Landscape family: Difference between revisions

(15 intermediate revisions by 9 users not shown)

Line 1:

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

~~This is an imported revision from Wikispaces.~~ The ~~revision metadata is included below for reference:<br>~~

__FORCETOC__

~~: This revision was by author~~ [[~~User:genewardsmith|genewardsmith~~]] ~~and made on <tt>2014-05-03 19:40:41 UTC</tt>.<br>~~

The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.

~~: The original revision id was <tt>506252638</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~~]]

~~The landscape family of rank three temperaments tempers out the landscape comma, 250047/250000.~~

== Landscape ==

~~=Landscape=~~

[[Subgroup]]: 2.3.5.7

~~Comma~~: ~~250047/250000~~

~~7-limit minimax tuning~~

[[Comma list]]: 250047/250000

[~~|9 0 0 0>, |4 3 6 -3>, |0 0 9 0>, |4 -6 6 6>~~]/9

~~Eigenmonzos~~: ~~7/6, 5~~/4

~~9-limit minimax tuning~~

[|12 0 0 0~~>, |4 6 6~~ -~~3>,~~ |0 0 ~~12 0>, |8 -12 12 6>]/12~~

~~Eigenmonzos: 5/4, 9/7~~

~~Map~~: [~~<~~3 0 0 4|~~, <~~0 1 0 -2|~~, <~~0 0 ~~1 2~~|]

: mapping generators: ~63/50, ~3, ~5

~~Generators~~: 63/~~50, 3, 5~~

~~EDOs:~~ 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555

[[Minimax tuning]]:

10^5*Badness: 2.~~130~~<~~/pre~~></~~div~~>

* [[7-odd-limit]]

~~<h4>Original HTML content:</h4>~~

: {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9

~~<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>Landscape family</title></head><body><a href="#Landscape">Landscape</a>

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3

~~<br />~~

* [[9-odd-limit]]

~~The landscape family of rank three temperaments~~ tempers out the landscape comma~~, 250047/250000~~.~~<br />~~

: {{monzo list| 12 0 0 0 | 4 6 6 -3 | 0 0 12 0 | 8 -12 12 6 }}/12

~~<br />~~

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

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

Comma: 250047/250000~~<br~~ /~~>~~

{{Optimal ET sequence|legend=1| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}

~~<br />~~

~~7-limit minimax tuning<br />~~

[[Badness]]: 0.02130 × 10<sup>-3</sup>

[|9 0 0 ~~0&gt;, |~~4 3 6 ~~-3&gt;,~~ |0 0 ~~9 0&gt;, |4~~ -~~6 6 6&gt;]/9<br />~~

== House ==

~~Eigenmonzos: 7/6,~~ 5~~/4<br />~~

House tempers out the [[quartisma]] alongside the landscape comma.

~~<br />~~

~~9-limit minimax tuning<br~~ /~~>~~

[[Subgroup]]: 2.3.5.7.11

~~[|12 0 0 0&gt;~~, ~~|4 6 6 -~~3~~&gt;, |0 0 12 0&gt;, |8 -12 12 6&gt;]/12<br />~~

~~Eigenmonzos: 5/4~~, 9/~~7<br />~~

[[Comma list]]: 250047/250000, 117440512/117406179

~~<br />~~

~~Map:~~ [~~&lt;3 0 0 4|, &lt;0 1 0 -2|, &lt;0 0 1 2|~~]~~<br />~~

~~Generators:~~ 63/50, 3, ~~5<br~~ /~~>~~

~~EDOs: 3, 12~~, 27, 45, 57, ~~60, 72, 99, 171, 441, 612~~, 1236, ~~1407, 1578~~, ~~1848~~, ~~2019~~, ~~6498~~, ~~8346~~, ~~8517~~, ~~10536~~, ~~12555<br />~~

: mapping generators: ~63/50, ~3, ~9801/5120

10^5*Badness: 2.~~130<~~/~~body></html>~~<~~/pre~~><~~/div~~>

[[Optimal tuning]] ([[CTE]]) ~63/50 = 1\3, ~3/2 = 701.9592, ~9801/5120 = 1124.2969

{{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}

[[Badness]]: 1.92 × 10<sup>-3</sup>

== Odin ==

== Tyr ==

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Landscape family| ]]

[[Category:Landscape| ]]

[[Category:Rank 3]]

