Mint family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>xenwolf
**Imported revision 238464837 - Original comment: **
 
(18 intermediate revisions by 7 users not shown)
Line 1: Line 1:
<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]]s 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


Map: [&lt;1 0 0 2 -2|, &lt;0 1 0 2 2|, &lt;0 0 1 -1 1|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809
EDOs: 7, 9, 12, [[21edo|21]], [[28edo|28]]
Badness: 0.000463


===13-limit===
{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12 }}
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]]: 0.0637 × 10<sup>-3</sup>
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]] ([[POTE]]): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0000637&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }}
&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;
 
Commas: 36/35, 45/44&lt;br /&gt;
[[Badness]]: 0.463 × 10<sup>-3</sup>
&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;
=== 13-limit ===
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;
Subgroup: 2.3.5.7.11.13
Badness: 0.000463&lt;br /&gt;
 
&lt;br /&gt;
Comma list: [[27/26]], 36/35, 45/44
&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;
 
Commas: 27/26, 36/35, 45/44&lt;br /&gt;
Mapping: {{mapping| 1 0 0 2 -2 -1 | 0 1 0 2 2 3 | 0 0 1 -1 1 0 }}
&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;
Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 685.0048, ~5/4 = 390.2563
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>
{{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }}
 
Badness: 0.647 × 10<sup>-3</sup>
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Mint family| ]] <!-- main article -->
[[Category:Mint| ]] <!-- key article -->
[[Category:Rank 3]]

Latest revision as of 00:41, 24 June 2025

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809

Optimal ET sequence: 4, 5, 7, 8d, 9, 12

Badness: 0.0637 × 10-3

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 tuning (POTE): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801

Optimal ET sequence: 7, 9, 12, 21, 28

Badness: 0.463 × 10-3

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 tuning (POTE): ~2 = 1\1, ~3/2 = 685.0048, ~5/4 = 390.2563

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

Badness: 0.647 × 10-3

Retrieved from "https://en.xen.wiki/index.php?title=Mint_family&oldid=201264"