Chromatic pairs: Difference between revisions
Wikispaces>genewardsmith **Imported revision 549962436 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 580992069 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2016-04-23 17:06:35 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580992069</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=Definitions= | =Definitions= | ||
By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing [[Tp tuning#T2 | By a //chromatic pair// is meant a pair of [[xenharmonic/MOSScales|MOS]] in some rank two temperament (which may often be a [[xenharmonic/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, the smaller scale of the pair is called "albitonic" from the Latin word for "white". Also included at times are "haplotonic" scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing [[Tp tuning#T2%20tuning|RMS error]], which is an appropriate error measure for subgroups as well as full p-limit groups. | ||
=Terrain= | =Terrain= | ||
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[[xenharmonic/petrtri13|Thirteen note chromatic scale]] | [[xenharmonic/petrtri13|Thirteen note chromatic scale]] | ||
=Barton= | =Barton= | ||
Subgroup: 2.5.11.13 | Subgroup: 2.5.11.13 | ||
Commas: 2200/2197, 6656/6655 | Commas: 2200/2197, 6656/6655 | ||
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[[xenharmonic/barton13|Thirteen note mega chromatic scale]] | [[xenharmonic/barton13|Thirteen note mega chromatic scale]] | ||
=Voltage= | =Voltage= | ||
Subgroup: 2.7.13 | Subgroup: 2.7.13 | ||
Comma: 28672/28561 | Comma: 28672/28561 | ||
Sval name: 3&7 | Sval name: 3&7 | ||
[[Tp tuning|POT2 generator]]: | [[Tp tuning|POT2 generator]]: ~16/13 = 357.677 | ||
[[TOP tuning|POTT generator]]: ~16/13 = 1200 - 300 log₂(7) (357.794) | [[TOP tuning|POTT generator]]: ~16/13 = 1200 - 300 log₂(7) (357.794) | ||
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[[xenharmonic/haumea19|Nineteen note mega chromatic scale]] | [[xenharmonic/haumea19|Nineteen note mega chromatic scale]] | ||
= | =Neuter= | ||
Subgroup: 2.3.11 | Subgroup: 2.3.11 | ||
Commas: 243/242 | Commas: 243/242 | ||
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[[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] | [[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] | ||
==Music== | ==Music== | ||
[[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]] by Jake Freivald in | [[https://soundcloud.com/jdfreivald/mo-happy-happy|Mo - Happy - Happy]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3|play]] by Jake Freivald in Neuter[7], 24et tuning | ||
=Slendric= | =Slendric= | ||
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[[xenharmonic/huntington17|Seventeen note chromatic scale]] | [[xenharmonic/huntington17|Seventeen note chromatic scale]] | ||
=Tobago= | =Tobago= | ||
Subgroup: 2.3.11.13/5 | Subgroup: 2.3.11.13/5 | ||
Commas: 243/242, 676/675 | Commas: 243/242, 676/675 | ||
Sval name: 10&14 | Sval name: 10&14 | ||
Related temperaments: [[Chromatic pairs# | Related temperaments: [[Chromatic pairs#Neuter|neuter]], [[xenharmonic/The Archipelago|barbados]] | ||
[[Tp tuning|POT2 generator]]: ~15/13 = 249.312 | [[Tp tuning|POT2 generator]]: ~15/13 = 249.312 | ||
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[[xenharmonic/pepperoni12|Twelve note chromatic scale]] | [[xenharmonic/pepperoni12|Twelve note chromatic scale]] | ||
=Wizz= | =Wizz= | ||
Subgroup: 2.5.11 | Subgroup: 2.5.11 | ||
Commas: 15625/15488 | Commas: 15625/15488 | ||
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Map: [<1 0 -1 6|, <0 5 6 -4|] | Map: [<1 0 -1 6|, <0 5 6 -4|] | ||
EDOs: 8, 11, 30, 41, 52 | EDOs: 8, 11, 30, 41, 52 | ||
