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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate."
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<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">&lt;span style="display: block; display: none;"&gt;
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The biosphere is the name given to the collection of temperaments that are children of or related to **//biome temperament//**, the rank 3 2.3.7.13/10 subgroup temperament eliminating 91/90. The term "biome" loosely means "ecosystem" or "climate." This temperament is so named because temperaments that arise from eliminating 91/90 can evoke synesthetic associations of different "natural" settings, some very familiar and some much less so.


This temperament makes the utonal inverse of 6:7:9 out to be 10:13:15, whereas it is normally the much more complex (and arguably more dissonant) 14:18:21. Eliminating 91/90 thus enriches septimal harmony by increasing the concordance of "utonal" septimal triads such as 6:7:9 or tetrads such as 4:6:7:9.
The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to [[9-odd-limit]] harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15.


Biome temperament, from which is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice.
The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI.


The barbados triad is of particular theoretical interest because, when reduced to lowest terms, it is the 10:13:15 triad. Thus, this triad is only slightly higher in complexity than the 5-limit 10:12:15 minor triad, which means it may be of distinct value as a relatively unexplored musical consonance. It is one of only a few low-complexity triads with a 3/2 on the outer dyad, some others being 4:5:6, 6:7:9, and 10:12:15. It works out to 0-454-702 cents, which means that it is an //ultramajor// triad, with a third sharper even than the 9/7 supermajor third.
This lattice can also be extended to deal with "higher primes", as can 5-limit JI. However, we instead expand the subgroup outward from the center, so that the "higher primes" we look at are things like like 5, 11, and 13. However, it may prove more useful at first to think purely within the 2.3.7.13/5 subgroup, so as to first come to understand the xenharmonic possibilities of the system.


Compared to the 7-limit 14:18:21 supermajor triad, 10:13:15 is lower in triadic complexity (10:13:15 vs 14:18:21), but contains dyads that are on average higher in complexity (9/7 vs 13/10 and 7/6 vs 15/13). Its inverse, however, is the ultraminor 26:30:39, which is far more complex than the 7-limit subminor 6:7:9. Temperaments in which 91/90 vanishes equate the two types of triads.
== Parent Temperaments ==
=== Biome ===
Subgroup: 2.3.7.13/5


[[24edo]] approximates this triad to within an error of four cents, and [[29edo]] does even better, getting it to within 1.5 cents; either may be used as a tuning for the barbados temperament discussed below.
Comma list: 91/90


Comma: 676/675
Mapping:  


Map
{{val| 1 0 0 1 }}<br>
&lt;1 0 0 0 0 -1|
{{val| 0 1 0 2 }}<br>
&lt;0 2 0 0 0 3|
{{val| 0 0 1 -1 }}
&lt;0 0 1 0 0 1|
&lt;0 0 0 1 0 0|
&lt;0 0 0 0 1 0|
EDOs: 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940
[[Optimal patent val]]: [[940edo]]


=[[#Rank four temperaments]]Rank four temperaments=
{{Optimal ET sequence|legend=1| 5, 9, 14, 17, 22, 27, 32, 46 }}


==[[#Rank four temperaments-1001/1000]]1001/1000==  
=== Biosphere ===
Commas: 676/675, 1001/1000
Subgroup: 2.3.5.7.11.13


EDOs: 15, 19, 29, 43, 53, 58, 72, 87, 111, 130, 183, 198, 270, 940
Comma list: 91/90
[[Optimal patent val]]: [[940edo]]


==[[#Rank four temperaments-49/48]]49/48==
Mapping:  
Commas: 49/48, 91/90


==[[#Rank four temperaments-1716/1715]]1716/1715==
{{val| 1 0 0 0 0 1 }}<br>
Commas: 676/675, 1716/1715
{{val| 0 1 0 0 0 2 }}<br>
{{val| 0 0 1 0 0 1 }}<br>
{{val| 0 0 0 1 0 -1 }}<br>
{{val| 0 0 0 0 1 0 }}