@@ 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>
+__FORCETOC__
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-05-03 19:40:41 UTC</tt>.<br>
+The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.
-: The original revision id was <tt>506252638</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]]
-The landscape family of rank three temperaments tempers out the landscape comma, 250047/250000.
+== Landscape  ==
-=Landscape=
+[[Subgroup]]: 2.3.5.7
-Comma: 250047/250000
--limit minimax tuning
+[[Comma list]]: 250047/250000
-[|9 0 0 0&gt;, |4 3 6 -3&gt;, |0 0 9 0&gt;, |4 -6 6 6&gt;]/9
-Eigenmonzos: 7/6, 5/4
--limit minimax tuning
+{{Mapping|legend=1| 3 0 0 4 | 0 1 0 -2 | 0 0 1 2 }}
-[|12 0 0 0&gt;, |4 6 6 -3&gt;, |0 0 12 0&gt;, |8 -12 12 6&gt;]/12
-Eigenmonzos: 5/4, 9/7
-Map: [&lt;3 0 0 4|, &lt;0 1 0 -2|, &lt;0 0 1 2|]
+: mapping generators: ~63/50, ~3, ~5
-Generators: 63/50, 3, 5
-EDOs: 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555
+[[Minimax tuning]]:
-^5*Badness: 2.130</pre></div>
+* [[7-odd-limit]]
-<h4>Original HTML content:</h4>
+: {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9
-<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;Landscape family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:2:&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:2 --&gt;&lt;!-- ws:start:WikiTextTocRule:3: --&gt;&lt;a href="#Landscape"&gt;Landscape&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:3 --&gt;&lt;!-- ws:start:WikiTextTocRule:4: --&gt;
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
-&lt;!-- ws:end:WikiTextTocRule:4 --&gt;&lt;br /&gt;
+* [[9-odd-limit]]
-The landscape family of rank three temperaments tempers out the landscape comma, 250047/250000.&lt;br /&gt;
+: {{monzo list| 12 0 0 0 | 4 6 6 -3 | 0 0 12 0 | 8 -12 12 6 }}/12
-&lt;br /&gt;
+:  [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Landscape"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Landscape&lt;/h1&gt;
-Comma: 250047/250000&lt;br /&gt;
+{{Optimal ET sequence|legend=1| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}
-&lt;br /&gt;
--limit minimax tuning&lt;br /&gt;
+[[Badness]]: 0.02130 × 10<sup>-3</sup>
-[|9 0 0 0&amp;gt;, |4 3 6 -3&amp;gt;, |0 0 9 0&amp;gt;, |4 -6 6 6&amp;gt;]/9&lt;br /&gt;
+== House ==
-Eigenmonzos: 7/6, 5/4&lt;br /&gt;
+House tempers out the [[quartisma]] alongside the landscape comma.
-&lt;br /&gt;
--limit minimax tuning&lt;br /&gt;
+[[Subgroup]]: 2.3.5.7.11
-[|12 0 0 0&amp;gt;, |4 6 6 -3&amp;gt;, |0 0 12 0&amp;gt;, |8 -12 12 6&amp;gt;]/12&lt;br /&gt;
-Eigenmonzos: 5/4, 9/7&lt;br /&gt;
+[[Comma list]]: 250047/250000, 117440512/117406179
-&lt;br /&gt;
-Map: [&amp;lt;3 0 0 4|, &amp;lt;0 1 0 -2|, &amp;lt;0 0 1 2|]&lt;br /&gt;
+{{Mapping|legend=1| 3 0 2 8 16 | 0 1 4 6 0 | 0 0 -5 -10 2 }}
-Generators: 63/50, 3, 5&lt;br /&gt;
-EDOs: 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555&lt;br /&gt;
+: mapping generators: ~63/50, ~3, ~9801/5120
-^5*Badness: 2.130&lt;/body&gt;&lt;/html&gt;</pre></div>
+[[Optimal tuning]] ([[CTE]]) ~63/50 = 1\3, ~3/2 = 701.9592, ~9801/5120 = 1124.2969
+{{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}
+[[Badness]]: 1.92 × 10<sup>-3</sup>
+== Odin  ==
+{{See also| Kalismic temperaments #Odin }}
+== Tyr  ==
+{{See also| Lehmerismic temperaments #Tyr }}
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Landscape family| ]] <!-- main article -->
+[[Category:Landscape| ]] <!-- key article -->
+[[Category:Rank 3]]