Xenharmonic Wiki

Orgonia: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 284290504 - Original comment: **
m Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"
 
(13 intermediate revisions by 9 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>
'''Orgonia''' is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the [[orgonisma]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-09 15:16:42 UTC</tt>.<br>
: The original revision id was <tt>284290504</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]]


Welcome to Orgonia, the commatic realm of the orgonisma, the [[11-limit]] [[comma]] 65536/65219!
== Orgonismic ==
[[Subgroup]]: 2.3.5.7.11


=Orgonismic temperament=
[[Comma list]]: 65536/65219
Comma: 65536/65219


[[Eigenmonzo subgroup|Minimax tuning subgroup]]: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)^(1/5), which is 1.679 cents, and the [[5-limit]] just.
[[Mapping]]: <br>
[{{val| 1 0 0 2 4 }}<br>
{{val| 0 1 0 0 0 }}<br>
{{val| 0 0 1 0 0 }}<br>
{{val| 0 0 0 3 -2 }}]


Map: &lt;&lt;1 0 0 2 4]
[[Minimax tuning]]:  
[0 1 0 0 0]
* [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)<sup>1/5</sup>, which is 1.679 cents, and the [[5-limit]] just.
[0 0 1 0 0]
[0 0 0 3 -2]||


EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282
{{Optimal ET sequence|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}
[[Spectrum of a temperament|Spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11


=Subgroup temperaments=
[[Complexity spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11


==Orgone==  
== Subgroup temperaments ==
Commas:65536/65219
=== Orgone ===
Subgroup: 2.7.11
{{Main|Orgone}}
{{See also| Chromatic pairs #Orgone }}


POTE generator: ~77/64 = 323.372
[[File:orgone_heptatonic.jpg|thumb|alt=orgone_heptatonic.jpg|Orgone heptatonic]]


Sval map: [&lt;1 2 4|, &lt;0 3 -2|]
Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc


[[image:orgone_heptatonic.jpg]]
[[Subgroup]]: 2.7.11


==Oregon==
[[Comma list]]: [[65536/65219]]
Commas: 55/54, 64/63, 100/99
Subgroup: 2.9.15.7.11


POTE generator: ~6/5 = 326.139
{{Mapping|legend=2| 1 2 4 | 0 3 -2 }}


Sval map: [&lt;1 1 1 5 2|, &lt;0 3 4 -3 2|]
{{Mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}
EDOs: 7, 11, 59b, 70bc, 81bcd, 92bcd


The subgroup 2.9.15.7.11 is the [[11-limit]] [[k*N subgroups|2*11 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine family|porcupine temperament]] restricted to this subgroup.
: [[gencom]]: [2 77/64; 65536/65219]


===Orca===
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372
Commas: 55/54, 64/63, 100/99, 85/84
 
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents
 
==== Oregon ====
{{See also| Chromatic pairs #Oregon }}
 
The subgroup 2.9.15.7.11 is the [[11-limit]] [[k*N_subgroups|2*11 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[porcupine]] restricted to this subgroup.
 
[[Subgroup]]: 2.9.15.7.11
 
[[Comma list]]: 55/54, 64/63, 100/99
 
{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
 
{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}
 
: [[gencom]]: [2 6/5; 55/54 64/63 100/99]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
[[Optimal tuning]] (inharmonic [[POTE]]): ~2 = 1\1,  ~6/5 = 326.139
 
{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents
 
===== Orca =====
Subgroup: 2.9.15.7.11.17
Subgroup: 2.9.15.7.11.17
Comma list: 55/54, 64/63, 100/99, 85/84
Sval mapping: [{{val| 1 1 1 5 2 7 }}, {{val| 0 3 4 -3 2 -4 }}]


POTE generator: ~6/5 = 326.644
POTE generator: ~6/5 = 326.644


Sval map: [&lt;1 1 1 5 2 7|, &lt;0 3 4 -3 2 -4|]
{{Optimal ET sequence|legend=1| 7, 11, 92bcd, 103bcd }}
EDOs: 7, 11, 92bcd, 103bcd