==[[#Rank four temperaments-364/363]]364/363==
{{Optimal ET sequence|legend=1| 8d, 9, 10, 14cf, 15, 17c, 19, 22, 27e, 29, 31f, 37, 38df, 46 }}
Commas: 364/363, 676/675


===[[#Rank four temperaments-364/363-351/350]]351/350===
== Rank two temperaments ==
Commas: 351/350, 676/675
=== Oceanfront ===
Oceanfront is very similar to the familiar 7-limit superpyth temperament, in which 16/9 is equated with 7/4, 32/27 equated with 7/6, and 81/64 with 9/7. Oceanfront aims to equate 81/64 with 13/10 instead, however, so the fifths are even sharper than those of superpyth - 713.910 cents is the optimal POTE generator. The general structure of this scale is similar to that of meantone[7], except that the "major" triads in this scale are 10:13:15, and the minor triads are 6:7:9.


=[[#Rank three temperaments]]Rank three temperaments=
The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard.


==[[#Rank three temperaments-Greenland]][[Breed family|Greenland]]==
Subgroup: 2.3.7.13/5
Commas: 676/675, 1001/1000, 1716/1715


Map: [&lt;2 0 1 3 7 -1|, &lt;0 2 1 1 -2 4|, &lt;0 0 2 1 3 2|]
[[Comma list]]: 64/63, 91/90
Edos: 58, 72, 130, 198, 270, 940
[[Optimal patent val]]: [[940edo]]
Badness: 0.000433


[[Spectrum of a temperament|Spectrum]]: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -1 2 -4 }}]


[[POTE generator]]: ~4/3 = 486.090


==[[#Rank three temperaments-History]][[Werckismic temperaments|History]]==
{{Optimal ET sequence|legend=1| 27, 32 }}
Commas: 364/363, 441/440, 1001/1000


EDOs: 15, 29, 43, 58, 72, 87, 130, 217, 289
Scales: [[Oceanfront scales]]
[[Optimal patent val]]: [[289edo]]
Badness: 0.000540


Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7
==== Superpyth ====
{{see also| Archytas clan #Superpyth }}


Extends 11-limit superpyth as 22&amp;49.


==[[#Rank three temperaments-Borneo]]Borneo==
Subgroup: 2.3.5.7.11.13
Commas: 676/675, 1001/1000, 3025/3024


Map: [&lt;3 0 0 4 8 -3|, &lt;0 2 0 -4 1 3|, &lt;0 0 1 2 0 1|]
[[Comma list]]: 64/63, 78/77, 91/90, 100/99
EDOs: 15, 72, 87, 111, 159, 183, 198, 270
[[Optimal patent val]]: [[270edo]]
Badness: 0.000549


[[Mapping]]: [{{val| 1 2 6 2 10 9 }}, {{val| 0 -1 -9 2 -16 -13 }}]


Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7
[[POTE generator]]: ~4/3 = 489.521


==[[#Rank three temperaments-Madagascar]][[Cataharry family|Madagascar]]==
{{Optimal ET sequence|legend=1| 22, 27e, 49, 76bcde }}
Commas: 351/350, 540/539, 676/675


EDOs: 19, 53, 58, 72, 111, 130, 183, 313
[[Badness]]: 0.024673
[[Optimal patent val]]: [[313edo]]
Badness: 0.000560


Spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11
==== Quasisupra ====
[[madagascar19]]
{{see also| Archytas clan #Quasisuper }}


==[[#Rank three temperaments-Baffin]]Baffin==
Subgroup: 2.3.5.7.11.13
Commas: 676/675, 1001/1000, 4225/4224


Map: [&lt;1 0 0 13 -9 1|, &lt;0 2 0 -7 4 3|, &lt;0 0 1 -2 4 1|]
[[Comma list]]: 64/63, 78/77, 91/90, 121/120
EDOs: 34, 43, 53, 87, 130, 183, 217, 270, 940
[[Optimal patent val]]: [[940edo]]
Badness: 0.000604


Spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11
[[Mapping]]: [{{val| 1 2 -3 2 1 0 }}, {{val| 0 -1 13 2 6 9 }}]


=[[#Rank two temperaments]]Rank two temperaments=  
[[POTE generator]]: ~4/3 = 491.996
Rank two temperaments tempering out 676/675 include the 13-limit versions of [[Ragismic microtemperaments|hemiennealimmal]], [[Breedsmic temperaments|harry]], [[Kleismic family|tritikleismic]], [[Kleismic family|catakleimsic]], [[Marvel temperaments|negri]], [[Hemifamity temperaments|mystery]], [[Hemifamity temperaments|buzzard]], [[Kleismic family|quadritikleismic]].


It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo]] alone.
{{Optimal ET sequence|legend=1| 17c, 22, 39d, 61df, 100bcdf }}


==[[#Rank two temperaments-Decitonic]]Decitonic==
[[Badness]]: 0.030219
Commas: 676/675, 1001/1000, 1716/1715, 4225/4224


[[POTE tuning|POTE generator]]: ~15/13 = 248.917
==== Ultrapyth ====
{{see also| Archytas clan #Ultrapyth }}


Map: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]
Subgroup: 2.3.5.7.13
EDOs: 130, 270, 940, 1480
Badness: 0.0135


==[[#Rank two temperaments-Avicenna]]Avicenna==
[[Comma list]]: 64/63, 91/90, 4394/4375
Commas: 676/675, 1001/1000, 3025/3024, 4096/4095


[[POTE tuning|POTE generator]]: ~13/12 = 137.777
[[Mapping]]: [{{val|1 2 8 2 11}}, {{val|0 -1 -14 2 -18}}]


Map: [&lt;3 2 8 16 9 8|, &lt;0 8 -3 -22 4 9|]
[[POTE generator]]: ~4/3 = 486.255
EDOs: 87, 183, 270
Badness: 0.0156


=[[#Subgroup temperaments]]Subgroup temperaments=
{{Optimal ET sequence|legend=1| 5, 32, 37 }}


==[[#Subgroup temperaments-Barbados]]Barbados==  
===== Full 13-limit ultrapyth =====
Subgroup: 2.3.13/5
Subgroup: 2.3.5.7.11.13
Commas: 676/675


Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[Just intonation subgroups|just intontation subgroup]]. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568


[[POTE tuning|POTE generator]]: ~15/13 = 248.621
[[Mapping]]: [{{val| 1 2 8 2 -1 11 }}, {{val| 0 -1 -14 2 11 -18 }}]


[[Smonzos and Svals|Sval map]]: [&lt;1 0 -1|, &lt;0 2 3|]
[[POTE generator]]: ~4/3 = 486.500
EDOs: 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362
Badness: 0.002335


==[[#Subgroup temperaments-Trinidad]]Trinidad==
{{Optimal ET sequence|legend=1| 5, 32, 37 }}
Subgroup: 2.3.5.13
Commas: 325/324, 625/624


Trinidad may be viewed as the reduction of [[Kleismic family|catakleismic temperament]] to the 2.3.5.13 subgroup. Another way to put it is that it is the rank two 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675.
[[Badness]]: 0.049172


[[POTE tuning|POTE generator]]: 317.076
===== Ultramarine =====
Subgroup: 2.3.5.7.11.13


[[Smonzos and Svals|Sval map]]: [&lt;1 0 1 0 |, &lt;0 6 5 14|]
[[Comma list]]: 64/63, 91/90, 100/99, 847/845
EDOs: 15, 19, 34, 53, 87, 140, 193, 246


==[[#Subgroup temperaments-Parizekmic]]Parizekmic==
[[Mapping]]: [{{val| 1 2 8 2 14 11 }}, {{val| 0 -1 -14 2 -26 -18 }}]
Subgroup: 2.3.5.13
Commas: 676/675


Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat.
[[POTE generator]]: ~4/3 = 486.189


[[Smonzos and Svals|Sval map]]
{{Optimal ET sequence|legend=1| 5e, 32e, 37, 79bcef, 116bbcef }}
&lt;1 0 0 -1|
&lt;0 2 0 3|
&lt;0 0 1 1|


===[[#Subgroup temperaments-Parizekmic-Music]]Music===
[[Badness]]: 0.045653
[[http://micro.soonlabel.com/petr_parizek/pp_pump_675.mp3|Petr's Pump]], a comma pump based ditty in Pariekmic temperament.
EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270 </pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;The Biosphere&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; display: none;"&gt;&lt;br /&gt;


==== Porcupinefish ====
{{see also| Porcupine family #Porcupinefish }}


&lt;table class="wiki_table"&gt;
Porcupinefish is the 13-limit extension of [[Porcupine|porcupine]] that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments.
    &lt;tr&gt;
        &lt;th&gt;Details&lt;br /&gt;
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&lt;/span&gt;&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
The biosphere is the name given to the collection of temperaments that are children of or related to &lt;strong&gt;&lt;em&gt;biome temperament&lt;/em&gt;&lt;/strong&gt;, the rank 3 2.3.7.13/10 subgroup temperament eliminating 91/90. The term &amp;quot;biome&amp;quot; loosely means &amp;quot;ecosystem&amp;quot; or &amp;quot;climate.&amp;quot; This temperament is so named because temperaments that arise from eliminating 91/90 can evoke synesthetic associations of different &amp;quot;natural&amp;quot; settings, some very familiar and some much less so.&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 55/54, 64/63, 91/90, 100/99
This temperament makes the utonal inverse of 6:7:9 out to be 10:13:15, whereas it is normally the much more complex (and arguably more dissonant) 14:18:21. Eliminating 91/90 thus enriches septimal harmony by increasing the concordance of &amp;quot;utonal&amp;quot; septimal triads such as 6:7:9 or tetrads such as 4:6:7:9.&lt;br /&gt;
 
&lt;br /&gt;
[[Mapping]]: [{{val| 1 2 3 2 4 6 }}, {{val| 0 -3 -5 6 -4 -17 }}]
Biome temperament, from which is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice.&lt;br /&gt;
 
&lt;br /&gt;
[[POTE generator]]: ~10/9 = 162.277
The barbados triad is of particular theoretical interest because, when reduced to lowest terms, it is the 10:13:15 triad. Thus, this triad is only slightly higher in complexity than the 5-limit 10:12:15 minor triad, which means it may be of distinct value as a relatively unexplored musical consonance. It is one of only a few low-complexity triads with a 3/2 on the outer dyad, some others being 4:5:6, 6:7:9, and 10:12:15. It works out to 0-454-702 cents, which means that it is an &lt;em&gt;ultramajor&lt;/em&gt; triad, with a third sharper even than the 9/7 supermajor third.&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 15, 22, 37, 59 }}
Compared to the 7-limit 14:18:21 supermajor triad, 10:13:15 is lower in triadic complexity (10:13:15 vs 14:18:21), but contains dyads that are on average higher in complexity (9/7 vs 13/10 and 7/6 vs 15/13). Its inverse, however, is the ultraminor 26:30:39, which is far more complex than the 7-limit subminor 6:7:9. Temperaments in which 91/90 vanishes equate the two types of triads.&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.025314
&lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; approximates this triad to within an error of four cents, and &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; does even better, getting it to within 1.5 cents; either may be used as a tuning for the barbados temperament discussed below.&lt;br /&gt;
 
&lt;br /&gt;
=== Tropic ===
Comma: 676/675&lt;br /&gt;
Tropic is the merger of the biosphere and the [[The Archipelago|archipelago]]. It is also a subgroup relative of semaphore temperament, since [[49/48]] vanishes. Of note is that [[676/675]] vanishes, so that two 7/6's (or 15/13)'s is equated with 4/3. While this temperament doesn't take advantage of the nearly pure harmonies that biome tempering can offer, particularly where 7/4 is involved, it still has some use, particularly for those who don't mind a bit more error in their tunings.
&lt;br /&gt;
 