[[Tp tuning#T2%20tuning|RMS error]]: | [[Tp tuning#T2%20tuning|RMS error]]: 0.4262 cents | ||
[[xenharmonic/penta5|Five note haplotonic scale]] | [[xenharmonic/penta5|Five note haplotonic scale]] | ||
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[[xenharmonic/penta19|Nineteen note mega chromatic scale]] | [[xenharmonic/penta19|Nineteen note mega chromatic scale]] | ||
=Bluebirds= | =Bluebirds= | ||
Subgroup: 2.11.13 | Subgroup: 2.11.13 | ||
Comma: 265837/262144 | Comma: 265837/262144 | ||
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[[xenharmonic/lovecraft13|Thirteen note chromatic scale]] | [[xenharmonic/lovecraft13|Thirteen note chromatic scale]] | ||
=Blackbirds= | =Blackbirds= | ||
Subgroup: 2.11.13 | Subgroup: 2.11.13 | ||
Comma: 29282/28561 | Comma: 29282/28561 | ||
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[[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]] | [[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]] | ||
=Joan= | =Joan= | ||
Subgroup: 2.9.7.11 | Subgroup: 2.9.7.11 | ||
Commas: 99/98, 9317/9216 | Commas: 99/98, 9317/9216 | ||
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Gencom map: [<1 0 0 1 3|, <0 7/2 0 4 1|] | Gencom map: [<1 0 0 1 3|, <0 7/2 0 4 1|] | ||
Map: | Map: [<1 0 1 3|, <0 7 4 1|] | ||
EDOs: 11, 20, 31, | EDOs: 11, 20, 31, 42, 115bd, 157bd | ||
[[Tp tuning#T2%20tuning|RMS error]]: 1.424 cents | [[Tp tuning#T2%20tuning|RMS error]]: 1.424 cents | ||
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[[xenharmonic/leantone13|Thirteen note chromatic scale]]</pre></div> | [[xenharmonic/leantone13|Thirteen note chromatic scale]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:171:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --> | <a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --> | <a href="#Petrtri">Petrtri</a><!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --> | <a href="#Barton">Barton</a><!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --> | <a href="#Voltage">Voltage</a><!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --> | <a href="#Haumea">Haumea</a><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --> | <a href="# | <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>Chromatic pairs</title></head><body><!-- ws:start:WikiTextTocRule:171:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:171 --><!-- ws:start:WikiTextTocRule:172: --><a href="#Definitions">Definitions</a><!-- ws:end:WikiTextTocRule:172 --><!-- ws:start:WikiTextTocRule:173: --> | <a href="#Terrain">Terrain</a><!-- ws:end:WikiTextTocRule:173 --><!-- ws:start:WikiTextTocRule:174: --> | <a href="#Petrtri">Petrtri</a><!-- ws:end:WikiTextTocRule:174 --><!-- ws:start:WikiTextTocRule:175: --> | <a href="#Barton">Barton</a><!-- ws:end:WikiTextTocRule:175 --><!-- ws:start:WikiTextTocRule:176: --> | <a href="#Voltage">Voltage</a><!-- ws:end:WikiTextTocRule:176 --><!-- ws:start:WikiTextTocRule:177: --> | <a href="#Tridec">Tridec</a><!-- ws:end:WikiTextTocRule:177 --><!-- ws:start:WikiTextTocRule:178: --> | <a href="#Nestoria">Nestoria</a><!-- ws:end:WikiTextTocRule:178 --><!-- ws:start:WikiTextTocRule:179: --> | <a href="#Orgone">Orgone</a><!-- ws:end:WikiTextTocRule:179 --><!-- ws:start:WikiTextTocRule:180: --> | <a href="#Marveltwintri">Marveltwintri</a><!-- ws:end:WikiTextTocRule:180 --><!-- ws:start:WikiTextTocRule:181: --> | <a href="#Cata">Cata</a><!-- ws:end:WikiTextTocRule:181 --><!-- ws:start:WikiTextTocRule:182: --> | <a href="#Bridgetown">Bridgetown</a><!-- ws:end:WikiTextTocRule:182 --><!-- ws:start:WikiTextTocRule:183: --><!-- ws:end:WikiTextTocRule:183 --><!-- ws:start:WikiTextTocRule:184: --> | <a href="#Haumea">Haumea</a><!