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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''hemimean family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] 3136/3125, the [[hemimean comma]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-02 04:05:02 UTC</tt>.<br>
: The original revision id was <tt>190464590</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">[[Comma]]: 3136/3125, hemimean


7 and 9 limit minimax
The hemimean comma is the difference between the [[126/125|septimal semicomma (126/125)]] and the [[225/224|septimal kleisma (225/224)]]. This fact alone makes hemimean a very notable rank-3 temperament, as any non-meantone tuning of hemimean will split the [[81/80|syntonic comma (81/80)]] into two equal parts, each representing 126/125~225/224.
[|1 0 0 0&gt;, |0 1 0 0&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 7/6, 4/3


Lattice basis: 28/25 length 0.5055 3/2 length 1.5849
Other equivalences characteristic to hemimean are [[128/125]]~[[50/49]] and [[49/45]]~([[25/24]])<sup>2</sup>.
Angle(28/25, 3/2) = 90 degrees
Map to lattice: [&lt;0 0 2 5|, &lt;0 1 0 0|]


Map: [&lt;1 0 0 -3|, &lt;0 1 0 0|, &lt;0 0 2 5|]
== Hemimean ==
[[Generator|Generators]]: 2, 3, 56/25
[[Subgroup]]: 2.3.5.7
[[edo|Edos]]: [[217edo|217]], [[229edo|229]], [[328edo|328]], [[359edo|359]], [[446edo|446]]
Badness: 0.000160


==Belobog==
[[Comma list]]: 3136/3125
[[Comma|Commas]]: 3136/3125, 441/440


11 limit minimax
{{Mapping|legend=1| 1 0 0 -3 | 0 1 0 0 | 0 0 2 5 }}
[|1 0 0 0 0&gt;, |27/22 6/11 -5/22 -3/11 5/22&gt;,
: Mapping generators: ~2, ~3, ~56/25
|24/11 -4/11 -2/11 2/11 2/11&gt;,
|27/11 -10/11 -5/11 5/11 5/11&gt;,
|24/11 -4/11 -13/11 2/11 13/11&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 9/7


Lattice basis: 28/25 0.3829 16/15 1.1705
[[Mapping to lattice]]: {{mapping| 0 0 2 5 | 0 1 0 0 }}
Angle(28/25, 16/15) = 93.2696
Map to lattice: [&lt;0 -2 2 5 4|, &lt;0 -1 0 0 -2|]


Map: [&lt;1 0 0 -3 -9|, &lt;0 1 0 0 2|, [0 0 2 5 8|]
Lattice basis:  
[[Generator|Generators]]: 2, 3, 56/25
: 28/25 length = 0.5055, 3/2 length = 1.5849
[[edo|Edos]]: 12, 31, 87, 118, 130, 217, [[248edo|248]], [[378edo|378]], [[626edo|626]]
: Angle (28/25, 3/2) = 90 degrees
Badness: 0.000609
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8194{{c}}, ~3/2 = 702.1353{{c}}, ~28/25 = 193.7425{{c}}
: [[error map]]: {{val| -0.181 -0.000 +0.810 -0.474 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.1118{{c}}, ~28/25 = 193.7167{{c}}
: error map: {{val| 0.000 +0.157 +1.120 -0.243 }}
 
[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 6/5 0 0 2/5 }}, {{monzo| 0 0 0 1 }}]
: [[eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.7
 
{{Optimal ET sequence|legend=1| 12, 19, 31, 68, 80, 87, 99, 217, 229, 328, 347, 446, 675c }}
 
[[Badness]] (Sintel): 0.706
 
[[Complexity spectrum]]: 5/4, 7/5, 4/3, 6/5, 8/7, 7/6, 9/8, 10/9, 9/7
 
[[Projection pair]]s: <code>5 3136/625, 7 68841472/9765625</code> to 2.3.25/7
 
== Belobog ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 441/440, 3136/3125
 
{{Mapping|legend=1| 1 0 0 -3 -9 | 0 1 0 0 2 | 0 0 2 5 8 }}
: Mapping generators: ~2, ~3, ~56/25
 
Mapping to lattice: {{mapping| 0 -2 2 5 4 | 0 -1 0 0 -2 }}
 
Lattice basis:
: 28/25 length = 0.3829, 16/15 length = 1.1705
: Angle (28/25, 16/15) = 93.2696
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0098{{c}}, ~3/2 = 701.7170{{c}}, ~28/25 = 193.5520{{c}}
: [[error map]]: {{val| +0.010 -0.228 +0.810 -1.046 +0.542 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7144{{c}}, ~28/25 = 193.5518{{c}}
: error map: {{val| 0.000 -0.241 +0.790 -1.067 +0.525 }}
 
