&46 54.294

Bamity: 46et 14c&46 35.504

Accord: 46et 7d&46 42.468

Vines: 46et 4&42 44.499

Doublewide: 48et 4&18 32.058

Superpyth: 49et 22&49 24.976

Passion: 49et 12&37 40.809

Catalan: 49et 15&49 36.894

Bimeantone: 50et 12&50 38.122

Porky: 51et 22&51 27.268

Orwell: 53et 9&22 15.231

Tricot: 53et 53&70 56.134

Cataclysmic: 53et 53&140d 39.954

Hamity: 53et 14c&53 42.947

Kleiboh: 53et 49&53 52.805

Maja: 53et 45e&53 49.991

Helenus: 53et 12&53 35.637

Hemigari: 53et 29&53 50.681

Quartz: 53et 26&53 53.285

Sycamore: 56et 18&19 55.940

Diaschismic: 58et 12&46 25.034

Hemififths: 58et 41&58 23.498

Thuja: 58et 15&43 33.078

Alicorn: 58et 19&58 39.156

Secant: 58et 26&58 46.373

Infraorwell: 58et 9&49 40.721

Sruti: 58et 24&58 41.459

Qilin: 58et 58&77 41.426

Gorgik: 58et 21&37 59.260

Porcupine: 59et 7&15 21.562

Worschmidt: 65et 31&65 33.436

Hemisensi: 65et 27e&65 48.714

Ammonite: 66et 29&37 45.694

Hemikleismic: 68et 15&38 38.023

Miracle: 72et 10&31 10.684

Catakleismic: 72et 19&53 21.849

Compton: 72et 12&72 22.235

Hours: 72et 24&48 36.248

Bikleismic: 72et 72&106 29.319

Ennealimnic: 72et 27e&72 20.697

Ennealiminal: 72et 27&45 31.123

Marvolo: 72et 29&43 28.965

Catalytic: 72et 53e&72 30.422

Enneaportent: 72et 9&54 30.426

Marrakesh: 73et 31&73 40.539

Valentine: 77et 15&31 16.687

Camahueto 77et 19&77 65.940

Keen: 78et 22&56 45.270

Sentinel: 79et 14&17 39.595

Echidna: 80et 22&58 25.987

Paradigmic: 80et 19&80 41.720

Bidia: 80et 12&68 40.191

Quartonic: 80et 53&80 34.031

Meanpop: 81et 19&31 21.543

Newspeak: 81et 31&84 31.438

Merman: 84et 2&41 36.383

Rodan: 87et 5&41 23.093

Clyde: 87et 19&68 47.41686

Misty: 87et 12&87 35.932

Emka: 87et 37&50 54.744

Mothra: 88et 5&26 25.642

Myna: 89et 31&58 16.842

Amigo: 89et 43&46 43.438

Septimin: 91et 9&32 31.309

Prajapati: 93et 31&93 42.959

Cassandra: 94et 41&53 27.396

Sanjaab: 94et 29&94 58.040

Magus: 95et 46&95 45.108

Interpental: 96et 43&53 51.806

Hitchcock: 99et 7&39 35.187

Hemiwur: 99et 6&31 29.270

Hendecatonic: 99et 22&55 46.088

Nusecond: 101et 31&101 25.621

Magic: 104et 19&22 25.621

Meantone: 105et 12&31 17.027

Bisemidim: 108et 50&58 41.190

Leapweek: 109et 17&46 50.679

Buzzard: 111et 53&58 34.484

Shrutar: 114et 22&46 26.489

Submajor: 116et 10&53 50.582

Hemithirds: 118et 31&87 19.003

Parakleismic: 118et 19&99 49.711

Quasitemp: 119et 4&37 43.209

Pluto: 121et 41&80 29.844

Subfourth: 121et 58&121 45.323

Tritoni: 122et 31&91 45.456

Slender: 125et 31&63 25.342

Srutal: 126et 46&80 35.315

Würschmidt: 127et 31&96 24.413

Mosura: 129et 31&129 31.334

Hemiwürschmidt: 130et 31&130 21.069

Sesquart: 130et 41&89 29.306

Bosonic: 130et 26&130 65.219

Hemimaquila: 130et 9&121 47.440

Borwell: 137et 31&106 38.377

Tertia: 140et 31&109 30.171

Fibo: 140et 37&103 56.514

Ketchup: 140et 46&94 39.555

Mystery: 145et 29&58 34.291

Echidnic: 148et 10&46 45.127