Map&lt;br /&gt;
Subgroup: 2.3.7.13/5
&amp;lt;1 0 0 0 0 -1|&lt;br /&gt;
 
&amp;lt;0 2 0 0 0 3|&lt;br /&gt;
[[Comma list]]: 49/48, 91/90
&amp;lt;0 0 1 0 0 1|&lt;br /&gt;
 
&amp;lt;0 0 0 1 0 0|&lt;br /&gt;
[[Mapping]]: [{{val| 1 2 3 2 }}, {{val| 0 -2 -1 -3 }}]
&amp;lt;0 0 0 0 1 0|&lt;br /&gt;
 
EDOs: 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940&lt;br /&gt;
[[POTE generator]]: ~7/6 = 251.507
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/940edo"&gt;940edo&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 19, 24 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Rank four temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:40:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank four temperaments&amp;quot; title=&amp;quot;Anchor: Rank four temperaments&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank four temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:40 --&gt;Rank four temperaments&lt;/h1&gt;
 
&lt;br /&gt;
==== Godzilla ====
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Rank four temperaments-1001/1000"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:41:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank four temperaments-1001/1000&amp;quot; title=&amp;quot;Anchor: Rank four temperaments-1001/1000&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank four temperaments-1001/1000"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:41 --&gt;1001/1000&lt;/h2&gt;
{{see also| Meantone family #Godzilla }}
Commas: 676/675, 1001/1000&lt;br /&gt;
 
&lt;br /&gt;
Subgroup: 2.3.5.7.13
EDOs: 15, 19, 29, 43, 53, 58, 72, 87, 111, 130, 183, 198, 270, 940&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/940edo"&gt;940edo&lt;/a&gt;&lt;br /&gt;
[[Comma list]]: 49/48, 81/80, 91/90
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Rank four temperaments-49/48"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:42:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank four temperaments-49/48&amp;quot; title=&amp;quot;Anchor: Rank four temperaments-49/48&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank four temperaments-49/48"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:42 --&gt;49/48&lt;/h2&gt;
[[Mapping]]: [{{val|1 0 -4 2 -5}}, {{val|0 2 8 1 11}}]
Commas: 49/48, 91/90&lt;br /&gt;
 
&lt;br /&gt;
[[POTE generator]]: ~7/6 = 252.429
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Rank four temperaments-1716/1715"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:43:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank four temperaments-1716/1715&amp;quot; title=&amp;quot;Anchor: Rank four temperaments-1716/1715&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank four temperaments-1716/1715"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:43 --&gt;1716/1715&lt;/h2&gt;
 
Commas: 676/675, 1716/1715&lt;br /&gt;
{{Optimal ET sequence|legend=1| 5, 14cf, 19 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Rank four temperaments-364/363"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:44:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank four temperaments-364/363&amp;quot; title=&amp;quot;Anchor: Rank four temperaments-364/363&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank four temperaments-364/363"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:44 --&gt;364/363&lt;/h2&gt;
===== Full 13-limit godzilla =====
Commas: 364/363, 676/675&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Rank four temperaments-364/363-351/350"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:45:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank four temperaments-364/363-351/350&amp;quot; title=&amp;quot;Anchor: Rank four temperaments-364/363-351/350&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank four temperaments-364/363-351/350"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:45 --&gt;351/350&lt;/h3&gt;
[[Comma list]]: 45/44, 49/48, 78/77, 81/80
Commas: 351/350, 676/675&lt;br /&gt;
 
&lt;br /&gt;
[[Mapping]]: [{{val|1 0 -4 2 -6 -5}}, {{val|0 2 8 1 12 11}}]
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Rank three temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:46:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank three temperaments&amp;quot; title=&amp;quot;Anchor: Rank three temperaments&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank three temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:46 --&gt;Rank three temperaments&lt;/h1&gt;
 
