Chromatic pairs: Difference between revisions

Revision as of 22:10, 5 March 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-03-05 22:10:44 UTC.

The original revision id was 207675348.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

By a //chromatic pair// is meant a pair of MOS in some rank two temperament (which may often be a [[Just intonation subgroups|subgroup temperament]]) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, smaller scale of the pair is called "albitonic" from the Latin word for "white".

==Greeley==
Subgroup: 2.5/3.7/3.11/3
Commas: 121/120, 126/125

POTE generator: ~11/10 = 156.055

Map: [<1 1 2 2|, <0 -2 -6 -1|]
EDOs: 8, 15, 23, 77, 100
Badness: 0.0634

[[greeley8|Eight note albitonic scale]]
[[greeley15|Fifteen note chromatic scale]]

==Pepperoni==
Subgroup: 2.3.11/7.13/7
Commas: 352/351, 364/363

POTE generator: ~3/2 = 704.052

Map: [<1 0 7 12|, <0 1 -4 -7|]
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271
Badness: 0.0659

[[pepperoni7|Albitonic scale]]
[[pepperoni12|Chromatic scale]]
! pepperoni12.scl
!
Pepperoni[12] 2.3.11/7.13/7 subgroup scale in 271et tuning
 12
!
 79.70480
 208.11808
 287.82288
 367.52768
 495.94096
 575.64576
 704.05904
 783.76384
 912.17712
 991.88192
 1071.58672
 2/1

==Bridgetown==
Subgroup: 2.3.11/5.13/5
Commas: 352/351, 676/675

POTE generator: ~15/13 = 248.285

Map: [<1 0 -6 -1|, <0 2 9 3|]
EDOs: 5, 9, 14, 19, 24, 29
Badness: 0.0173

===Albitonic scale===
! bridgetown9.scl
!
Bridgetown[9] 2.3.11/5.13/5 subgroup MOS in 29et
 9
!
 41.37931
 248.27586
 455.17241
 496.55172
 703.44828
 744.82759
 951.72414
 993.10345
 2/1

===Chromatic scale===
! bridgetown14.scl
!
Bridgetown[14] 2.3.11/5.13/5 subgroup MOS in 29et
 14
!
 41.37931
 82.75862
 248.27586
 289.65517
 455.17241
 496.55172
 537.93103
 703.44828
 744.82759
 786.20690
 951.72414
 993.10345
 1034.48276
 2/1

==Pompey==
Subgroup: 2.3.7.11
Commas: 896/891, 1029/1024

POTE generator: ~8/7 = 234.381

Map: [<1 1 3 6|, <0 3 -1 -13|]
EDOs: 5, 36, 41, 87, 128
Badness: 0.0164

===Pentacircle scale===
! pompey5.scl
!
Pompey[5] 2.3.7.11 subgroup scale in 128et
 5
!
 234.37500
 468.75000
 703.12500
 965.62500
 2/1

===Albitonic scale===
! pompey11.scl
!
Pompey[11] 2.3.7.11 subgroup scale in 128et
 11
!
 206.25000
 234.37500
 440.62500
 468.75000
 496.87500
 703.12500
 731.25000
 937.50000
 965.62500
 1171.87500
 2/1

===Chromatic scale===
! pompey16.scl
!
Pompey[16] 2.3.7.11 subgroup scale in 128et
 16
!
 28.12500
 56.25000
 234.37500
 262.50000
 290.62500
 468.75000
 496.87500
 525.00000
 553.12500
 731.25000
 759.37500
 787.50000
 965.62500
 993.75000
 1021.87500
 2/1

Original HTML content:

<html><head><title>Chromatic pairs</title></head><body>By a <em>chromatic pair</em> is meant a pair of MOS in some rank two temperament (which may often be a <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup temperament</a>) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, smaller scale of the pair is called &quot;albitonic&quot; from the Latin word for &quot;white&quot;.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Greeley"></a><!-- ws:end:WikiTextHeadingRule:0 -->Greeley</h2>
Subgroup: 2.5/3.7/3.11/3<br />
Commas: 121/120, 126/125<br />
<br />
POTE generator: ~11/10 = 156.055<br />
<br />
Map: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]<br />
EDOs: 8, 15, 23, 77, 100<br />
Badness: 0.0634<br />
<br />
<a class="wiki_link" href="/greeley8">Eight note albitonic scale</a><br />
<a class="wiki_link" href="/greeley15">Fifteen note chromatic scale</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:2 -->Pepperoni</h2>
Subgroup: 2.3.11/7.13/7<br />
Commas: 352/351, 364/363<br />
<br />
POTE generator: ~3/2 = 704.052<br />
<br />
Map: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]<br />
EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br />
Badness: 0.0659<br />
<br />
<a class="wiki_link" href="/pepperoni7">Albitonic scale</a><br />
<a class="wiki_link" href="/pepperoni12">Chromatic scale</a><br />
! pepperoni12.scl<br />
!<br />
Pepperoni[12] 2.3.11/7.13/7 subgroup scale in 271et tuning<br />
 12<br />
!<br />
 79.70480<br />
 208.11808<br />
 287.82288<br />
 367.52768<br />
 495.94096<br />
 575.64576<br />
 704.05904<br />
 783.76384<br />
 912.17712<br />
 991.88192<br />
 1071.58672<br />
 2/1<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:4 -->Bridgetown</h2>
Subgroup: 2.3.11/5.13/5<br />
Commas: 352/351, 676/675<br />
<br />
POTE generator: ~15/13 = 248.285<br />
<br />
Map: [&lt;1 0 -6 -1|, &lt;0 2 9 3|]<br />
EDOs: 5, 9, 14, 19, 24, 29<br />
Badness: 0.0173<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Bridgetown-Albitonic scale"></a><!-- ws:end:WikiTextHeadingRule:6 -->Albitonic scale</h3>
! bridgetown9.scl<br />
!<br />
Bridgetown[9] 2.3.11/5.13/5 subgroup MOS in 29et<br />
 9<br />
!<br />
 41.37931<br />
 248.27586<br />
 455.17241<br />
 496.55172<br />
 703.44828<br />
 744.82759<br />
 951.72414<br />
 993.10345<br />
 2/1<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Bridgetown-Chromatic scale"></a><!-- ws:end:WikiTextHeadingRule:8 -->Chromatic scale</h3>
! bridgetown14.scl<br />
!<br />
Bridgetown[14] 2.3.11/5.13/5 subgroup MOS in 29et<br />
 14<br />
!<br />
 41.37931<br />
 82.75862<br />
 248.27586<br />
 289.65517<br />
 455.17241<br />
 496.55172<br />
 537.93103<br />
 703.44828<br />
 744.82759<br />
 786.20690<br />
 951.72414<br />
 993.10345<br />
 1034.48276<br />
 2/1<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Pompey"></a><!-- ws:end:WikiTextHeadingRule:10 -->Pompey</h2>
Subgroup: 2.3.7.11<br />
Commas: 896/891, 1029/1024<br />
<br />
POTE generator: ~8/7 = 234.381<br />
<br />
Map: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]<br />
EDOs: 5, 36, 41, 87, 128<br />
Badness: 0.0164<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x-Pompey-Pentacircle scale"></a><!-- ws:end:WikiTextHeadingRule:12 -->Pentacircle scale</h3>
! pompey5.scl<br />
!<br />
Pompey[5] 2.3.7.11 subgroup scale in 128et<br />
 5<br />
!<br />
 234.37500<br />
 468.75000<br />
 703.12500<br />
 965.62500<br />
 2/1<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Pompey-Albitonic scale"></a><!-- ws:end:WikiTextHeadingRule:14 -->Albitonic scale</h3>
! pompey11.scl<br />
!<br />
Pompey[11] 2.3.7.11 subgroup scale in 128et<br />
 11<br />
!<br />
 206.25000<br />
 234.37500<br />
 440.62500<br />
 468.75000<br />
 496.87500<br />
 703.12500<br />
 731.25000<br />
 937.50000<br />
 965.62500<br />
 1171.87500<br />
 2/1<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Pompey-Chromatic scale"></a><!-- ws:end:WikiTextHeadingRule:16 -->Chromatic scale</h3>
! pompey16.scl<br />
!<br />
Pompey[16] 2.3.7.11 subgroup scale in 128et<br />
 16<br />
!<br />
 28.12500<br />
 56.25000<br />
 234.37500<br />
 262.50000<br />
 290.62500<br />
 468.75000<br />
 496.87500<br />
 525.00000<br />
 553.12500<br />
 731.25000<br />
 759.37500<br />
 787.50000<br />