Heinz: 149et 46&103 42.412

Hemiseven: 149et 5&72 28.467

Grendel: 152et 31&121 19.845

Kwai: 152et 41&111 26.219

Supers: 152et 58&94 28.240

Amity: 152et 53&152 31.506

Whoops: 152et 15&137 43.743

Monocerus: 154et 58&154 52.757

Guiron: 159et 41&77 26.648

Mintone: 161et 58&103 39.962

Wizard: 166et 22&50 18.539

Polypyth: 167et 46&121 51.131

Parkleismic: 179et 80&179 55.844

Unidec: 190et 26&46 15.479

Triwell: 190et 31&97 29.807

Widefourth: 190et 16&71 40.785

Semihemi: 198et 58&140 42.487

Harry: 202et 58&72 15.867

Tertiaseptal: 202et 31&171 35.576

Swetneus: 207et 58&149 55.163

Metakleismic: 208et 87&121 48.570

Marvo: 209et 72&137 26.882

Kleischismic: 212et 24&94 36.749

Slithy: 215et 94&121 45.895

Arch: 217et 43&87 36.541

Octoid: 224et 72&152 14.097

Quanharuk: 224et 41&142 31.549

Countercata: 227et 34&53 39.770

Tritikleismic: 231et 15&57 19.333

Subpental: 241et 19&111 45.352

Ennealimnic: 243et 72&171 20.347

Bischismic: 248et 12&118 28.160

Birds: 248et 31&217 39.921

Essence: 248et 58&190 46.447

Mirkat: 255et 72&183 22.126

Sqrtphi: 265et 49&72 25.515

Quasiorwell: 270et 31&208 17.540

Counteracro: 270et 270&1061e 42.572

Marvo: 281et 72&281 31.685

Septisuperfourth: 282et 22&86 24.619

Sensa: 283et 22&65 35.844

Quadritikleismic: 284et 4&68 23.406

Quincy: 289et 72&217 30.875

Commatic: 294et 58&118 30.461

Neominor: 305et 72&161 27.958

Bison: 306et 46&84 37.132

Unthirds: 311et 72&167 22.926

Hemischis: 313et 53&130 36.289

Semiparakleismic: 316et 80&118 34.208

Octowerck: 320et 72&176 30.159

Decal: 320et 130&190 40.633

Hemitert: 342et 31&280 15.633

Hemiamity: 350et 46&106 31.307

Stearnscape: 354et 72&282 32.096

Degrees: 360et 80&140 46.770

Catafourth: 363et 103&130 36.785

Neusec: 388et 190&388 59.127

Alphaquarter: 391et 87&152 29.638

Novemkleismic: 405et 72&261 51.730

Subsemifourth: 407et 49&103 34.276

Semiennealimmal: 441et 72&441 34.196

Emkay: 535et 87&137 35.586

Pogo: 578et 36&94 31.857

Quatracot: 638et 190&224 41.043

Hemigamera: 646et 26&198 40.955

Brahmagupta: 665et 7&217 52.190

Eris: 703et 31&193 27.621

Abigail: 764et 46&132 12.860

Sextile: 1092et 12&270 29.677

Orga: 1106et 26&244 16.188

Octant: 1168et 24&224 44.778

Decoid: 1210et 130&270 18.735

Deca: 1270et 80&190 24.329

Trinealimmal: 1323et 27&243 29.812

Trillium: 1429et 53&441 46.758

Quasithird: 1448et 164&224 21.125

Bisesqui: 1498et 130&212 16.968

Vishnu: 1502et 118&152 14.180

Hemiennealimmal: 1566et 72&198 6.283

Acrokleismic: 1639et 19&251 36.878

Quadraennealimmal: 1737et 342&1053 21.320

Newt: 1972et 41&188 19.461

Semisupermajor: 2554et 80&342 12.773

11-limit rank three

Name: ET w/ optimal patent val: Val name: 10^5 * badness

Vulcan: 15et 2&3&10 57.7113

Potassium: 19et 2&9&10 46.3665

Festival: 26et 2&10&26 68.8510

Nickel: 28et 7&9&12 46.3463

Thrasher: 34et 3&4&12 48.0188

