Septisemi temperaments: 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>
This is a collection of very low [[complexity]] temperaments [[tempering out]] the septimal minor semitone, [[21/20]], and hence equating 5/3 with 7/4, and 10/7 with 3/2.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-05 20:52:25 UTC</tt>.<br>
: The original revision id was <tt>298704404</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">[[toc|flat]]


These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4, and 10/7 with 3/2.
Temperaments discussed elsewhere are:
* ''[[Mother]]'' (+16/15) → [[Father family #Mother|Father family]]
* ''[[Sharptone]]'' (+28/27) → [[Meantone family #Sharptone|Meantone family]]
* ''[[Pelogic]]'' (+135/128) → [[Mavila family #Pelogic|Mavila family]]
* ''[[Flattie]]'' (+25/24) → [[Dicot family #Flattie|Dicot family]]
* [[Beep]] (+27/25) → [[Bug family #Beep|Bug family]]
* ''[[Deflated]]'' (+128/125) → [[Augmented family #Deflated|Augmented family]]
* ''[[Gidorah]]'' (+144/125) → [[Gamelismic clan #Gidorah|Gamelismic clan]]
* ''[[Oxygen]]'' (+175/162) → [[Very low accuracy temperaments #Oxygen|Very low accuracy temperaments]]


=Fluorine=
Considered below are fluorine and sodium.
Commas: 21/20, 243/224


POTE generator: ~3/2 = 663.059
== Fluorine ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Avila]].''


Map: [&lt;1 0 -7 -5|, &lt;0 1 6 5|]
[[Subgroup]]: 2.3.5.7
Wedgie: &lt;&lt;1 6 5 7 5 -5||
EDOs: 9, 20bd, 29bd
Badness: 0.0556


=Sodium=
[[Comma list]]: 21/20, 243/224
Commas: 21/20, 54/49


POTE generator: ~7/6 = 320.182
{{Mapping|legend=1| 1 0 -7 -5 | 0 1 6 5 }}
: mapping generators: ~2, ~3


Map: [&lt;1 1 1 2|, &lt;0 2 5 3|]
[[Optimal tuning]]s:  
Wedgie: &lt;&lt;2 5 3 3 -1 -7||
* [[WE]]: ~2 = 1211.420{{c}}, ~3/2 = 669.369{{c}}
EDOs: 4, 11, 15b
: [[error map]]: {{val| +11.420 -21.165 +18.481 -21.980 }}
Badness: 0.0558
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 665.210{{c}}
: error map: {{val| 0.000 -36.745 +4.945 -42.777 }}


=Oxygen=
{{Optimal ET sequence|legend=1| 2c, 7c, 9, 20bdd, 29bdd }}
Commas: 21/20, 175/162


POTE generator: ~7/6 = 169.112
[[Badness]] (Sintel): 1.41


Map: [&lt;1 2 3 3|, &lt;0 -3 -5 -2|]
== Sodium ==
Wedgie: &lt;&lt;3 5 2 1 -5 -9||
[[Subgroup]]: 2.3.5.7
EDOs: 7d, 8
Badness: 0.0599


[[Comma list]]: 21/20, 54/49


{{Mapping|legend=1| 1 1 1 2 | 0 2 5 3 }}
: mapping generators: ~2, ~7/6


[[Optimal tuning]]s:
* [[WE]]: ~2 = 1207.624{{c}}, ~7/6 = 322.216{{c}}
: [[error map]]: {{val| +7.624 -49.898 +32.393 +13.072 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/6 = 322.210{{c}}
: error map: {{val| 0.000 -57.535 +24.737 -2.196 }}


</pre></div>
{{Optimal ET sequence|legend=1| 4, 11 }}
<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;Septisemi temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&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:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Fluorine"&gt;Fluorine&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Sodium"&gt;Sodium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Oxygen"&gt;Oxygen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
[[Badness]] (Sintel): 1.41
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
 
These are very low complexity temperaments tempering out the minor septimal semitone, 21/20 and hence equating 5/3 with 7/4, and 10/7 with 3/2.&lt;br /&gt;
[[Category:Temperament collections]]
&lt;br /&gt;
[[Category:Septisemi temperaments| ]] <!-- main article -->
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Fluorine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Fluorine&lt;/h1&gt;
[[Category:Rank 2]]
Commas: 21/20, 243/224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 663.059&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -7 -5|, &amp;lt;0 1 6 5|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 6 5 7 5 -5||&lt;br /&gt;
EDOs: 9, 20bd, 29bd&lt;br /&gt;
Badness: 0.0556&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Sodium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Sodium&lt;/h1&gt;
Commas: 21/20, 54/49&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/6 = 320.182&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 2|, &amp;lt;0 2 5 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 5 3 3 -1 -7||&lt;br /&gt;
EDOs: 4, 11, 15b&lt;br /&gt;
Badness: 0.0558&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Oxygen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Oxygen&lt;/h1&gt;
Commas: 21/20, 175/162&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/6 = 169.112&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -3 -5 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 5 2 1 -5 -9||&lt;br /&gt;
EDOs: 7d, 8&lt;br /&gt;
Badness: 0.0599&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 12:31, 27 November 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.

This is a collection of very low complexity temperaments tempering out the septimal minor semitone, 21/20, and hence equating 5/3 with 7/4, and 10/7 with 3/2.

Temperaments discussed elsewhere are:

Considered below are fluorine and sodium.

Fluorine

For the 5-limit version, see Miscellaneous 5-limit temperaments #Avila.

Subgroup: 2.3.5.7

Comma list: 21/20, 243/224

Mapping: [⟨1 0 -7 -5], ⟨0 1 6 5]]

mapping generators: ~2, ~3

Optimal tunings:

  • WE: ~2 = 1211.420 ¢, ~3/2 = 669.369 ¢
error map: ⟨+11.420 -21.165 +18.481 -21.980]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 665.210 ¢
error map: ⟨0.000 -36.745 +4.945 -42.777]

Optimal ET sequence: 2c, 7c, 9, 20bdd, 29bdd

Badness (Sintel): 1.41

Sodium

Subgroup: 2.3.5.7

Comma list: 21/20, 54/49

Mapping: [⟨1 1 1 2], ⟨0 2 5 3]]

mapping generators: ~2, ~7/6

Optimal tunings:

  • WE: ~2 = 1207.624 ¢, ~7/6 = 322.216 ¢
error map: ⟨+7.624 -49.898 +32.393 +13.072]
  • CWE: ~2 = 1200.000 ¢, ~7/6 = 322.210 ¢
error map: ⟨0.000 -57.535 +24.737 -2.196]

Optimal ET sequence: 4, 11

Badness (Sintel): 1.41

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