-- ws:end:WikiTextTocRule:184 --><!-- ws:start:WikiTextTocRule:185: --> | <a href="#Neuter">Neuter</a><!-- ws:end:WikiTextTocRule:185 --><!-- ws:start:WikiTextTocRule:186: --><!-- ws:end:WikiTextTocRule:186 --><!-- ws:start:WikiTextTocRule:187: --> | <a href="#Slendric">Slendric</a><!-- ws:end:WikiTextTocRule:187 --><!-- ws:start:WikiTextTocRule:188: --><!-- ws:end:WikiTextTocRule:188 --><!-- ws:start:WikiTextTocRule:189: --> | <a href="#Huntington">Huntington</a><!-- ws:end:WikiTextTocRule:189 --><!-- ws:start:WikiTextTocRule:190: --> | <a href="#Tobago">Tobago</a><!-- ws:end:WikiTextTocRule:190 --><!-- ws:start:WikiTextTocRule:191: --> | <a href="#Pepperoni">Pepperoni</a><!-- ws:end:WikiTextTocRule:191 --><!-- ws:start:WikiTextTocRule:192: --> | <a href="#Wizz">Wizz</a><!-- ws:end:WikiTextTocRule:192 --><!-- ws:start:WikiTextTocRule:193: --> | <a href="#Bossier">Bossier</a><!-- ws:end:WikiTextTocRule:193 --><!-- ws:start:WikiTextTocRule:194: --> | <a href="#Penta">Penta</a><!-- ws:end:WikiTextTocRule:194 --><!-- ws:start:WikiTextTocRule:195: --> | <a href="#Bluebirds">Bluebirds</a><!-- ws:end:WikiTextTocRule:195 --><!-- ws:start:WikiTextTocRule:196: --> | <a href="#Marveltri">Marveltri</a><!-- ws:end:WikiTextTocRule:196 --><!-- ws:start:WikiTextTocRule:197: --> | <a href="#Edson">Edson</a><!-- ws:end:WikiTextTocRule:197 --><!-- ws:start:WikiTextTocRule:198: --> | <a href="#Photia">Photia</a><!-- ws:end:WikiTextTocRule:198 --><!-- ws:start:WikiTextTocRule:199: --> | <a href="#Shoe">Shoe</a><!-- ws:end:WikiTextTocRule:199 --><!-- ws:start:WikiTextTocRule:200: --> | <a href="#Roulette">Roulette</a><!-- ws:end:WikiTextTocRule:200 --><!-- ws:start:WikiTextTocRule:201: --> | <a href="#Silver">Silver</a><!-- ws:end:WikiTextTocRule:201 --><!-- ws:start:WikiTextTocRule:202: --> | <a href="#Baldy">Baldy</a><!-- ws:end:WikiTextTocRule:202 --><!-- ws:start:WikiTextTocRule:203: --> | <a href="#Guanyintet">Guanyintet</a><!-- ws:end:WikiTextTocRule:203 --><!-- ws:start:WikiTextTocRule:204: --> | <a href="#Radon">Radon</a><!-- ws:end:WikiTextTocRule:204 --><!-- ws:start:WikiTextTocRule:205: --> | <a href="#Gariberttet">Gariberttet</a><!-- ws:end:WikiTextTocRule:205 --><!-- ws:start:WikiTextTocRule:206: --> | <a href="#Namo">Namo</a><!-- ws:end:WikiTextTocRule:206 --><!-- ws:start:WikiTextTocRule:207: --> | <a href="#Sentry">Sentry</a><!-- ws:end:WikiTextTocRule:207 --><!-- ws:start:WikiTextTocRule:208: --> | <a href="#Hemif">Hemif</a><!-- ws:end:WikiTextTocRule:208 --><!-- ws:start:WikiTextTocRule:209: --> | <a href="#Garibaldi">Garibaldi</a><!-- ws:end:WikiTextTocRule:209 --><!-- ws:start:WikiTextTocRule:210: --> | <a href="#Mabila">Mabila</a><!-- ws:end:WikiTextTocRule:210 --><!-- ws:start:WikiTextTocRule:211: --> | <a href="#Indium">Indium</a><!-- ws:end:WikiTextTocRule:211 --><!-- ws:start:WikiTextTocRule:212: --><!-- ws:end:WikiTextTocRule:212 --><!-- ws:start:WikiTextTocRule:213: --> | <a href="#Starlingtet">Starlingtet</a><!-- ws:end:WikiTextTocRule:213 --><!-- ws:start:WikiTextTocRule:214: --> | <a href="#Lovecraft">Lovecraft</a><!-- ws:end:WikiTextTocRule:214 --><!-- ws:start:WikiTextTocRule:215: --> | <a href="#Blackbirds">Blackbirds</a><!-- ws:end:WikiTextTocRule:215 --><!-- ws:start:WikiTextTocRule:216: --> | <a href="#Laz">Laz</a><!-- ws:end:WikiTextTocRule:216 --><!-- ws:start:WikiTextTocRule:217: --> | <a href="#Myna">Myna</a><!-- ws:end:WikiTextTocRule:217 --><!-- ws:start:WikiTextTocRule:218: --> | <a href="#Greeley">Greeley</a><!-- ws:end:WikiTextTocRule:218 --><!-- ws:start:WikiTextTocRule:219: --><!-- ws:end:WikiTextTocRule:219 --><!-- ws:start:WikiTextTocRule:220: --> | <a href="#Semidim">Semidim</a><!