Selenium: 34et 4&5&10 66.5377

Calliope: 45et 7&12&19 52.9778

Jubilee: 48et 4&12&22 55.9842

Ares: 49et 3&7&12 46.8874

Sonic: 51et 7&15&51 52.3158

Big Brother: 53et 9&22&70 50.6556

Orwellian: 53et 4&5&17 71.513

Prodigy: 72et 2&10&29 33.4745

Mirwomo: 72et 7&10&24 64.0943

Gamel: 72et 5e&31&72 85.266

Oxpecker: 77et 8d&15&31 69.945

Starling: 77et 4&15&27 67.680

Erato: 81et 12&19&31 55.7521

Sensawer: 87et 41&46&73 79.632

Euterpe: 88et 5&12&26 53.5809

Thrush: 89et 3&12&31 35.2591

Aplonis: 89et 19&31&58 64.7511

Mandos: 89et 7&24&58 75.1090

Malcolm: 94et 19e&41&53 124.957

Shrusus: 95et 22&46&95 87.6795

Zeus: 99et 6&7&9 39.9882

Apollo: 104et 12&19&22 52.9766

Supermagic: 104et 4&7&15 64.0789

Supernatural: 104et 19&22&82e 88.8164

Octarod: 104et 19&22&49 58.0664

Guanyin: 111et 9&22&58 41.1252

Manwe: 111et 15&31&80 67.9150

Bisector : 114et 14c&22&46 108.9026

Zelda: 118et: 9&22&87 64.1882

Parahemif: 123et 17&24&58 134.547

Varda: 126et 12&22&46 72.8125

Minerva: 127et 1&9&12 38.1064

Clio: 129et 7&12&24 73.7590

Pele: 145et 5&12&29 64.8199

Laka: 152et 41&53&58 82.5317

Marvel: 166et 9&10&22 25.5033

Fantastic: 166et 12&22&50 74.3439

Portent: 190et 5&10&26 23.4092

Beyla: 190et 7&19&46 72.097

Jove: 202et 10&31&58 24.1055

Tolerant: 208et 5&41&80 103.923

Belobog: 248et 12&31&87 60.9402

Spectacle: 281et 10&31&281 49.8669

Jupiter: 282et 9&22&108 56.2368

Sensamagic: 283et 5&17&19 72.231

Agni: 284et 4&6&27 49.3790

Enlil: 284et 4&15&38 79.8062

Trimyna: 294et 2&29&58 81.4047

Triglav: 316et 31&80&87 81.896

Varuna: 320et 12&26&46 41.8714

Hera: 359et 46&53&84 223.1795

Semicanou: 410et 24&80&94 219.7478

Semiporwell: 480et 22&24&84 125.3053

History: 491et 15&29&43 60.3636

Hades: 578et 22&50&58 36.1398

Albus: 640et 19&53&58 62.1100

Indra: 703et 10&31&152 26.6020

Hanuman: 998et 15&57&152 49.965

Loki: 1092et 12&22&86 49.2550

Ganesha: 1502et 31&87&152 39.0462

Freya: 1566et 10&31&167 16.9702

Tyr: 1566et 15&57&183 25.8374

Baldur: 1696et 4&58&72 16.6115

Skadi: 2014et 31&97&121 34.8944

Thor: 2554et 26&46&152 8.8834

Lux: 2603et 41&46&137 50.834

Ennealimmic: 2619et 27&45&171 27.4685

Galaxy: 2665et 46&103&121 84.057

Van Gogh: 6992et 22&58&284 29.7565

Odin: 7464et 12&42&72 11.6151

13-limit rank two

Name: ET w/ optimal patent val: Val name: 1000*badness

Diminished: 4et 4&8d 19.509

Neutrominant: 7et 7&10c 27.214

Modus: 7et 7&27e 23.806

Arnold: 7et 5&7 23.300

Dominatrix: 7et 7&12f 18.289

Jamesbond: 7et 7&14c 23.003

Septimal: 7et 7&14cf 22.569

Ptolemy: 7et 7&38df 34.316

Progression: 9et 8d&9 18.158

Negric: 9et 1&9 20.205

Pentoid: 9et 5&9 21.159

Ringo: 10et 10&17c 22.619

Pajaric: 10et 10&12f 20.461

Pajaro: 10et 10&22f 27.355

Augustus: 12et 9&12 22.236

Dominion: 12et 5&12 27.295

Hexe: 12et 6f&12f 35.946

Ripple: 12f 1ce&12f 31.639

Smate: 14et 14&17c 36.836

Opossum: 15et 7d&8d 19.389

Kangaroo: 15et 2cde&15 32.653

