Septisemi temperaments: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

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:~~ [~~<1 0 -7 -5|, <0 1 6 5|~~]

[[Subgroup]]: 2.3.5.7

~~Wedgie~~: ~~<<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 generators: ~2, ~3

~~Map~~: [~~<1 1 1~~ 2|, ~~<0~~ 2 ~~5 3|~~]

[[Optimal tuning]]s:

~~Wedgie~~: ~~<<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=~~

~~Commas: 21/20~~, ~~175/162~~

~~POTE generator~~: ~~~7/6 = 169~~.~~112~~

[[Badness]] (Sintel): 1.41

~~Map:~~ [~~<1 2 3 3|, <0 -3 -5 -2|~~]

== Sodium ==

~~Wedgie~~: ~~<<~~3 5 ~~2 1 -5 -9||~~

[[Subgroup]]: 2.3.5.7

~~EDOs: 7d, 8~~

~~Badness: 0~~.~~0599~~

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

: 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>~~

~~<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"><html><head><title>Septisemi temperaments</title></head><body><a href="#Fluorine">Fluorine</a> | ~~<a href~~=~~"#Sodium">Sodium</a>~~ | ~~<a href="#Oxygen">Oxygen</a>~~

[[Badness]] (Sintel): 1.41

~~<br />~~

~~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.<br />~~

[[Category:Temperament collections]]

~~<br />~~

[[Category:Septisemi temperaments| ]]

~~<h1 id="toc0"><a name="Fluorine"></a>Fluorine</h1>~~

[[Category:Rank 2]]

~~Commas: 21/20, 243/224<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 663.059<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -7 -5|, &lt;0 1 6 5|~~]~~<br />~~

~~Wedgie~~: ~~&lt;&lt;~~1 ~~6 5 7 5 -5||<br />~~

~~EDOs: 9, 20bd, 29bd<br />~~

~~Badness: 0~~.~~0556<br />~~

~~<br />~~

~~<h1 id="toc1"><a name="Sodium"></a>Sodium</h1>~~

~~Commas~~: ~~21/20, 54/49<br />~~

~~<br />~~

~~POTE generator: ~7/6 = 320.182<br />~~

~~<br />~~

~~Map: [&lt;1 1 1 2|, &lt;0 2 5 3~~|]~~<br />~~

~~Wedgie: &lt;&lt;2 5 3 3 -1 -7||<br />~~

~~EDOs: 4, 11, 15b<br />~~

~~Badness: 0.0558<br />~~

~~<br />~~

~~<~~!-- ~~ws:start:WikiTextHeadingRule:4:&lt;h1&gt;~~ --~~><h1 id="toc2"><a name="Oxygen"></a>Oxygen</h1>~~

~~Commas: 21/20, 175/162<br />~~

~~<br />~~

~~POTE generator: ~7/6 = 169.112<br />~~

~~<br />~~

~~Map~~: ~~[&lt;1~~ 2 ~~3 3|, &lt;0 -3 -5 -2|~~]~~<br />~~

~~Wedgie: &lt;&lt;3 5 2 1 -5 -9||<br />~~

~~EDOs: 7d, 8<br />~~

~~Badness: 0.0599</body></html></pre></div>~~

@@ 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>
+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>