Chromatic pairs
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 21:55:05 UTC.
- The original revision id was 207673596.
- 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 ===Albitonic scale=== ! greeley8.scl ! Greeley[8] 2.5/3.7/3.11/3 subgroup scale in 100et 8 ! 156.00000 264.00000 420.00000 576.00000 732.00000 888.00000 1044.00000 2/1 ===Chromatic scale=== ! greeley15.scl ! Greeley[15] 2.5/3.7/3.11/3 subgroup scale in 100et 15 ! 108.00000 156.00000 264.00000 312.00000 420.00000 468.00000 576.00000 624.00000 732.00000 840.00000 888.00000 996.00000 1044.00000 1152.00000 2/1 ==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 ===Albitonic scale=== ! pepperoni7.scl ! Pepperoni[7] 2.3.11/7.13/7 subgroup scale, 271et tuning 7 ! 208.11808 287.82288 495.94096 704.05904 783.76384 991.88192 2/1 ===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 "albitonic" from the Latin word for "white".<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><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: [<1 1 2 2|, <0 -2 -6 -1|]<br /> EDOs: 8, 15, 23, 77, 100<br /> Badness: 0.0634<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Greeley-Albitonic scale"></a><!-- ws:end:WikiTextHeadingRule:2 -->Albitonic scale</h3> ! greeley8.scl<br /> !<br /> Greeley[8] 2.5/3.7/3.11/3 subgroup scale in 100et<br /> 8<br /> !<br /> 156.00000<br /> 264.00000<br /> 420.00000<br /> 576.00000<br /> 732.00000<br /> 888.00000<br /> 1044.00000<br /> 2/1<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Greeley-Chromatic scale"></a><!-- ws:end:WikiTextHeadingRule:4 -->Chromatic scale</h3> ! greeley15.scl<br /> !<br /> Greeley[15] 2.5/3.7/3.11/3 subgroup scale in 100et<br /> 15<br /> !<br /> 108.00000<br /> 156.00000<br /> 264.00000<br /> 312.00000<br /> 420.00000<br /> 468.00000<br /> 576.00000<br /> 624.00000<br /> 732.00000<br /> 840.00000<br /> 888.00000<br /> 996.00000<br /> 1044.00000<br /> 1152.00000<br /> 2/1<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-Pepperoni"></a><!-- ws:end:WikiTextHeadingRule:6 -->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: [<1 0 7 12|, <0 1 -4 -7|]<br /> EDOs: 5, 7, 12, 17, 29, 46, 75, 196, 271<br /> Badness: 0.0659<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Pepperoni-Albitonic scale"></a><!-- ws:end:WikiTextHeadingRule:8 -->Albitonic scale</h3> ! pepperoni7.scl<br /> !<br /> Pepperoni[7] 2.3.11/7.13/7 subgroup scale, 271et tuning<br /> 7<br /> !<br /> 208.11808<br /> 287.82288<br /> 495.94096<br /> 704.05904<br /> 783.76384<br /> 991.88192<br /> 2/1<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x-Pepperoni-Chromatic scale"></a><!-- ws:end:WikiTextHeadingRule:10 -->Chromatic scale</h3> ! 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:12:<h2> --><h2 id="toc6"><a name="x-Bridgetown"></a><!-- ws:end:WikiTextHeadingRule:12 -->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: [<1 0 -6 -1|, <0 2 9 3|]<br /> EDOs: 5, 9, 14, 19, 24, 29<br /> Badness: 0.0173<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x-Bridgetown-Albitonic scale"></a><!-- ws:end:WikiTextHeadingRule:14 -->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:16:<h3> --><h3 id="toc8"><a name="x-Bridgetown-Chromatic scale"></a><!-- ws:end:WikiTextHeadingRule:16 -->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:18:<h2> --><h2 id="toc9"><a name="x-Pompey"></a><!-- ws:end:WikiTextHeadingRule:18 -->Pompey</h2> Subgroup: 2.3.7.11<br /> Commas: 896/891, 1029/1024<br /> <br /> POTE generator: ~8/7 = 234.381<br /> <br /> Map: [<1 1 3 6|, <0 3 -1 -13|]<br /> EDOs: 5, 36, 41, 87, 128<br /> Badness: 0.0164<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h3> --><h3 id="toc10"><a name="x-Pompey-Pentacircle scale"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:<h3> --><h3 id="toc11"><a name="x-Pompey-Albitonic scale"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:24:<h3> --><h3 id="toc12"><a name="x-Pompey-Chromatic scale"></a><!-- ws:end:WikiTextHeadingRule:24 -->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>