Blacksmith: 15et 5&10 20.498

Archytas clan: 15et 5e&15 22.325

Progress: 15et 2&15 26.214

Porcupine: 15et 7&15 21.276

Belauensis: 15et 14c&15 29.816

Kumbaya: 15et 4&15 31.633

Darjeeling: 15et 15&19e 21.445

Augene: 15et 3&15 20.785

Ogene: 15et 12&15 22.890

Armodue: 16et 7&9 19.351

Domination: 17c 5e&12e 27.435

Dominant: 17c 12f&17c 24.108

Progressive: 17c 2f&15f 32.721

Negri: 19et 9&10 17.833

Sensis: 19et 8d&19 20.017

Meanenneadecal: 19et 12f&19 21.182

Meanplop: 19et 12e&19 27.666

Godzilla: 19et 14cf&19 22.503

Undevigintone: 19et 19&38df 22.933

Lisa: 19et 2cde&19 36.144

Keemun: 19et 4&19 29.749

Qeema: 19et 4ef&19 29.419

Cataleptic: 19et 19&34d 27.343

Rhinoceros: 19et 1ce&19 39.343

Spell: 19et 6&19 45.591

Cantrip: 19et 6f&19 41.603

Muggles: 19et 16&19 30.386

August: 21et 9&21 18.448

Oodako: 21et 6&21 42.323

Telepathy: 22et 19e&22 25.522

Sorcery: 22et 19&22 25.829

Divination: 22et 22f&60e 34.551

Blair: 22et 9&22 23.086

Hedgehog: 22et 14cf&22

Pajarous: 22et 10&22 25.176

Pajara: 22et 12&22 27.642

Porkpie: 22et 7&22 26.043

Ceratitid: 22et 1ce&22 44.739

Urchin: 22et 14c&22f 25.233

Fleetwood: 22et 22&84bdf 31.835

Suprapyth: 22et 17&22 36.336

Comic: 22et 2cde&22 41.470

Astrology: 22et 6&16 34.376

Quasisupra: 22et 17c&22 30.219

Catnip: 24et 12f&24 28.363

Triforce: 24et 9&15 20.248

Hemiaug: 24et 3de&24 30.159

Hemidim: 24et 4ef&24 39.030

Octonion: 24et 24&32c 30.597

Mohamaq: 24et 17c&24 28.738

Varan: 24et 19e&24 25.676

Injera: 26et 26&104bcf 21.565

Flattone: 26et 7&19 22.260

Lemba: 26et 10&16 25.477

Crepuscular: 26et 26&34d 24.368

Quarto: 26et 26&27e 27.692

Cynder: 26et 5e&26 34.124

Secundly: 26et 9&17 26.212

Cavalier: 26et 4ef&26 35.040

Sensa: 27et 19e&27 23.258

Ponens: 27et 7&27 39.043

Fervor: 27e 2f&27e 39.705

Octocat: 27e 14cf&27e 27.601

Minah: 27e 4ef&27e 27.568

Roman: 29et 3&23 30.043

Porky: 29et 22&29 26.543

Coendou: 29et 7&29 30.233

Nautilus: 29et 15&29 22.285

Negril: 29et 19&29 24.383

Negroni: 29et 10&29 21.559

Wilsec: 29et 9&20 25.192

Impunity: 29et 5e&29 33.196

Immunity: 29et 5&29 37.078

Quindecic: 30et 15&30 28.944

Meantone: 31et 12f&31 18.048

Squares: 31et 17c&31 25.514

Agora: 31et 31&76e 24.522

Mohajira: 31et 7&24 23.388

Winston: 31et 9&31 19.931

Revelation: 31et 21&31 29.452

Tritonic: 31et 29&31 22.993

Lupercalia: 31et 15&31 21.328

Murakuc: 31et 31&73f 41.394

Nusecond: 31et 31&70f 23.323

Cypress: 31et 11cdeef&31 37.849

Maneh: 31et 4ef&31 29.868

Prajapati: 31et 31&93f 37.885

Würschmidt: 31et 31&65d 23.593

Worseschmidt: 31et 3def&31 34.382

Hemithir: 31et 31&68e 31.199

Hemiwar: 31et 6f&31 44.886

Sentinel: 31et 14&17 37.408

Diesic: 31et 1ce&31 38.116

Semishly: 31et 31&49f 28.408

Slurpee: 33et 16&33 33.102

Kema: 34et 15&19 22.749

Wollemia: 34et 27e&34 31.219

Anguirus: 34et 10&24 30.829

Secund: 35et 9&35 49.684