===Ork===
===== Ork =====
Commas: 99/98, 121/120, 136/135, 256/255
Subgroup: 2.9.15.7.11.17
Subgroup: 2.9.15.7.11.17
Comma list: 99/98, 121/120, 136/135, 256/255
Sval mapping: [{{val| 1 1 5 2 4 3 }}, {{val| 0 8 -4 3 -2 4 }}]


POTE generator: ~17/14 = 325.714
POTE generator: ~17/14 = 325.714


Sval map: [&lt;1 1 5 2 4 3|, &lt;0 8 -4 3 -2 4|]
{{Optimal ET sequence|legend=1| 11, 37, 48, 59, 70c }}
EDOs: 11, 37, 48, 59, 70c
 


</pre></div>
[[Category:Orgonia]]
<h4>Original HTML content:</h4>
[[Category:Commatic realms]]
<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;Orgonia&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Orgonismic temperament"&gt;Orgonismic temperament&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Subgroup temperaments"&gt;Subgroup temperaments&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Subgroup temperaments-Orgone"&gt;Orgone&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Subgroup temperaments-Oregon"&gt;Oregon&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Subgroup temperaments-Oregon-Orca"&gt;Orca&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Subgroup temperaments-Oregon-Ork"&gt;Ork&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
Welcome to Orgonia, the commatic realm of the orgonisma, the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/comma"&gt;comma&lt;/a&gt; 65536/65219!&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Orgonismic temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Orgonismic temperament&lt;/h1&gt;
Comma: 65536/65219&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Minimax tuning subgroup&lt;/a&gt;: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)^(1/5), which is 1.679 cents, and the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; just.&lt;br /&gt;
&lt;br /&gt;
Map: &amp;lt;&amp;lt;1 0 0 2 4]&lt;br /&gt;
[0 1 0 0 0]&lt;br /&gt;
[0 0 1 0 0]&lt;br /&gt;
[0 0 0 3 -2]||&lt;br /&gt;
&lt;br /&gt;
EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11&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="Subgroup temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Subgroup temperaments&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Subgroup temperaments-Orgone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Orgone&lt;/h2&gt;
Commas:65536/65219&lt;br /&gt;
Subgroup: 2.7.11&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~77/64 = 323.372&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 2 4|, &amp;lt;0 3 -2|]&lt;br /&gt;
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:20:&amp;lt;img src=&amp;quot;/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:20 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Subgroup temperaments-Oregon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Oregon&lt;/h2&gt;
Commas: 55/54, 64/63, 100/99&lt;br /&gt;
Subgroup: 2.9.15.7.11&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 326.139&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 1 1 5 2|, &amp;lt;0 3 4 -3 2|]&lt;br /&gt;
EDOs: 7, 11, 59b, 70bc, 81bcd, 92bcd&lt;br /&gt;
&lt;br /&gt;
The subgroup 2.9.15.7.11 is the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;2*11 subgroup&lt;/a&gt;, the largest subgroup of the 11-limit on which &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; acts like &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit &lt;a class="wiki_link" href="/Porcupine%20family"&gt;porcupine temperament&lt;/a&gt; restricted to this subgroup.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Subgroup temperaments-Oregon-Orca"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Orca&lt;/h3&gt;
Commas: 55/54, 64/63, 100/99, 85/84&lt;br /&gt;
Subgroup: 2.9.15.7.11.17&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~6/5 = 326.644&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 1 1 5 2 7|, &amp;lt;0 3 4 -3 2 -4|]&lt;br /&gt;
EDOs: 7, 11, 92bcd, 103bcd&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Subgroup temperaments-Oregon-Ork"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Ork&lt;/h3&gt;
Commas: 99/98, 121/120, 136/135, 256/255&lt;br /&gt;
Subgroup: 2.9.15.7.11.17&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~17/14 = 325.714&lt;br /&gt;
&lt;br /&gt;
Sval map: [&amp;lt;1 1 5 2 4 3|, &amp;lt;0 8 -4 3 -2 4|]&lt;br /&gt;
EDOs: 11, 37, 48, 59, 70c&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Orgonia"