Syntonic–chromatic equivalence continuum: Difference between revisions

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 Also fractional values of ''n'': [[enipucrop]] (''n'' = 1.5), [[seville]] (''n'' = 2.{{overline|3}}), [[sixix]] (''n'' = 2.5), [[sevond]] (''n'' = 3.5), [[brahmagupta]] (''n'' = 5.25).
+== Absurdity ==
+The 5-limit 7&amp;84 temperament. So named because this is just an absurd temperament. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also part of the [[syntonic-chromatic equivalence continuum]], in this case where (81/80)<sup>5</sup> = 25/24.
+Commas: 10460353203/10240000000
+POTE generator: ~10/9 = 185.901 cents
+Map: [&lt;7 0 -17|, &lt;0 1 3|]
+EDOs: {{EDOs| 7, 70, 77, 84, 329 }}
+Badness: 0.3412
+[http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5 The temperament finder - 5-limit Absurdity]
+== Sevond ==
+This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4.
+Comma: 5000000/4782969
+POTE generator: ~3/2 = 706.288 cents
+Map: [&lt;7 0 -6|, &lt;0 1 2|]
+EDOs: {{EDOs| 7, 42, 49, 56, 119 }}
+Badness: 0.3393
+=== 7-limit ===
+Adding 875/864 to the commas extends this to the 7-limit:
+Commas: 875/864, 327680/321489
+POTE generator: ~3/2 = 705.613 cents
+Map: [&lt;7 0 -6 53|, &lt;0 1 2 -3|]
+EDOs: {{EDOs| 7, 56, 63, 119 }}
+[http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&limit=5 The temperament finder - 5-limit Sevond]
+== Seville ==
+This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4.
+Comma: 78125/69984
+POTE generator: ~3/2 = 706.410 cents
+Map: [&lt;7 0 5|, &lt;0 1 1|]
+EDOs: {{EDOs| 7, 35b, 42c, 49c, 56cc, 119cccc }}
+Badness: 0.4377
+[http://x31eq.com/cgi-bin/rt.cgi?ets=7_49c&limit=5 The temperament finder - 5-limit Seville]
 [[Category:Theory]]
 [[Category:Temperament]]