-- ws:end:WikiTextTocRule:220 --><!-- ws:start:WikiTextTocRule:221: --> | <a href="#Mothwelltri">Mothwelltri</a><!-- ws:end:WikiTextTocRule:221 --><!-- ws:start:WikiTextTocRule:222: --> | <a href="#Sulis">Sulis</a><!-- ws:end:WikiTextTocRule:222 --><!-- ws:start:WikiTextTocRule:223: --> | <a href="#Skwares">Skwares</a><!-- ws:end:WikiTextTocRule:223 --><!-- ws:start:WikiTextTocRule:224: --> | <a href="#Orwell">Orwell</a><!-- ws:end:WikiTextTocRule:224 --><!-- ws:start:WikiTextTocRule:225: --> | <a href="#Magicaltet">Magicaltet</a><!-- ws:end:WikiTextTocRule:225 --><!-- ws:start:WikiTextTocRule:226: --> | <a href="#Magic">Magic</a><!-- ws:end:WikiTextTocRule:226 --><!-- ws:start:WikiTextTocRule:227: --><!-- ws:end:WikiTextTocRule:227 --><!-- ws:start:WikiTextTocRule:228: --> | <a href="#Kiribati">Kiribati</a><!-- ws:end:WikiTextTocRule:228 --><!-- ws:start:WikiTextTocRule:229: --> | <a href="#Score">Score</a><!-- ws:end:WikiTextTocRule:229 --><!-- ws:start:WikiTextTocRule:230: --> | <a href="#Sensation">Sensation</a><!-- ws:end:WikiTextTocRule:230 --><!-- ws:start:WikiTextTocRule:231: --> | <a href="#Sensi">Sensi</a><!-- ws:end:WikiTextTocRule:231 --><!-- ws:start:WikiTextTocRule:232: --> | <a href="#Meantone">Meantone</a><!-- ws:end:WikiTextTocRule:232 --><!-- ws:start:WikiTextTocRule:233: --> | <a href="#Mohaha">Mohaha</a><!-- ws:end:WikiTextTocRule:233 --><!-- ws:start:WikiTextTocRule:234: --><!-- ws:end:WikiTextTocRule:234 --><!-- ws:start:WikiTextTocRule:235: --> | <a href="#Joan">Joan</a><!-- ws:end:WikiTextTocRule:235 --><!-- ws:start:WikiTextTocRule:236: --> | <a href="#Tutone">Tutone</a><!-- ws:end:WikiTextTocRule:236 --><!-- ws:start:WikiTextTocRule:237: --> | <a href="#Stacks">Stacks</a><!-- ws:end:WikiTextTocRule:237 --><!-- ws:start:WikiTextTocRule:238: --> | <a href="#Bleu">Bleu</a><!-- ws:end:WikiTextTocRule:238 --><!-- ws:start:WikiTextTocRule:239: --> | <a href="#Sephiroth">Sephiroth</a><!-- ws:end:WikiTextTocRule:239 --><!-- ws:start:WikiTextTocRule:240: --> | <a href="#Archy">Archy</a><!-- ws:end:WikiTextTocRule:240 --><!-- ws:start:WikiTextTocRule:241: --> | <a href="#Suhajira">Suhajira</a><!-- ws:end:WikiTextTocRule:241 --><!-- ws:start:WikiTextTocRule:242: --> | <a href="#Mohoho">Mohoho</a><!-- ws:end:WikiTextTocRule:242 --><!-- ws:start:WikiTextTocRule:243: --> | <a href="#Supra">Supra</a><!-- ws:end:WikiTextTocRule:243 --><!-- ws:start:WikiTextTocRule:244: --> | <a href="#Machine">Machine</a><!-- ws:end:WikiTextTocRule:244 --><!-- ws:start:WikiTextTocRule:245: --> | <a href="#Deutone">Deutone</a><!-- ws:end:WikiTextTocRule:245 --><!-- ws:start:WikiTextTocRule:246: --> | <a href="#Supraphon">Supraphon</a><!-- ws:end:WikiTextTocRule:246 --><!-- ws:start:WikiTextTocRule:247: --> | <a href="#Negra">Negra</a><!-- ws:end:WikiTextTocRule:247 --><!-- ws:start:WikiTextTocRule:248: --> | <a href="#Porkypine">Porkypine</a><!-- ws:end:WikiTextTocRule:248 --><!-- ws:start:WikiTextTocRule:249: --> | <a href="#Skateboard">Skateboard</a><!-- ws:end:WikiTextTocRule:249 --><!-- ws:start:WikiTextTocRule:250: --> | <a href="#Augment">Augment</a><!-- ws:end:WikiTextTocRule:250 --><!-- ws:start:WikiTextTocRule:251: --> | <a href="#Semaphore">Semaphore</a><!-- ws:end:WikiTextTocRule:251 --><!-- ws:start:WikiTextTocRule:252: --> | <a href="#Kryptonite">Kryptonite</a><!-- ws:end:WikiTextTocRule:252 --><!-- ws:start:WikiTextTocRule:253: --> | <a href="#Oregon">Oregon</a><!-- ws:end:WikiTextTocRule:253 --><!-- ws:start:WikiTextTocRule:254: --> | <a href="#Antikythera">Antikythera</a><!-- ws:end:WikiTextTocRule:254 --><!-- ws:start:WikiTextTocRule:255: --> | <a href="#Glacial">Glacial</a><!-- ws:end:WikiTextTocRule:255 --><!-- ws:start:WikiTextTocRule:256: --> | <a href="#Leantone">Leantone</a><!-- ws:end:WikiTextTocRule:256 --><!-- ws:start:WikiTextTocRule:257: --> | ||
