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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>
+These temper out the keema, {{monzo| -5 -3 3 1 }} = [[875/864]] = {{S|5/S6}}, whose fundamental equivalence entails that [[6/5]] is sharpened so that it stacks three times to reach [[7/4]], and the interval between 6/5 and [[5/4]] is compressed so that [[7/6]] - 6/5 - 5/4 - [[9/7]] are set equidistant from each other. As the [[Keemic family#Undecimal supermagic|canonical extension]] of rank-3 keemic to the [[11-limit]] tempers out the commas [[100/99]] and [[385/384]] (whereby ([[6/5]])<sup>2</sup> is identified with [[16/11]]), this provides a clean way to extend the various keemic temperaments to the 11-limit as well.
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-17 17:01:15 UTC</tt>.<br>
-: The original revision id was <tt>321733600</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]]
-These temper out the keema, |-5 -3 3 1&gt; = 875/864. Keemic temperaments include magic, keemun, flattone, porcupine, doublewide, superkleismic, sycamore anbd quasitemp.
+Full [[7-limit]] keemic temperaments discussed elsewhere are:
+* [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]]
+* ''[[Doublewide]]'' (+50/49) → [[Jubilismic clan #Doublewide|Jubilismic clan]]
+* [[Porcupine]] (+64/63) → [[Porcupine family #Septimal porcupine|Porcupine family]]
+* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
+* [[Magic]] (+225/224) → [[Magic family #Septimal magic|Magic family]]
+* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore|Sycamore family]]
+* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic|Gamelismic clan]]
+* ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]]
-=Quasitemp=
+Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond.
-Commas: 875/854, 2401/2400
-POTE generator ~25/21 = 292.710
+== Quasitemp ==
+: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Quasitemp]].''
-Map: [&lt;1 5 5 5|, &lt;0 -14 -11 -9|]
+Quasitemp is a full 7-limit strong extension of [[gariberttet]], the 2.5/3.7/3 subgroup temperament defined by tempering out [[3125/3087]]. In gariberttet, three generators reach [[5/3]] and five reach [[7/3]], so that the generator itself has the interpretation of [[25/21]] (which is equated to [[13/11]] in the 13-limit extension). This implies that 3:5:7 and 5:6:7 chords are reached rather quickly. In quasitemp, tempering out 875/864 entails that [[8/7]] is found after 9 generators, from which the mappings of 3 and 5 follow.
-Wedgie: &lt;&lt;14 11 9 -15 -25 -10||
-EDOs: 37, 41
-Badness: 0.0603
-==11-limit==
+[[Subgroup]]: 2.3.5.7
-Commas: 100/99, 385/384, 1375/1372
-POTE generator: ~25/21 = 292.547
+[[Comma list]]: 875/864, 2401/2400
-Map: [&lt;1 5 5 5 2|, &lt;0 -14 -11 -9 6|]
+{{Mapping|legend=1| 1 5 5 5 | 0 -14 -11 -9 }}
-EDOs: 37, 41, 119, 160c, 201ce
-Badness: 0.0432</pre></div>
+: Mapping generators: ~2, ~25/21
-<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;Keemic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;[[toc}flat]]&lt;br /&gt;
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 292.710
-&lt;br /&gt;
-These temper out the keema, |-5 -3 3 1&amp;gt; = 875/864. Keemic temperaments include magic, keemun, flattone, porcupine, doublewide, superkleismic, sycamore anbd quasitemp.&lt;br /&gt;
+{{Optimal ET sequence|legend=1| 4, 37, 41 }}
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Quasitemp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Quasitemp&lt;/h1&gt;
+[[Badness]]: 0.060269
-Commas: 875/854, 2401/2400&lt;br /&gt;
-&lt;br /&gt;
+=== 11-limit ===
-POTE generator ~25/21 = 292.710&lt;br /&gt;
+Subgroup: 2.3.5.7.11
-&lt;br /&gt;
-Map: [&amp;lt;1 5 5 5|, &amp;lt;0 -14 -11 -9|]&lt;br /&gt;
+Comma list: 100/99, 385/384, 1375/1372
-Wedgie: &amp;lt;&amp;lt;14 11 9 -15 -25 -10||&lt;br /&gt;
-EDOs: 37, 41&lt;br /&gt;
+Mapping: {{mapping| 1 5 5 5 2 | 0 -14 -11 -9 6 }}
-Badness: 0.0603&lt;br /&gt;
-&lt;br /&gt;
+Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.547
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Quasitemp-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
-Commas: 100/99, 385/384, 1375/1372&lt;br /&gt;
+{{Optimal ET sequence|legend=1| 4, 37, 41, 119 }}
-&lt;br /&gt;
-POTE generator: ~25/21 = 292.547&lt;br /&gt;
+Badness: 0.043209
-&lt;br /&gt;
-Map: [&amp;lt;1 5 5 5 2|, &amp;lt;0 -14 -11 -9 6|]&lt;br /&gt;
+==== 13-limit ====
-EDOs: 37, 41, 119, 160c, 201ce&lt;br /&gt;
+Subgroup: 2.3.5.7.11.13
-Badness: 0.0432&lt;/body&gt;&lt;/html&gt;</pre></div>
+Comma list: 100/99, 196/195, 275/273, 385/384
+Mapping: {{mapping| 1 5 5 5 2 2 | 0 -14 -11 -9 6 7 }}
+Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 292.457
+{{Optimal ET sequence|legend=1| 4, 37, 41, 78, 119f }}
+Badness: 0.032913
+=== Quato ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 625/616
+Mapping: {{mapping| 1 5 5 5 12 | 0 -14 -11 -9 -35 }}
+Optimal tuning (POTE): ~2 = 1\1, ~25/21 = 292.851
+{{Optimal ET sequence|legend=1| 41, 127cd, 168cd }}
+Badness: 0.041170
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 243/242, 275/273, 325/324
+Mapping: {{mapping| 1 5 5 5 12 12 | 0 -14 -11 -9 -35 -34 }}
+Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 292.928
+{{Optimal ET sequence|legend=1| 41, 86ce, 127cd }}
+Badness: 0.030081
+== Chromo ==
+: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Chromo]].''