 965.62500<br />
 993.75000<br />
 1021.87500<br />
 2/1</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-05 22:05:17 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-05 22:10:44 UTC</tt>.<br>
-: The original revision id was <tt>207674728</tt>.<br>
+: The original revision id was <tt>207675348</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>
@@ Line 31: / Line 31: @@
 Badness: 0.0659
-===Albitonic scale===
+[[pepperoni7|Albitonic scale]]
-! pepperoni7.scl
+[[pepperoni12|Chromatic scale]]
-!
-Pepperoni[7] 2.3.11/7.13/7 subgroup scale, 271et tuning
-!
-.11808
-.82288
-.94096
-.05904
-.76384
-.88192
-/1
-===Chromatic scale===
 ! pepperoni12.scl
 !
@@ Line 200: / Line 187: @@
 Badness: 0.0659&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Pepperoni-Albitonic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Albitonic scale&lt;/h3&gt;
+&lt;a class="wiki_link" href="/pepperoni7"&gt;Albitonic scale&lt;/a&gt;&lt;br /&gt;
-! pepperoni7.scl&lt;br /&gt;
+&lt;a class="wiki_link" href="/pepperoni12"&gt;Chromatic scale&lt;/a&gt;&lt;br /&gt;
-!&lt;br /&gt;
-Pepperoni[7] 2.3.11/7.13/7 subgroup scale, 271et tuning&lt;br /&gt;
-&lt;br /&gt;
-!&lt;br /&gt;
-.11808&lt;br /&gt;
-.82288&lt;br /&gt;
-.94096&lt;br /&gt;
-.05904&lt;br /&gt;
-.76384&lt;br /&gt;
-.88192&lt;br /&gt;
-/1&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Pepperoni-Chromatic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Chromatic scale&lt;/h3&gt;
 ! pepperoni12.scl&lt;br /&gt;
 !&lt;br /&gt;
@@ Line 233: / Line 207: @@
 /1&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Bridgetown"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Bridgetown&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Bridgetown"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Bridgetown&lt;/h2&gt;
 Subgroup: 2.3.11/5.13/5&lt;br /&gt;
 Commas: 352/351, 676/675&lt;br /&gt;
@@ Line 243: / Line 217: @@
 Badness: 0.0173&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="x-Bridgetown-Albitonic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Albitonic scale&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Bridgetown-Albitonic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Albitonic scale&lt;/h3&gt;
 ! bridgetown9.scl&lt;br /&gt;
 !&lt;br /&gt;
@@ Line 259: / Line 233: @@
 /1&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Bridgetown-Chromatic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Chromatic scale&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Bridgetown-Chromatic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Chromatic scale&lt;/h3&gt;
 ! bridgetown14.scl&lt;br /&gt;
 !&lt;br /&gt;
@@ Line 280: / Line 254: @@
 /1&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Pompey"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Pompey&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Pompey"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Pompey&lt;/h2&gt;
 Subgroup: 2.3.7.11&lt;br /&gt;
 Commas: 896/891, 1029/1024&lt;br /&gt;
@@ Line 290: / Line 264: @@
 Badness: 0.0164&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Pompey-Pentacircle scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Pentacircle scale&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Pompey-Pentacircle scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Pentacircle scale&lt;/h3&gt;
 ! pompey5.scl&lt;br /&gt;
 !&lt;br /&gt;
@@ Line 302: / Line 276: @@
 /1&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Pompey-Albitonic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Albitonic scale&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Pompey-Albitonic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Albitonic scale&lt;/h3&gt;
 ! pompey11.scl&lt;br /&gt;
 !&lt;br /&gt;
@@ Line 320: / Line 294: @@
 /1&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x-Pompey-Chromatic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Chromatic scale&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Pompey-Chromatic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Chromatic scale&lt;/h3&gt;
 ! pompey16.scl&lt;br /&gt;
 !&lt;br /&gt;

Chromatic pairs: Difference between revisions

Revision as of 22:10, 5 March 2011

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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