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 27/22 6/11 -5/22 -3/11 5/22 }}, {{monzo| 24/11 -4/11 -2/11 2/11 2/11 }}, {{monzo| 27/11 -10/11 -5/11 5/11 5/11 }}, {{monzo| 24/11 -4/11 -13/11 2/11 13/11 }}]
: [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/5
 
{{Optimal ET sequence|legend=1| 12, 19e, 31, 68e, 87, 99e, 118, 130, 217, 248 }}
 
[[Badness]] (Sintel): 0.732
 
[[Projection pair]]s: 5 3136/625, 7 68841472/9765625, 11 1700108992512/152587890625 to 2.3.25/7


Scales: [[belobog31]]
Scales: [[belobog31]]


===13-limit===
=== 13-limit ===
Commas: 441/440, 1001/1000, 3136/3125
Subgroup: 2.3.5.7.11.13
 
Comma list: 441/440, 1001/1000, 3136/3125
 
Mapping: {{mapping| 1 0 0 -3 -9 15 | 0 1 0 0 2 -2 | 0 0 2 5 8 -7 }}
 
Optimal tunings:
* WE: ~2 = 1199.9154{{c}}, ~3/2 = 701.7875{{c}}, ~28/25 = 193.5853{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8346{{c}}, ~28/25 = 193.5962{{c}}
 
{{Optimal ET sequence|legend=0| 31, 43, 56, 74, 87, 118, 130, 217, 248, 347e, 378, 465, 595e }}
 
Badness (Sintel): 1.03
 
=== Bellowblog ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 196/195, 352/351, 625/624
 
Mapping: {{mapping| 1 0 0 -3 -9 -4 | 0 1 0 0 2 -1 | 0 0 2 5 8 8 }}
 
Optimal tunings:
* WE: ~2 = 1200.000{{c}}, ~3/2 = 702.5857{{c}}, ~28/25 = 193.2930{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.6342{{c}}, ~28/25 = 193.2932{{c}}
 
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 56, 68e, 87, 118, 186ef, 205d }}
 
Badness (Sintel): 1.18
 
== Siebog ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 540/539, 3136/3125
 
{{Mapping|legend=1| 1 0 0 -3 8 | 0 1 0 0 3 | 0 0 2 5 -8 }}
: Mapping generators: ~2, ~3, ~56/25
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5790{{c}}, ~3/2 = 701.8397{{c}}, ~28/25 = 194.0111{{c}}
: [[error map]]: {{val| -0.421 -0.536 +0.867 +0.388 +0.849 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7235{{c}}, ~28/25 = 193.9948{{c}}
: error map: {{val| 0.000 -0.232 +1.676 +1.148 +1.894 }}
 
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 8/5 3/5 1/5 0 -1/5 }}, {{monzo| 1 3/2 1/2 0 -1/2 }}, {{monzo| 8/5 3/5 -4/5 0 4/5 }}]
: [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
 
{{Optimal ET sequence|legend=1| 12e, 18e, 19, 31, 68e, 80, 99e, 130, 210e, 241, 340ce, 371ce, 470cdee, 501cde, 581cdee, 711ccdee }}
 
[[Badness]] (Sintel): 1.05
 
== Triglav ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 3025/3024, 3136/3125
 
{{Mapping|legend=1| 1 0 -2 -8 0 | 0 1 2 5 2 | 0 0 4 10 1 }}
: Mapping generators: ~2, ~3, ~11/9
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8764{{c}}, ~3/2 = 702.4302{{c}}, ~11/9 = 345.5856{{c}}
: [[error map]]: {{val| -0.124 +0.352 +0.889 -0.448 -1.119 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4067{{c}}, ~11/9 = 345.6505{{c}}
: error map: {{val| 0.000 +0.452 +1.102 -0.288 -0.854 }}
 
{{Optimal ET sequence|legend=1| 24d, 31, 80, 87, 111, 118, 198, 316, 514c, 545c }}
 
[[Badness]] (Sintel): 0.984
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 1001/1000, 3025/3024
 