Greenwood: 35et 21&35 54.009

Liesel: 36et 19&36 27.304

Niner: 36et 9&36 24.143

Beatles: 37et 27e&37 30.161

Enjera: 38et 12f&26f 26.542

Horoscope: 38et 16&38 35.284

Miraculous: 41et 10&31 18.669

Superkleismic: 41et 15&26 21.478

Varan: 41et 5e&41 32.284

Hemimiracle: 41et 20&21 43.151

Andromeda: 41et 29&41 20.749

Octacot: 41et 27e&41 23.276

Octopod: 41et 14cf&41 28.326

Monkey: 41et 7&34 28.410

Bunya: 41et 7d&41 24.886

Magic: 41et 19&41 21.509

Hocus: 41et 41&79d 30.280

Witchcraft: 41et 41&60e 23.547

Trismegistus: 41et 16&41 33.081

Bohpier: 41et 41&90ef 24.864

Salsa: 41et 17&24 30.793

Plutino: 41et 2cde&41 40.182

Quato: 41et 4ef&41 30.081

Slendi: 41et 41&124ef 43.644

Jerome: 43et 26&43 29.285

Amavil: 43et 9&43 25.791

Meridetone: 43et 43&117df 26.421

Kumonga: 43et 16&43 28.920

Vigin: 44et 22&44 29.849

Sensor: 46et 19&27 25.474

Sensus: 46et 46&73 20.789

Dwynwen: 46et 15&46 23.461

Leapday: 46et 29&46 24.732

Twothirdtonic: 46et 9&37 25.941

Bamity: 46et 14cf&46 30.885

Magus: 46et 3de&46 43.024

Aerodactyl: 46et 5&46 33.986

Aerodino: 46et 5e&46 35.836

Vines: 46et 4&42 29.693

Superpyth: 49et 22&49 24.673

Bimeantone: 50et 12f&50 28.817

Cataclysmic: 53et 53&140d 22.554

Hemikleismic: 53et 15&53 26.005

Orwell: 53et 22&31 19.718

Doublethink: 53et 9&44 27.120

Tricot: 53et 53&70 32.102

Hamity: 53et 14cf&53 29.753

Kleiboh: 53et 4ef&53 31.074

Maja: 53et 45ef&53 27.532

Helenus: 53et 53&118d 26.284

Hemigari: 53et 29&53 27.464

Quartz: 53et 26&53 28.818

Sycamore: 56et 18&19 34.295

Diaschismic: 58et 46&58 18.926

Myna: 58et 31&58 17.125

Hemififths: 58et 41&58 19.090

Infraorwell: 58et 9&58 23.683

Thuja: 58et 15&43 22.838

Alicorn: 58et 19&58 23.667

Bisemidim: 58et 50&58 23.877

Sruti: 58et 24&58 23.791

Qilin: 58et 58&77 22.842

Gorgik: 58et 21&37 32.205

Gallium: 62et 31&62 25.484

Semivalentine: 62et 16&30 32.749

Hemimeantone: 62et 43&62 31.433

Ammonite: 66et 29&37 27.168

Hemiwur: 68et 6&31 28.432

Manna: 72et 41&72 17.012

Hendec: 72et 26&46 17.707

Catakleismic: 72et 19&53 16.883

Lizard: 72et 22&50 21.781

Neominor: 72et 72&161f 26.942

Compton: 72et 72&228f 21.852

Comptone: 72et 12&72 25.144

Hours: 72et 24&72 26.931

Bikleismic: 72et 72&106 21.814

Marvolo: 72et 29&43 21.470

Semimiracle: 72et 10&62 24.622

Catalytic: 72et 19e&72 22.337

Enneaportent: 72et 9&54 22.322

Ennealim: 72et 27e&72 20.697

Ennealiminal: 72et 27&72 30.325

Marrakesh: 73et 31&73 40.774

Grosstone: 74et 12&31 25.899

Valentino: 77et 31&46 20.665

Camahueto 77et 19&77 36.155

Echidna: 80et 22&58 23.679

Bidia: 80et 12&68 41.137

Paradigmic: 80et 19&80 35.781

Quartonic: 80et 53&80 23.875

Meanpop: 81et 19&31 20.883

Soothsaying: 82et 22&60 55.443

Secant: 84et 26&58 46.373

Rodan: 87et 41&46 18.448

Clyde: 87et 19&68 26.842

Misty: 87et 12f&87 27.820

Emka: 87et 37&50 29.741

Mothra: 88et 5&26 23.954

Amigo: 89et 43&46 30.666

