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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 '''minortonic family''' tempers out the minortone comma (also known as "minortonma"), {{monzo| -16 35 -17 }}. The head of this family is 5-limit minortone temperament, with generator a minor tone.
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:29:29 UTC</tt>.<br>
: The original revision id was <tt>214064634</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">This tempers out the minortone comma, |-16 35 -17&gt;. The head of the family is minortonic temperament, with generator a minor tone.


[[Comma]]: |-16 35 -17&gt;
== Minortone ==
[[Subgroup]]: 2.3.5


[[POTE tuning|POTE generator]]: ~10/9 = 182.466
[[Comma list]]: {{monzo| -16 35 -17 }}


[[Map]]: [&lt;1 16 32|, &lt;0 -17 -35|]
{{Mapping|legend=1| 1 -1 -3 | 0 17 35 }}
[[EDO]]s: [[46edo|46]], [[125edo|125]], [[171edo|171]], [[388edo|388]], 559, 730, 1289, 2019, 2749, 4768, 16323, 21091


[[toc|flat]]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.466


=Mitonic=
{{Optimal ET sequence|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}
As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&gt;. Flipping that gives the 5-limit wedgie &lt;&lt;17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.


However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. The wedgie is now &lt;&lt;17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.
[[Badness]]: 0.029765


[[Comma]]s: 4375/4374, 2100875/2097152
== Mitonic ==
As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, {{monzo| -16 35 -17 }}. 10/9 can be taken as the generator, with 17 of them giving a ~6, 18 of them a ~20/3, and 35 of them giving a ~40. The generator should be tuned about 1/16 of a cent flat, with 6<sup>1/17</sup> being 0.06423 cents flat and 40<sup>1/35</sup> being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.


[[POTE generator]]: ~10/9 = 182.458
However, as noted before, 32/21 is only a ragisma shy of (10/9)<sup>4</sup>, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. 21 generators gives a ~64/7. [[Mos scale]]s of size 20, 33, 46 or 79 notes can be used for mitonic.


[[Map]]: [&lt;1 16 32 -15|, &lt;0 -17 -35 21|]
[[Subgroup]]: 2.3.5.7
[[EDO]]s: [[7edo|7]], [[13edo|13]], [[33edo|33]], [[46edo|46]], [[125edo|125]], [[171edo|171]]
[[Badness]]: 0.0252


=Domain=
[[Comma list]]: 4375/4374, 2100875/2097152
Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Chromatic pairs#Terrain|terrain]].


[[Comma]]s: 250047/250000, 645700815/645657712
{{Mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}


[[POTE generator]]: ~10/9 = 182.467
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.458


[[Map]]: [&lt;3 14 26 28|, &lt;0 -17 -35 -36|]
{{Optimal ET sequence|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}
[[EDO]]S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038
 
[[Badness]]: 0.0140</pre></div>
[[Badness]]: 0.025184
<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;Minortonic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tempers out the minortone comma, |-16 35 -17&amp;gt;. The head of the family is minortonic temperament, with generator a minor tone.&lt;br /&gt;
=== Mineral ===
&lt;br /&gt;
Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: ''mineral'' (46 &amp; 171) and ''ore'' (46 &amp; 125). The mineral temperament tempers out 441/440 and 16384/16335 in the 11-limit. In the 17-limit, both mineral and ore temper out 833/832, 1225/1224, 1701/1700, and 4096/4095 (2.3.5.7.13.17 commas). The word "mineral" is related to "mine" (an excavation from which ore or solid minerals are taken) and "miner" (a person who works in a mine, also as a pun on "minor").
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: |-16 35 -17&amp;gt;&lt;br /&gt;
 
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.466&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 441/440, 4375/4374, 16384/16335
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 16 32|, &amp;lt;0 -17 -35|]&lt;br /&gt;
 