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<!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definitions</h1> | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="Definitions"></a><!-- ws:end:WikiTextHeadingRule:1 -->Definitions</h1> | ||
By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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, the smaller scale of the pair is called &quot;albitonic&quot; from the Latin word for &quot;white&quot;. Also included at times are &quot;haplotonic&quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing <a class="wiki_link" href="/Tp%20tuning#T2 | By a <em>chromatic pair</em> is meant a pair of <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> in some rank two temperament (which may often be a <a class="wiki_link" href="http://xenharmonic.wikispaces.com/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, the smaller scale of the pair is called &quot;albitonic&quot; from the Latin word for &quot;white&quot;. Also included at times are &quot;haplotonic&quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>, which is an appropriate error measure for subgroups as well as full p-limit groups.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:3 -->Terrain</h1> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Terrain"></a><!-- ws:end:WikiTextHeadingRule:3 -->Terrain</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Barton"></a><!-- ws:end:WikiTextHeadingRule:7 -->Barton</h1> | <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Barton"></a><!-- ws:end:WikiTextHeadingRule:7 -->Barton</h1> | ||
Subgroup: 2.5.11.13<br /> | Subgroup: 2.5.11.13<br /> | ||
Commas: 2200/2197, 6656/6655<br /> | Commas: 2200/2197, 6656/6655<br /> | ||
Svalname: 11&amp;13<br /> | Svalname: 11&amp;13<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="Voltage"></a><!-- ws:end:WikiTextHeadingRule:9 -->Voltage</h1> | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="Voltage"></a><!-- ws:end:WikiTextHeadingRule:9 -->Voltage</h1> | ||
Subgroup: 2.7.13<br /> | Subgroup: 2.7.13<br /> | ||
Comma: 28672/28561<br /> | Comma: 28672/28561<br /> | ||
Sval name: 3&amp;7<br /> | Sval name: 3&amp;7<br /> | ||
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<a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: | <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~16/13 = 357.677<br /> | ||
<a class="wiki_link" href="/TOP%20tuning">POTT generator</a>: ~16/13 = 1200 - 300 log₂(7) (357.794)<br /> | <a class="wiki_link" href="/TOP%20tuning">POTT generator</a>: ~16/13 = 1200 - 300 log₂(7) (357.794)<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/haumea19">Nineteen note mega chromatic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/haumea19">Nineteen note mega chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:27:&lt;h1&gt; --><h1 id="toc13"><a name=" | <!-- ws:start:WikiTextHeadingRule:27:&lt;h1&gt; --><h1 id="toc13"><a name="Neuter"></a><!-- ws:end:WikiTextHeadingRule:27 -->Neuter</h1> | ||
Subgroup: 2.3.11<br /> | Subgroup: 2.3.11<br /> | ||
Commas: 243/242<br /> | Commas: 243/242<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:29:&lt;h2&gt; --><h2 id="toc14"><a name=" | <!-- ws:start:WikiTextHeadingRule:29:&lt;h2&gt; --><h2 id="toc14"><a name="Neuter-Music"></a><!-- ws:end:WikiTextHeadingRule:29 -->Music</h2> | ||