Septimin: 91et 9&41 23.117

Kumhar: 93et 31&93 48.582

Slender: 94et 31&63 25.913

Sanjaab: 94et 29&94 33.849

Supers: 94et 58&94 21.644

Interpental: 96et 43&53 29.680

Mosura: 98et 31&67 36.857

Hitchcock: 99et 7&39 22.448

Echidnic: 102et 10&46 28.874

Benediction: 103et 31&72 15.715

Phicordial: 103et 10&103 33.198

Hemisecordite: 103et 41&62 25.589

Necromancy: 104et 22&41 25.275

Leapweek: 109et 17&46 32.727

Buzzard: 111et 53&58 18.842

Semisept: 111et 31&80 25.204

Kwai: 111et 41&111 24.555

Shrutar: 114et 46&68 28.057

Submajor: 116et 10&53 27.689

Guiron: 118et 41&77 28.444

Hemithirds: 118et 31&56 21.738

Kleischismic: 118et 24&94 37.640

Grendel: 121et 31&121 24.839

Pluto: 121et 41&80 25.717

Subfourth: 121et 58&121 23.800

Harry: 130et 58&72 13.046

Bosonic: 130et 26&130 32.946

Bison: 130et 46&84 23.504

Sesquart: 130et 41&89 22.396

Septisuperquad: 130et 22&108 33.038

Hemimaquila: 130et 9&121 24.445

Countercata: 140et 34&53 20.156

Degrees: 140et 80&140 32.718

Ketchup: 140et 46&94 24.824

Fibo: 140et 37&103 27.429

Omicronbeta: 144et 72&144 29.956

Heinz: 149et 46&103 25.779

Hemiseven: 149et 5&72 21.900

Octopus: 152et 72&152 21.679

Monocerus: 154et 58&154 28.795

Tritikleismic: 159et 15&72 15.652

Mintone: 161et 58&103 21.849

Gizzard: 166et 72&166 20.252

Polypyth: 167et 46&121 30.292

Tertiaseptal: 171et 31&171 36.876

Parkleismic: 179et 80&179 36.559

Mirkat: 183et 72&111 18.632

Ekadash: 190et 72&118 20.381

Widefourth: 190et 16&71 21.636

Sqrtphi: 193et 72&121 20.040

Hemimist: 198et 87&111 22.923

Semihemi: 198et 58&140 21.188

Amity: 205et 53&205 28.008

Quanic: 205et 94&111 32.481

Swetneus: 207et 58&149 28.876

Metakleismic: 208et 87&121 24.371

Quadritikleismic: 212et 68&72 18.731

Slithy: 215et 94&121 28.492

Arch: 217et 43&87 19.504

Octoid: 224et 72&224 15.274

Quanharuk: 224et 41&142 21.392

Mystery: 232et 29&58 18.591

Subpental: 241et 19&111 23.940

Ennealimnic: 243et 72&171 20.250

Essence: 248et 58&190 26.107

Subsemifourth: 255et 103&255 28.387

Hemiennealimmal: 270et 72&198 12.505

Acrokleismic: 270et 19&251 26.818

Counteracro: 270et 270&1331c 26.028

Septisuperfourth: 282et 130&282 22.887

Escaped: 283et 22&65 31.366

Sextilifourths: 289et 29&130 25.276

Quincy: 289et 72&145 23.862

Hemiwürschmidt: 291et 31&130 23.074

Hemischis: 313et 53&130 20.816

Octowerck: 320et 72&248 27.632

Decile: 320et 130&190 23.948

Novemkleismic: 333et 72&261 39.072

Catafourth: 363et 103&130 21.694

Bischismic: 378et 12&118 28.722

Neusec: 388et 190&198 30.941

Hemigamera: 422et 26&198 20.416

Semiennealimmal: 441et 72&441 26.122

Birds: 465et 31&217 35.680

Emkay: 535et 87&137 17.853

Fermionic: 546et 130&286 43.581

Pogo: 578et 36&94 17.514

Quatracot: 638et 190&224 22.643

Unthirds: 694et 72&311 20.888

Octant: 696et 24&224 30.425

Quasithird: 836et 164&224 29.501

Newt: 851et 41&229 13.830