&lt;br /&gt;
[[POTE generator]]: ~7/6 = 253.603
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Rank three temperaments-Greenland"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:47:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank three temperaments-Greenland&amp;quot; title=&amp;quot;Anchor: Rank three temperaments-Greenland&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank three temperaments-Greenland"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:47 --&gt;&lt;a class="wiki_link" href="/Breed%20family"&gt;Greenland&lt;/a&gt;&lt;/h2&gt;
 
Commas: 676/675, 1001/1000, 1716/1715&lt;br /&gt;
{{Optimal ET sequence|legend=1| 5e, 14cf, 19, 33cdff, 52cdff }}
&lt;br /&gt;
 
Map: [&amp;lt;2 0 1 3 7 -1|, &amp;lt;0 2 1 1 -2 4|, &amp;lt;0 0 2 1 3 2|]&lt;br /&gt;
[[Badness]]: 0.022503
Edos: 58, 72, 130, 198, 270, 940&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/940edo"&gt;940edo&lt;/a&gt;&lt;br /&gt;
===== Varan =====
Badness: 0.000433&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9&lt;br /&gt;
[[Comma list]]: 49/48, 66/65, 77/75, 81/80
&lt;br /&gt;
 
&lt;br /&gt;
[[Mapping]]: [{{val|1 0 -4 2 -10 -5}}, {{val|0 2 8 1 17 11}}]
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Rank three temperaments-History"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:48:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank three temperaments-History&amp;quot; title=&amp;quot;Anchor: Rank three temperaments-History&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank three temperaments-History"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:48 --&gt;&lt;a class="wiki_link" href="/Werckismic%20temperaments"&gt;History&lt;/a&gt;&lt;/h2&gt;
 
Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;
[[POTE generator]]: ~7/6 = 251.165
&lt;br /&gt;
 
EDOs: 15, 29, 43, 58, 72, 87, 130, 217, 289&lt;br /&gt;
{{Optimal ET sequence|legend=1| 19e, 24, 43de }}
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/289edo"&gt;289edo&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.000540&lt;br /&gt;
[[Badness]]: 0.025676
&lt;br /&gt;
 
Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7&lt;br /&gt;
===== Baragon =====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Rank three temperaments-Borneo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:49:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank three temperaments-Borneo&amp;quot; title=&amp;quot;Anchor: Rank three temperaments-Borneo&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank three temperaments-Borneo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:49 --&gt;Borneo&lt;/h2&gt;
[[Comma list]]: 49/48, 56/55, 81/80, 91/90
Commas: 676/675, 1001/1000, 3025/3024&lt;br /&gt;
 
&lt;br /&gt;
[[Mapping]]: [{{val|1 0 -4 2 9 -5}}, {{val|0 2 8 1 -7 11}}]
Map: [&amp;lt;3 0 0 4 8 -3|, &amp;lt;0 2 0 -4 1 3|, &amp;lt;0 0 1 2 0 1|]&lt;br /&gt;
 
EDOs: 15, 72, 87, 111, 159, 183, 198, 270&lt;br /&gt;
[[POTE generator]]: ~7/6 = 251.198
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/270edo"&gt;270edo&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.000549&lt;br /&gt;
{{Optimal ET sequence|legend=1| 5, 14cef, 19, 24, 43d }}
&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.026703
Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7&lt;br /&gt;
 
&lt;br /&gt;
==== Anguirus ====
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Rank three temperaments-Madagascar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:50:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank three temperaments-Madagascar&amp;quot; title=&amp;quot;Anchor: Rank three temperaments-Madagascar&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank three temperaments-Madagascar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:50 --&gt;&lt;a class="wiki_link" href="/Cataharry%20family"&gt;Madagascar&lt;/a&gt;&lt;/h2&gt;
{{see also| Diaschismic family #Anguirus }}
Commas: 351/350, 540/539, 676/675&lt;br /&gt;
 