+Chromo represents the [[13edf]] chain as a rank-2 temperament, with [[6/5]] and [[5/4]] mapped to 6 and 7 steps, respectively. Since the difference of those two intervals is abbreviated considerably from just, keemic provides the most meaningful 7-limit extension (setting [[7/6]], 6/5, 5/4, [[9/7]] equidistant) so that the temperament then approximates the [[4:5:6:7]] tetrad with 0:7:13:18 generator steps.
+Note that if one allows a more complex mapping for prime 7 and wants a larger prime limit, one may prefer [[escapade]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 875/864, 2430/2401
+{{Mapping|legend=1| 1 1 2 2 | 0 13 7 18 }}
+: Mapping generators: ~2, ~25/24
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/24 = 53.816
+{{Optimal ET sequence|legend=1| 22, 45, 67c }}
+[[Badness]]: 0.090769
+== Barbad ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 875/864, 16875/16807
+{{Mapping|legend=1| 1 9 7 11 | 0 -19 -12 -21 }}
+: Mapping generators: ~2, ~98/75
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 468.331
+{{Optimal ET sequence|legend=1| 18, 23d, 41 }}
+[[Badness]]: 0.110448
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 245/242, 540/539, 625/616
+Mapping: {{mapping| 1 9 7 11 14 | 0 -19 -12 -21 -27 }}
+Optimal tuning (POTE): ~2 = 1\1, ~98/75 = 468.367
+{{Optimal ET sequence|legend=1| 18e, 23de, 41, 228ccdd }}
+Badness: 0.050105
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 144/143, 196/195, 245/242, 275/273
+Mapping: {{mapping| 1 9 7 11 14 8 | 0 -19 -12 -21 -27 -11 }}
+Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 468.270
+{{Optimal ET sequence|legend=1| 18e, 23de, 41 }}
+Badness: 0.039183
+== Hyperkleismic ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 875/864, 51200/50421
+{{Mapping|legend=1| 1 -3 -2 2 | 0 17 16 3 }}
+: Mapping generators: ~2, ~6/5
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 323.780
+{{Optimal ET sequence|legend=1| 26, 37, 63 }}
+[[Badness]]: 0.157830
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 100/99, 385/384, 2420/2401
+Mapping: {{mapping| 1 -3 -2 2 4 | 0 17 16 3 -2}}
+Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.796
+{{Optimal ET sequence|legend=1| 26, 37, 63 }}
+Badness: 0.065356
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 100/99, 169/168, 275/273, 385/384
+Mapping: {{mapping| 1 -3 -2 2 4 1 | 0 17 16 3 -2 10 }}
+Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 323.790
+{{Optimal ET sequence|legend=1| 26, 37, 63 }}
+Badness: 0.035724
+== Sevond ==
+/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 875/864, 327680/321489
+{{Mapping|legend=1| 7 0 -6 53 | 0 1 2 -3 }}
+: Mapping generators: ~10/9, ~3
+[[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~3/2 = 705.613
+{{Optimal ET sequence|legend=1| 7, 56, 63, 119 }}
+[[Badness]]: 0.206592
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 100/99, 385/384, 6655/6561
+Mapping: {{mapping| 7 0 -6 53 2 | 0 1 2 -3 2 }}
+Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.518
+{{Optimal ET sequence|legend=1| 7, 56, 63, 119 }}
+Badness: 0.070437
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 100/99, 169/168, 352/351, 385/384
+Mapping: {{mapping| 7 0 -6 53 2 37 | 0 1 2 -3 2 -1 }}
+Optimal tuning (POTE): ~10/9 = 1\7, ~3/2 = 705.344
+{{Optimal ET sequence|legend=1| 7, 56, 63, 119 }}
+Badness: 0.041238
+[[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Keemic temperaments| ]] <!-- main article -->
+[[Category:Rank 2]]

Keemic temperaments: Difference between revisions