Mint family: Difference between revisions

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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 '''mint family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-23 17:28:25 UTC</tt>.<br>
: The original revision id was <tt>238464837</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">The quartonic temperament tempers out [[36_35|36/35]], identifying both [[7_6|7/6]] with [[6_5|6/5]] and [[5_4|5/4]] with [[9_7|9/7]].


[[Comma]]: 36/35
== Mint ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 0 0 2|, &lt;0 1 0 2|, &lt;0 0 1 -1|]
[[Comma list]]: 36/35
EDOs: [[4edo|4]], [[5edo|5]], [[7edo|7]], [[9edo|9]], [[12edo|12]]
[[Badness]]: 0.0000637


==Nickel==
{{Mapping|legend=1| 1 0 0 2 | 0 1 0 2 | 0 0 1 -1 }}
Commas: 36/35, 45/44
: mapping generators: ~2, ~3, ~5


Map: [&lt;1 0 0 2 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 -1 1|]
[[Optimal tuning]]s:  
EDOs: 7, 9, 12, [[21edo|21]], [[28edo|28]]
* [[WE]]: ~2 = 1196.3575{{c}}, ~3/2 = 696.5144{{c}}, ~5/4 = 403.0537{{c}}
Badness: 0.000463
: [[error map]]: {{val| -3.643 -9.083 +9.455 +13.864 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}}
: error map: {{val| 0.000 -6.708 +14.813 +20.543 }}


===13-limit===
{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }}
Commas: 27/26, 36/35, 45/44


Map: [&lt;1 0 0 2 -2 -1|, &lt;0 1 0 2 2 3|, &lt;0 0 1 -1 1 0|]
[[Badness]] (Sintel): 0.281
EDOs: 7, 9, [[16edo|16]], 21, 28
 
Badness: 0.000647</pre></div>
== Nickel ==
<h4>Original HTML content:</h4>
[[Subgroup]]: 2.3.5.7.11
<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;Mint family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The quartonic temperament tempers out &lt;a class="wiki_link" href="/36_35"&gt;36/35&lt;/a&gt;, identifying both &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; with &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt; and &lt;a class="wiki_link" href="/5_4"&gt;5/4&lt;/a&gt; with &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;.&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 36/35, 45/44
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 36/35&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 2 2 | 0 0 1 -1 1 }}
Map: [&amp;lt;1 0 0 2|, &amp;lt;0 1 0 2|, &amp;lt;0 0 1 -1|]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/4edo"&gt;4&lt;/a&gt;, &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;&lt;br /&gt;
[[Optimal tuning]]s:
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0000637&lt;br /&gt;
* [[WE]]: ~2 = 1198.7814{{c}}, ~3/2 = 688.1375{{c}}, ~5/4 = 391.4822{{c}}
&lt;br /&gt;
: [[error map]]: {{val| -1.219 -15.036 +2.731 +13.530 +14.002 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Nickel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Nickel&lt;/h2&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}}
Commas: 36/35, 45/44&lt;br /&gt;
: error map: {{val| 0.000 -13.956 +4.914 +15.945 +15.908 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 0 2 -2|, &amp;lt;0 1 0 2 2|, &amp;lt;0 0 1 -1 1|]&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }}
EDOs: 7, 9, 12, &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/28edo"&gt;28&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.000463&lt;br /&gt;
[[Badness]] (Sintel): 0.557
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Nickel-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;13-limit&lt;/h3&gt;
=== 13-limit ===
Commas: 27/26, 36/35, 45/44&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Map: [&amp;lt;1 0 0 2 -2 -1|, &amp;lt;0 1 0 2 2 3|, &amp;lt;0 0 1 -1 1 0|]&lt;br /&gt;
Comma list: 27/26, 36/35, 45/44
EDOs: 7, 9, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, 21, 28&lt;br /&gt;
 
Badness: 0.000647&lt;/body&gt;&lt;/html&gt;</pre></div>
Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }}
 
Optimal tunings:
* WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}}
 
{{Optimal ET sequence|legend=0| 7, 9, 12f, 16, 21, 28, 37b }}
 
Badness (Sintel): 0.605
 
[[Category:Mint family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]

Latest revision as of 12:13, 14 August 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The mint family of rank-3 temperaments tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.

Mint

Subgroup: 2.3.5.7

Comma list: 36/35

Mapping: [⟨1 0 0 2], ⟨0 1 0 2], ⟨0 0 1 -1]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

  • WE: ~2 = 1196.3575 ¢, ~3/2 = 696.5144 ¢, ~5/4 = 403.0537 ¢
error map: ⟨-3.643 -9.083 +9.455 +13.864]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 695.2474 ¢, ~5/4 = 401.1263 ¢
error map: ⟨0.000 -6.708 +14.813 +20.543]

Optimal ET sequence: 4, 5, 7, 8d, 9, 12, 41cd, 53cdd

Badness (Sintel): 0.281

Nickel

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44

Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 2 2], ⟨0 0 1 -1 1]]

Optimal tunings:

  • WE: ~2 = 1198.7814 ¢, ~3/2 = 688.1375 ¢, ~5/4 = 391.4822 ¢
error map: ⟨-1.219 -15.036 +2.731 +13.530 +14.002]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 687.9993 ¢, ~5/4 = 391.2274 ¢
error map: ⟨0.000 -13.956 +4.914 +15.945 +15.908]

Optimal ET sequence: 7, 9, 12, 21, 28

Badness (Sintel): 0.557

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44

Mapping: [⟨1 0 0 2 -2 -1], ⟨0 1 0 2 2 3], ⟨0 0 1 -1 1 0]]

Optimal tunings:

  • WE: ~2 = 1199.6174 ¢, ~3/2 = 684.7864 ¢, ~5/4 = 390.1319 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 684.7716 ¢, ~5/4 = 390.0622 ¢

Optimal ET sequence: 7, 9, 12f, 16, 21, 28, 37b

Badness (Sintel): 0.605

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