Mapping: {{Mapping| 1 0 -2 -8 0 5 | 0 1 2 5 2 -1 | 0 0 4 10 1 1 }}
 
Optimal tunings:
* WE: ~2 = 1199.6554{{c}}, ~3/2 = 702.8049{{c}}, ~11/9 = 345.3412{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9366{{c}}, ~11/9 = 345.4458{{c}}
 
{{Optimal ET sequence|legend=0| 24d, 31, 56, 80, 87, 111, 118, 167, 198 }}
 
Badness (Sintel): 1.16
 
== Semihemimean ==
Named by [[Xenllium]] in 2026, semihemimean tempers out [[9801/9800]] and splits the octave in halves.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 3136/3125, 9801/9800
 
{{Mapping|legend=1| 2 0 0 -6 -3 | 0 1 0 0 -2 | 0 0 2 5 7 }}
: Mapping generators: ~99/70, ~3, ~56/25
 
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 599.9102{{c}}, ~3/2 = 702.1314{{c}}, ~28/25 = 193.7431{{c}}
: [[error map]]: {{val| -0.180 -0.003 +0.813 -0.470 -0.008 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1353{{c}}, ~28/25 = 193.7122{{c}}
: error map: {{val| 0.000 +0.180 +1.111 -0.265 +0.397 }}
 
{{Optimal ET sequence|legend=1| 12, …, 38d, 50, 68, 80, 118, 130, 198, 248, 328, 446, 774c }}
 
[[Badness]] (Sintel): 1.79
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1001/1000, 3136/3125, 4459/4455
 
Mapping: {{Mapping| 2 0 0 -6 -3 15 | 0 1 0 0 -2 2 | 0 0 2 5 7 -6 }}
 
Optimal tunings:
* WE: ~99/70 = 599.8791{{c}}, ~3/2 = 702.1476{{c}}, ~28/25 = 193.7877{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1740{{c}}, ~28/25 = 193.7869{{c}}
 
{{Optimal ET sequence|legend=0| 12, …, 50, 68, 80, 118, 130, 198, 328, 576cf, 774cf, 904cef }}
 
Badness (Sintel): 1.55
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 289/288, 561/560, 1001/1000, 1632/1625
 
Mapping: {{Mapping| 2 0 0 -6 -3 15 5 | 0 1 0 0 -2 2 1 | 0 0 2 5 7 -6 0 }}
 
Optimal tunings:
* WE: ~17/12 = 599.9481{{c}}, ~3/2 = 702.2594{{c}}, ~28/25 = 193.7763{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 702.2692{{c}}, ~28/25 = 193.7762{{c}}
 
{{Optimal ET sequence|legend=0| 12, …, 50, 68, 80, 118, 130, 198 }}
 
Badness (Sintel): 1.74
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 289/288, 361/360, 456/455, 476/475, 561/560
 
Mapping: {{Mapping| 2 0 0 -6 -3 15 5 3 | 0 1 0 0 -2 2 1 1 | 0 0 2 5 7 -6 0 1 }}
 
Optimal tunings:
* WE: ~17/12 = 599.9687{{c}}, ~3/2 = 702.3501{{c}}, ~19/17 = 193.7922{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 702.3549{{c}}, ~19/17 = 193.7919{{c}}
 
{{Optimal ET sequence|legend=0| 12, …, 50, 68, 80, 118, 130, 198 }}
 
Badness (Sintel): 1.32
 
== Subgroup extensions ==
=== Hemimean orion (2.3.5.7.17) ===
As the second generator of hemimean, [[28/25]], is close to [[19/17]], and as the latter is the [[mediant]] of [[10/9]] and [[9/8]], it is natural to extend hemimean to the 2.3.5.7.17.19 subgroup by tempering out their difference [[476/475]], or equivalently stated, the [[semiparticular]] (5/4)/(19/17)<sup>2</sup> = [[1445/1444]]. Notice 3136/3125 = (476/475)⋅([[2128/2125]]) and that 2128/2125 = ([[1216/1215]])⋅([[1701/1700]]), so it makes sense to temper out 1216/1215 and/or 1701/1700 as well. An interesting tuning not in the optimal ET sequence is [[111edo]]. This temperament finds the harmonic 17 and 19 at (+5, +1) and (+5, +2), respectively, with virtually no additional error.
 
The [[S-expression]]-based comma list for the 2.3.5.7.17.19-subgroup extension is {[[1216/1215|S16/S18]], [[1445/1444|S17/S19]], [[1701/1700|S18/S20]](, ([[136/135|S16⋅S17]])/([[190/189|S19⋅S20]]) = [[476/475|(S16/S18)⋅(S17/S19)⋅(S18/S20)]])}.
 