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 19, 53, 58, 72, 111, 130, 183, 313&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/313edo"&gt;313edo&lt;/a&gt;&lt;br /&gt;
[[Comma list]]: 49/48, 56/55, 91/90, 352/351
Badness: 0.000560&lt;br /&gt;
 
&lt;br /&gt;
[[Mapping]]: [{{val| 2 4 3 6 9 7 }}, {{val| 0 -2 4 -1 -5 1 }}]
Spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11&lt;br /&gt;
 
&lt;a class="wiki_link" href="/madagascar19"&gt;madagascar19&lt;/a&gt;&lt;br /&gt;
[[POTE generator]]: ~8/7 = 247.691
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Rank three temperaments-Baffin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:51:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank three temperaments-Baffin&amp;quot; title=&amp;quot;Anchor: Rank three temperaments-Baffin&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank three temperaments-Baffin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:51 --&gt;Baffin&lt;/h2&gt;
{{Optimal ET sequence|legend=1| 10, 24, 34, 58d, 92def }}
Commas: 676/675, 1001/1000, 4225/4224&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.030829
Map: [&amp;lt;1 0 0 13 -9 1|, &amp;lt;0 2 0 -7 4 3|, &amp;lt;0 0 1 -2 4 1|]&lt;br /&gt;
 
EDOs: 34, 43, 53, 87, 130, 183, 217, 270, 940&lt;br /&gt;
=== Echidnic ===
&lt;a class="wiki_link" href="/Optimal%20patent%20val"&gt;Optimal patent val&lt;/a&gt;: &lt;a class="wiki_link" href="/940edo"&gt;940edo&lt;/a&gt;&lt;br /&gt;
{{see also| Diaschismic family #Echidnic }}
Badness: 0.000604&lt;br /&gt;
 
&lt;br /&gt;
13-limit echidnic temperament, the 10&amp;46 temperament, is about as accurate as a biosphere temperament can get.
Spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11&lt;br /&gt;
 
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:52:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank two temperaments&amp;quot; title=&amp;quot;Anchor: Rank two temperaments&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:52 --&gt;Rank two temperaments&lt;/h1&gt;
 
Rank two temperaments tempering out 676/675 include the 13-limit versions of &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;hemiennealimmal&lt;/a&gt;, &lt;a class="wiki_link" href="/Breedsmic%20temperaments"&gt;harry&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;tritikleismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleimsic&lt;/a&gt;, &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;negri&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments"&gt;buzzard&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;quadritikleismic&lt;/a&gt;.&lt;br /&gt;
[[Comma list]]: 91/90, 169/168, 385/384, 441/440
&lt;br /&gt;
 
It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; alone.&lt;br /&gt;
[[Mapping]]: [{{val| 2 2 7 6 3 7 }}, {{val| 0 3 -6 -1 10 1 }}]
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Rank two temperaments-Decitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:53:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank two temperaments-Decitonic&amp;quot; title=&amp;quot;Anchor: Rank two temperaments-Decitonic&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank two temperaments-Decitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:53 --&gt;Decitonic&lt;/h2&gt;
[[POTE generator]]: ~8/7 = 235.088
Commas: 676/675, 1001/1000, 1716/1715, 4225/4224&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 10, 46, 102, 148f, 194bcdf }}
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~15/13 = 248.917&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.028874
Map: [&amp;lt;10 0 47 36 98 37|, &amp;lt;0 2 -3 -1 -8 0|]&lt;br /&gt;
 