&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s: &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;, &lt;a class="wiki_link" href="/388edo"&gt;388&lt;/a&gt;, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091&lt;br /&gt;
Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextTocRule:4:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;!-- ws:start:WikiTextTocRule:5: --&gt;&lt;a href="#Mitonic"&gt;Mitonic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:5 --&gt;&lt;!-- ws:start:WikiTextTocRule:6: --&gt; | &lt;a href="#Domain"&gt;Domain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.482
&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Mitonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mitonic&lt;/h1&gt;
{{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}
As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, |-16 35 -17&amp;gt;. Flipping that gives the 5-limit wedgie &amp;lt;&amp;lt;17 35 16||, which tells us that 10/9 can be taken as the generator, with 17 of them giving a 6, 18 of them a 20/3, and 35 of them giving a 40. The generator should be tuned about 1/16 of a cent flat, with 6^(1/17) being 0.06423 cents flat and 40^(1/35) being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.059060
However, as noted before, 32/21 is only a ragisma shy of (10/9)^4, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt;. The wedgie is now &amp;lt;&amp;lt;17 35 -21 16 -81 -147||, with 21 10/9 generators giving a 64/7. MOS of size 20, 33, 46 or 79 notes can be used for mitonic.&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 4375/4374, 2100875/2097152&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/POTE%20generator"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.458&lt;br /&gt;
Comma list: 364/363, 441/440, 3584/3575, 4375/4374
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 16 32 -15|, &amp;lt;0 -17 -35 21|]&lt;br /&gt;
Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}
&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/13edo"&gt;13&lt;/a&gt;, &lt;a class="wiki_link" href="/33edo"&gt;33&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/171edo"&gt;171&lt;/a&gt;&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0252&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Domain"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Domain&lt;/h1&gt;
{{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}
Domain temperament adds the landscape comma, 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament &lt;a class="wiki_link" href="/Chromatic%20pairs#Terrain"&gt;terrain&lt;/a&gt;.&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.033140
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 250047/250000, 645700815/645657712&lt;br /&gt;
 
&lt;br /&gt;
==== 17-limit ====
&lt;a class="wiki_link" href="/POTE%20generator"&gt;POTE generator&lt;/a&gt;: ~10/9 = 182.467&lt;br /&gt;
Subgroup: 2.3.5.7.11.13.17
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;3 14 26 28|, &amp;lt;0 -17 -35 -36|]&lt;br /&gt;
Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575
&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;S: 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0140&lt;/body&gt;&lt;/html&gt;</pre></div>
Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481
 
{{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}
 
Badness: 0.019792
 
=== Ore ===
The ore temperament tempers out 385/384 and 1331/1323 in the 11-limit, and maps [[11/8]] to three generators.
 
Subgroup: 2.3.5.7.11
 
Comma list: 385/384, 1331/1323, 4375/4374
 
Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.449
 
{{Optimal ET sequence|legend=1| 46, 125, 171e }}
 
Badness: 0.053662
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 385/384, 1331/1323, 3267/3250
 
Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.470
 
{{Optimal ET sequence|legend=1| 46, 125, 171e, 388ee }}
 
Badness: 0.046170
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445
 
Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.471
 
{{Optimal ET sequence|legend=1| 46, 125, 171e, 388ee }}
 
Badness: 0.028423
 
==== Goldmine ====
The goldmine temperament (46 &amp; 79) is another 13-limit extension of ore, equating [[13/12]] with [[14/13]] and [[16/13]] with two [[10/9]]s.
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 325/324, 385/384, 1331/1323
 
Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.437
 
{{Optimal ET sequence|legend=1| 46, 79, 125f, 171ef, 296eff }}
 
Badness: 0.039302
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 273/272, 325/324, 385/384, 1331/1323
 
Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.444
 
{{Optimal ET sequence|legend=1| 46, 125f, 171ef }}
 
Badness: 0.027440
 
=== Seminar ===
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 4375/4374, 2100875/2097152
 
Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}
 
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.457
 
{{Optimal ET sequence|legend=1| 46, 204c, 250, 296, 342 }}
 
Badness: 0.026808
 
== Domain ==
{{See also| Landscape microtemperaments #Domain }}
 
Domain adds the [[landscape comma]], 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Subgroup temperaments #Terrain|terrain]].
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 250047/250000, 645700815/645657712
 
{{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}
 
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467
 
{{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}
 
[[Badness]]: 0.013979
 
=== Hemidomain ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 250047/250000, 14348907/14348180
 
Mapping: {{mapping| 6 11 17 20 24 | 0 -17 -35 -36 -37 }}
 
: mapping generators: ~55/49 = 1\6, ~100/99 = 17.533
 
Optimal tuning (CTE): ~100/99 = 17.533
 
{{Optimal ET sequence|legend=1| 342, 480, 822, 1164, 1506, 1848, … }}
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Minortonic family| ]] <!-- main article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Minortonic_family"