Subgroup: 2.3.5.7.17
 
Comma list: 1701/1700, 3136/3125
 
Subgroup-val mapping: {{mapping| 1 0 0 -3 -5 | 0 1 0 0 5 | 0 0 2 5 1 }}
 
Optimal tunings:
* WE: ~2 = 1199.7919{{c}}, ~3/2 = 702.2561{{c}}, ~28/25 = 193.7586{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3042{{c}}, ~28/25 = 193.7365{{c}}
 
{{Optimal ET sequence|legend=0| 12, 19g, 31g, …, 87, 99, 217, 229, 316, 328, 446, 545c, 873cg }}
 
Badness (Sintel): 0.884
 
==== 2.3.5.7.17.19 subgroup ====
Subgroup: 2.3.5.7.17.19
 
Comma list: 476/475, 1216/1215, 1445/1444
 
Subgroup-val mapping: {{mapping| 1 0 0 -3 -5 -6 | 0 1 0 0 5 5 | 0 0 2 5 1 2 }}
 
Optimal tunings:
* WE: ~2 = 1199.8239{{c}}, ~3/2 = 702.1623{{c}}, ~19/17 = 193.7325{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.2129{{c}}, ~19/17 = 193.7161{{c}}
 
{{Optimal ET sequence|legend=0| 12, 19gh, 31gh, …, 87, 99, 118, 210gh, 217, 229, 328h, 446 }}
 
Badness (Sintel): 0.578
 
=== Semiorion (2.3.5.7.17) ===
Semiorion is an alternative subgroup extension of lower complexity, which splits the octave into two. The [[S-expression]]-based comma list for the 2.3.5.7.17.19 subgroup extension is {[[289/288|S17]], [[361/360|S19]], [[1216/1215|S16/S18]], ([[1701/1700|S18/S20]], [[476/475]] = [[2128/2125|S16/S20]]⋅[[1445/1444|S17/S19]])}.
 
Subgroup: 2.3.5.7.17
 
Comma list: 289/288, 3136/3125
 
Subgroup-val mapping: {{mapping| 2 0 0 -6 5 | 0 1 0 0 1 | 0 0 2 5 0 }}
: mapping generators: ~17/12, ~3, ~56/25
 
Optimal tunings:
* WE: ~17/12 = 600.0551{{c}}, ~3/2 = 702.1998{{c}}, ~28/25 = 193.5929{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 702.2183{{c}}, ~28/25 = 193.6044{{c}}
 
{{Optimal ET sequence|legend=0| 12, 30d, 38d, 50, 62, 68, 106d, 118, 248g, 316g }}
 
Badness (Sintel): 1.69
 
==== 2.3.5.7.17.19 subgroup ====
Subgroup: 2.3.5.7.17.19


Map: [&lt;1 0 0 -3 -9 15|, &lt;0 1 0 0 2 -2|, &lt;0 0 2 5 8 -7|]
Comma list: 289/288, 361/360, 476/475
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 378, 465
Badness: 0.00111


===Bellowblog===
Mapping: {{mapping| 2 0 0 -6 5 3 | 0 1 0 0 1 1 | 0 0 2 5 0 1 }}
Commas: 196/195, 352/351, 625/624


Map: [&lt;1 0 0 -3 -9 -4|, &lt;0 1 0 0 2 -1|, &lt;0 0 2 5 8 8|]
Optimal tunings:  
EDOs: 31, 56, 87, 118
* WE: ~17/12 = 600.0873{{c}}, ~3/2 = 702.2450{{c}}, ~19/17 = 193.5751{{c}}
Badness: 0.00126
* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 702.2791{{c}}, ~19/17 = 193.5923{{c}}


==Siebog==
{{Optimal ET sequence|legend=0| 12, 30dh, 38d, 50, 68, 106d, 118, 248g, 316g }}
[[Comma|Commas]]: 3136/3125, 540/539


11 limit minimax
Badness (Sintel): 0.722
[|1 0 0 0 0&gt;, |0 1 0 0 0&gt;, |8/5 3/5 1/5 0 -1/5&gt;,
|1 3/2 1/2 0 -1/2&gt;, |8/5 3/5 -4/5 0 4/5&gt;]
[[Eigenmonzo|Eigenmonzos]]: 2, 11/10, 4/3


