Orgonia: 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>
'''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>2011-05-28 12:03:05 UTC</tt>.<br>
: The original revision id was <tt>232586572</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">Welcome to Orgonia, the commatic realm of the orgonisma, the [[11-limit]] [[comma]] 65536/65219!


=Orgonismic temperament=
== Orgonismic ==
Comma: 65536/65219
[[Subgroup]]: 2.3.5.7.11


[[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.
[[Comma list]]: 65536/65219


Map: &lt;&lt;1 0 0 2 4]
[[Mapping]]: <br>
[0 1 0 0 0]
[{{val| 1 0 0 2 4 }}<br>
[0 0 1 0 0]
{{val| 0 1 0 0 0 }}<br>
[0 0 0 3 -2]||
{{val| 0 0 1 0 0 }}<br>
{{val| 0 0 0 3 -2 }}]


EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282
[[Minimax tuning]]:  
[[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
* [[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.


=Subgroup temperaments=
{{Optimal ET sequence|legend=1| 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 }}


==Orgone==
[[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
Commas:65536/65219
Subgroup: 2.7.11


POTE generator: ~77/64 = 323.372
== Subgroup temperaments ==
=== Orgone ===
{{Main|Orgone}}
{{See also| Chromatic pairs #Orgone }}


Sval map: [&lt;1 2 4|, &lt;0 3 -2|]
[[File:orgone_heptatonic.jpg|thumb|alt=orgone_heptatonic.jpg|Orgone heptatonic]]
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308


==Oregon==
Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].
Commas: 55/54, 64/63, 100/99
Subgroup: 2.9.15.7.11


POTE generator: ~6/5 = 326.139
[[Subgroup]]: 2.7.11


Sval map: [&lt;1 1 1 5 2|, &lt;0 3 4 -3 2|]
[[Comma list]]: [[65536/65219]]
EDOs: 7, 11


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.</pre></div>
{{Mapping|legend=2| 1 2 4 | 0 3 -2 }}
<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;Orgonia&lt;/title&gt;&lt;/head&gt;&lt;body&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;
{{Mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}
&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;
: [[gencom]]: [2 77/64; 65536/65219]
Comma: 65536/65219&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372
&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;
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783 }}
Map: &amp;lt;&amp;lt;1 0 0 2 4] &lt;br /&gt;
 
[0 1 0 0 0] &lt;br /&gt;
[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents
[0 0 1 0 0] &lt;br /&gt;
 
[0 0 0 3 -2]||&lt;br /&gt;
==== Oregon ====
&lt;br /&gt;
{{See also| Chromatic pairs #Oregon }}
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;
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.
&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;
[[Subgroup]]: 2.9.15.7.11
&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;
[[Comma list]]: 55/54, 64/63, 100/99
Commas:65536/65219&lt;br /&gt;
 
Subgroup: 2.7.11&lt;br /&gt;
{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
&lt;br /&gt;
 
POTE generator: ~77/64 = 323.372&lt;br /&gt;
{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}
&lt;br /&gt;
 
Sval map: [&amp;lt;1 2 4|, &amp;lt;0 3 -2|]&lt;br /&gt;
: [[gencom]]: [2 6/5; 55/54 64/63 100/99]
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
&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;
[[Optimal tuning]] (inharmonic [[POTE]]): ~2 = 1\1, ~6/5 = 326.139
Commas: 55/54, 64/63, 100/99&lt;br /&gt;
 
Subgroup: 2.9.15.7.11&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}
&lt;br /&gt;
 
POTE generator: ~6/5 = 326.139&lt;br /&gt;
[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents
&lt;br /&gt;
 
Sval map: [&amp;lt;1 1 1 5 2|, &amp;lt;0 3 4 -3 2|]&lt;br /&gt;
===== Orca =====
EDOs: 7, 11&lt;br /&gt;
Subgroup: 2.9.15.7.11.17
&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;/body&gt;&lt;/html&gt;</pre></div>
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
 
{{Optimal ET sequence|legend=1| 7, 11, 92bcd, 103bcd }}
 
===== Ork =====
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
 
{{Optimal ET sequence|legend=1| 11, 37, 48, 59, 70c }}
 
[[Category:Orgonia]]
[[Category:Commatic realms]]

Latest revision as of 13:45, 13 April 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.

Orgonia is a collection of temperaments of different ranks, including subgroup temperaments, that all temper out the orgonisma.

Orgonismic

Subgroup: 2.3.5.7.11

Comma list: 65536/65219

Mapping:
[⟨1 0 0 2 4]
⟨0 1 0 0 0]
⟨0 0 1 0 0]
⟨0 0 0 3 -2]]

Minimax tuning:

Optimal ET sequence: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282

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

Subgroup temperaments

Orgone

Main article: Orgone
See also: Chromatic pairs § Orgone
orgone_heptatonic.jpg
Orgone heptatonic

Orgone, the 4 & 7 temperament in the 2.7.11 subgroup, is related to superkleismic.

Subgroup: 2.7.11

Comma list: 65536/65219

Sval mapping: [⟨1 2 4], ⟨0 3 -2]]

Gencom mapping: [⟨1 0 0 2 4], ⟨0 0 0 3 -2]]

gencom: [2 77/64; 65536/65219]

Optimal tuning (POTE): ~2 = 1\1, ~77/64 = 323.372

Optimal ET sequence: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475, 783

RMS error: 0.1888 cents

Oregon

See also: Chromatic pairs § Oregon

The subgroup 2.9.15.7.11 is the 11-limit 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

Sval mapping: [⟨1 1 1 5 2], ⟨0 3 4 -3 2]]

Gencom mapping: [⟨1 2 3 2 4], ⟨0 -3/2 -5/2 3 -2]]

gencom: [2 6/5; 55/54 64/63 100/99]

Optimal tuning (subgroup POTE): ~2 = 1\1, ~6/5 = 325.495 Optimal tuning (inharmonic POTE): ~2 = 1\1, ~6/5 = 326.139

Optimal ET sequence: 7, 11, 37b, 48b, 59b

RMS error: 2.550 cents

Orca

Subgroup: 2.9.15.7.11.17

Comma list: 55/54, 64/63, 100/99, 85/84

Sval mapping: [⟨1 1 1 5 2 7], ⟨0 3 4 -3 2 -4]]

POTE generator: ~6/5 = 326.644

Optimal ET sequence: 7, 11, 92bcd, 103bcd

Ork

Subgroup: 2.9.15.7.11.17

Comma list: 99/98, 121/120, 136/135, 256/255

Sval mapping: [⟨1 1 5 2 4 3], ⟨0 8 -4 3 -2 4]]

POTE generator: ~17/14 = 325.714

Optimal ET sequence: 11, 37, 48, 59, 70c

Retrieved from "https://en.xen.wiki/index.php?title=Orgonia&oldid=191807"