EDOs: 130, 270, 940, 1480&lt;br /&gt;
[[Category:Regular temperament theory]]
Badness: 0.0135&lt;br /&gt;
[[Category:Commatic realms]]
&lt;br /&gt;
[[Category:Biome]]
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Rank two temperaments-Avicenna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:54:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Rank two temperaments-Avicenna&amp;quot; title=&amp;quot;Anchor: Rank two temperaments-Avicenna&amp;quot;/&amp;gt; --&gt;&lt;a name="Rank two temperaments-Avicenna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:54 --&gt;Avicenna&lt;/h2&gt;
[[Category:Biosphere]]
Commas: 676/675, 1001/1000, 3025/3024, 4096/4095&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~13/12 = 137.777&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 2 8 16 9 8|, &amp;lt;0 8 -3 -22 4 9|]&lt;br /&gt;
EDOs: 87, 183, 270&lt;br /&gt;
Badness: 0.0156&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Subgroup temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:55:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Subgroup temperaments&amp;quot; title=&amp;quot;Anchor: Subgroup temperaments&amp;quot;/&amp;gt; --&gt;&lt;a name="Subgroup temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:55 --&gt;Subgroup temperaments&lt;/h1&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Subgroup temperaments-Barbados"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:56:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Subgroup temperaments-Barbados&amp;quot; title=&amp;quot;Anchor: Subgroup temperaments-Barbados&amp;quot;/&amp;gt; --&gt;&lt;a name="Subgroup temperaments-Barbados"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:56 --&gt;Barbados&lt;/h2&gt;
Subgroup: 2.3.13/5&lt;br /&gt;
Commas: 676/675&lt;br /&gt;
&lt;br /&gt;
Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intontation subgroup&lt;/a&gt;. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; and &lt;a class="wiki_link" href="/111edo"&gt;111edo&lt;/a&gt;, with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~15/13 = 248.621&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;: [&amp;lt;1 0 -1|, &amp;lt;0 2 3|]&lt;br /&gt;
EDOs: 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362&lt;br /&gt;
Badness: 0.002335&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Subgroup temperaments-Trinidad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:57:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Subgroup temperaments-Trinidad&amp;quot; title=&amp;quot;Anchor: Subgroup temperaments-Trinidad&amp;quot;/&amp;gt; --&gt;&lt;a name="Subgroup temperaments-Trinidad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:57 --&gt;Trinidad&lt;/h2&gt;
Subgroup: 2.3.5.13&lt;br /&gt;
Commas: 325/324, 625/624&lt;br /&gt;
&lt;br /&gt;
Trinidad may be viewed as the reduction of &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt; to the 2.3.5.13 subgroup. Another way to put it is that it is the rank two 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.076&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;: [&amp;lt;1 0 1 0 |, &amp;lt;0 6 5 14|]&lt;br /&gt;
EDOs: 15, 19, 34, 53, 87, 140, 193, 246&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Subgroup temperaments-Parizekmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:58:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Subgroup temperaments-Parizekmic&amp;quot; title=&amp;quot;Anchor: Subgroup temperaments-Parizekmic&amp;quot;/&amp;gt; --&gt;&lt;a name="Subgroup temperaments-Parizekmic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:58 --&gt;Parizekmic&lt;/h2&gt;
Subgroup: 2.3.5.13&lt;br /&gt;
Commas: 676/675&lt;br /&gt;
&lt;br /&gt;
Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;&lt;br /&gt;
&amp;lt;1 0 0 -1|&lt;br /&gt;
&amp;lt;0 2 0 3|&lt;br /&gt;
&amp;lt;0 0 1 1|&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc19"&gt;&lt;a name="Subgroup temperaments-Parizekmic-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:59:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Subgroup temperaments-Parizekmic-Music&amp;quot; title=&amp;quot;Anchor: Subgroup temperaments-Parizekmic-Music&amp;quot;/&amp;gt; --&gt;&lt;a name="Subgroup temperaments-Parizekmic-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:59 --&gt;Music&lt;/h3&gt;
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/petr_parizek/pp_pump_675.mp3" rel="nofollow"&gt;Petr's Pump&lt;/a&gt;, a comma pump based ditty in Pariekmic temperament.&lt;br /&gt;
EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270&lt;/body&gt;&lt;/html&gt;</pre></div>
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