Map: [&lt;1 0 0 -3 8|, &lt;0 1 0 0 3|, &lt;0 0 2 5 -8|]
[[Category:Hemimean family| ]] <!-- main article -->
[[Generator|Generators]]: 2, 3, 768/343
[[Category:Temperament families]]
[[edo|Edos]]: 19, 31, 80, 111, [[130edo|130]], [[241edo|241]]
[[Category:Catalogs of rank-3 temperaments]]
Badness: 0.000870</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;Hemimean family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 3136/3125, hemimean&lt;br /&gt;
&lt;br /&gt;
7 and 9 limit minimax&lt;br /&gt;
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |6/5 0 0 2/5&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 7/6, 4/3&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 28/25 length 0.5055 3/2 length 1.5849&lt;br /&gt;
Angle(28/25, 3/2) = 90 degrees&lt;br /&gt;
Map to lattice: [&amp;lt;0 0 2 5|, &amp;lt;0 1 0 0|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3|, &amp;lt;0 1 0 0|, &amp;lt;0 0 2 5|] &lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 56/25&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/217edo"&gt;217&lt;/a&gt;, &lt;a class="wiki_link" href="/229edo"&gt;229&lt;/a&gt;, &lt;a class="wiki_link" href="/328edo"&gt;328&lt;/a&gt;, &lt;a class="wiki_link" href="/359edo"&gt;359&lt;/a&gt;, &lt;a class="wiki_link" href="/446edo"&gt;446&lt;/a&gt;&lt;br /&gt;
Badness: 0.000160&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Belobog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Belobog&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3136/3125, 441/440&lt;br /&gt;
&lt;br /&gt;
11 limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |27/22 6/11 -5/22 -3/11 5/22&amp;gt;, &lt;br /&gt;
|24/11 -4/11 -2/11 2/11 2/11&amp;gt;, &lt;br /&gt;
|27/11 -10/11 -5/11 5/11 5/11&amp;gt;, &lt;br /&gt;
|24/11 -4/11 -13/11 2/11 13/11&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 9/7&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 28/25 0.3829 16/15 1.1705&lt;br /&gt;
Angle(28/25, 16/15) = 93.2696&lt;br /&gt;
Map to lattice: [&amp;lt;0 -2 2 5 4|, &amp;lt;0 -1 0 0 -2|]&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 -9|, &amp;lt;0 1 0 0 2|, [0 0 2 5 8|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 56/25&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 12, 31, 87, 118, 130, 217, &lt;a class="wiki_link" href="/248edo"&gt;248&lt;/a&gt;, &lt;a class="wiki_link" href="/378edo"&gt;378&lt;/a&gt;, &lt;a class="wiki_link" href="/626edo"&gt;626&lt;/a&gt;&lt;br /&gt;
Badness: 0.000609&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/belobog31"&gt;belobog31&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Belobog-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
Commas: 441/440, 1001/1000, 3136/3125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 -9 15|, &amp;lt;0 1 0 0 2 -2|, &amp;lt;0 0 2 5 8 -7|]&lt;br /&gt;
EDOs: 12, 31, 43, 56, 74, 87, 118, 130, 217, 248, 378, 465&lt;br /&gt;
Badness: 0.00111&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Belobog-Bellowblog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Bellowblog&lt;/h3&gt;
Commas: 196/195, 352/351, 625/624&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 -9 -4|, &amp;lt;0 1 0 0 2 -1|, &amp;lt;0 0 2 5 8 8|]&lt;br /&gt;
EDOs: 31, 56, 87, 118&lt;br /&gt;
Badness: 0.00126&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Siebog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Siebog&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 3136/3125, 540/539&lt;br /&gt;
&lt;br /&gt;
11 limit minimax&lt;br /&gt;
[|1 0 0 0 0&amp;gt;, |0 1 0 0 0&amp;gt;, |8/5 3/5 1/5 0 -1/5&amp;gt;, &lt;br /&gt;
|1 3/2 1/2 0 -1/2&amp;gt;, |8/5 3/5 -4/5 0 4/5&amp;gt;]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzos&lt;/a&gt;: 2, 11/10, 4/3&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -3 8|, &amp;lt;0 1 0 0 3|, &amp;lt;0 0 2 5 -8|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 768/343&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: 19, 31, 80, 111, &lt;a class="wiki_link" href="/130edo"&gt;130&lt;/a&gt;, &lt;a class="wiki_link" href="/241edo"&gt;241&lt;/a&gt;&lt;br /&gt;
Badness: 0.000870&lt;/body&gt;&lt;/html&gt;</pre></div>
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