<a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/mo-happy-happy" rel="nofollow">Mo - Happy - Happy</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3" rel="nofollow">play</a> by Jake Freivald in | <a class="wiki_link_ext" href="https://soundcloud.com/jdfreivald/mo-happy-happy" rel="nofollow">Mo - Happy - Happy</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3" rel="nofollow">play</a> by Jake Freivald in Neuter[7], 24et tuning<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc15"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:31 -->Slendric</h1> | <!-- ws:start:WikiTextHeadingRule:31:&lt;h1&gt; --><h1 id="toc15"><a name="Slendric"></a><!-- ws:end:WikiTextHeadingRule:31 -->Slendric</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc18"><a name="Tobago"></a><!-- ws:end:WikiTextHeadingRule:37 -->Tobago</h1> | <!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc18"><a name="Tobago"></a><!-- ws:end:WikiTextHeadingRule:37 -->Tobago</h1> | ||
Subgroup: 2.3.11.13/5<br /> | Subgroup: 2.3.11.13/5<br /> | ||
Commas: 243/242, 676/675<br /> | Commas: 243/242, 676/675<br /> | ||
Sval name: 10&amp;14<br /> | Sval name: 10&amp;14<br /> | ||
Related temperaments: <a class="wiki_link" href="/Chromatic%20pairs# | Related temperaments: <a class="wiki_link" href="/Chromatic%20pairs#Neuter">neuter</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Archipelago">barbados</a><br /> | ||
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<a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~15/13 = 249.312<br /> | <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~15/13 = 249.312<br /> | ||
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Subgroup: 2.5.11<br /> | Subgroup: 2.5.11<br /> | ||
Commas: 15625/15488<br /> | Commas: 15625/15488<br /> | ||
Sval name: 6&amp;16<br /> | Sval name: 6&amp;16<br /> | ||
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Map: [&lt;1 0 -1 6|, &lt;0 5 6 -4|]<br /> | Map: [&lt;1 0 -1 6|, &lt;0 5 6 -4|]<br /> | ||
EDOs: 8, 11, 30, 41, 52<br /> | EDOs: 8, 11, 30, 41, 52<br /> | ||
<a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: | <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.4262 cents<br /> | ||
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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta5">Five note haplotonic scale</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/penta5">Five note haplotonic scale</a><br /> | ||
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Subgroup: 2.11.13<br /> | Subgroup: 2.11.13<br /> | ||
Comma: 265837/262144<br /> | Comma: 265837/262144<br /> | ||
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Subgroup: 2.11.13<br /> | Subgroup: 2.11.13<br /> | ||
Comma: 29282/28561<br /> | Comma: 29282/28561<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:127:&lt;h1&gt; --><h1 id="toc63"><a name="Joan"></a><!-- ws:end:WikiTextHeadingRule:127 -->Joan</h1> | <!-- ws:start:WikiTextHeadingRule:127:&lt;h1&gt; --><h1 id="toc63"><a name="Joan"></a><!-- ws:end:WikiTextHeadingRule:127 -->Joan</h1> | ||
Subgroup: 2.9.7.11<br /> | Subgroup: 2.9.7.11<br /> | ||
Commas: 99/98, 9317/9216<br /> | Commas: 99/98, 9317/9216<br /> | ||
Related temperaments: casablanca, orwell<br /> | Related temperaments: casablanca, orwell<br /> | ||
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Gencom map: [&lt;1 0 0 1 3|, &lt;0 7/2 0 4 1|]<br /> | Gencom map: [&lt;1 0 0 1 3|, &lt;0 7/2 0 4 1|]<br /> | ||
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Map: | Map: [&lt;1 0 1 3|, &lt;0 7 4 1|]<br /> | ||
EDOs: 11, 20, 31, | EDOs: 11, 20, 31, 42, 115bd, 157bd<br /> | ||
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<a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.424 cents<br /> | <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.424 cents<br /> | ||