Decoid: 940et 130&270 13.475

Semihemiennealimmal 954et 126&144 13.104

Acyuta: 962et 270&692 15.805

Deca: 1000et 80&190 16.810

Quasiorwell: 1111et 31&239 17.921

Abigail: 1258et 46&178 8.856

Trillium: 1429et 53&441 19.393

Ananta: 1468et 118&152 23.678

13-limit rank three

Name: ET w/ optimal patent val: Val name: 10^5 * badness

Mockingbird: 15et 3&4&15 85.942

Catbird: 19et 4&12f&19 90.475

Potassium: 19et 9&10&11 73.346

Nickel: 28et 7&9&21 64.705

Negric: 29et 1&9&10 80.756

Nightingale: 31et 3&15&28 83.714

Thrasher: 34et 12&15&19 87.636

Selenium: 34et 5&9&10 78.368

Krypton: 36et 9&10&36 72.673

Foreboding: 41et 5&10&26 87.267

Prodigy: 41et 10&29&31 73.639

Veery: 46et 12&15&46 99.122

Athene: 53et 12f&22&53 81.781

Thrush: 58et 31&46&58 67.663

Bluebird: 58et 12&15&31 91.548

Aplonis: 58et 19&31&58 82.078

Jofur: 58et 10&31&58 74.932

Parahemif: 58et 17&24&58 119.366

Deecee: 72et 9&22&41 92.048

Prodigious: 72et 2&29&41 89.974

Marvelcat: 72et 9&10&44 99.966

Beyla: 72et 7&19&46 83.962

Varda: 80et 22&46&58 97.041

Sensawer: 87et 41&46&73 92.807

Tripod: 91et 9&10&31 74.546

Isis: 94et 10&22&31 86.583

Malcolm: 94et 19e&41&53 107.452

Marvel: 103et 19&22&31 68.977

Prodigal: 103et 31&72&84 88.910

Mirage: 103et 10&31&62 73.850

Apollo: 104et 22&29&41 103.106

Cerberus: 130et 22&50&58 76.512

Ominous: 149et 5&26&46 75.055

Portending: 159et 15&26&46 62.715

Momentous: 164et 10&31&46 83.202

Hecate: 166et 19&41&53 72.113

Marvell: 166et 9&31&63 86.160

Ulmo: 179et 7&39&80 93.162

Vibhu: 183et 31&72&111 82.598

Portentous: 190et 15&31&56 66.119

Vish: 193et 41&72&121 92.976

Minos: 193et 9&54&58 72.381

Namaka: 198et 29&53&58 78.124

Laka: 205et 41&53&58 82.186

Kujuku 208et 24&29&58 105.976

Tolerant: 208et 41&46&80 102.099

Spectacle: 209et 31&72&209 100.924

Agni: 212et 6&31&72 92.251

Yajna: 224et 31&72&121 69.986

Pele: 232et 29&41&46 70.328

Trimyna: 232et 29&31&56 81.405

Jovial: 243et 41&58&72 62.380

Borneo: 270et 15&72&111 54.937

History: 289et 15&29&43 53.955

Enlil: 299et 15&19&53 68.005

Madagascar: 313et 19&53&58 56.006

Hera: 313et 46&53&84 129.736

Akea: 321et 7&34&46 82.191

Semiporwell: 328et 46&68&84 122.026

Jovis: 363et 31&58&72 54.221

Semicanou: 410et 94&198&212 297.443

Hanuman: 535et 15&72&137 65.278

Hades: 578et 36&58&72 53.531

Vili: 643et 37&93&103 73.821

Shibi: 703et 41&72&111 72.094

Greenland: 940et 58&72&198 44.343

Baffin: 940et 34&43&53 60.443

Ennealimmic: 981et 27&72&171 75.488

Zisa: 1241et 21&31&109 82.974

Thunor: 1258et 26&46&178 34.135

Frigg: 1344et 6&58&103 93.387

Donar: 1448et 46&80&144 32.154

Rym: 1870et 46&106&118 54.933

Galaxy: 2125et 46&103&121 46.311

Lux: 2333et 41&46&137 36.015

Freya: 2615et 10&31&229 85.515

See also

Todo: improve layout, increase applicability

add structure by switching to tables

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