Jubilismic family: Difference between revisions

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-The '''jubilismic family''' contains temperaments that temper out the [[jubilisma|jubilisma (50/49)]] (also called tritonic diesis, or septimal sixth-tone). It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While most rank-three temperaments are planar, a jubilismic temperament divides the octave in two.
+{{Technical data page}}
+The '''jubilismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] [[50/49]] in the full [[7-limit]]. It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While many rank-3 temperaments are planar, a jubilismic temperament divides the [[2/1|octave]] in two. Related to this is the 2.5.7-subgroup {50/49} temperament [[jubilic]].
-[[Comma]]: 50/49
+== Jubilismic ==
+[[Subgroup]]: 2.3.5.7
-and 9 limit minimax tuning
+[[Comma list]]: 50/49
-[|1 0 0 0&gt;, |0 1 0 0&gt;, |-1/4 0 1/2 1/2&gt;,
+{{Mapping|legend=1| 2 0 0 1 | 0 1 0 0 | 0 0 1 1 }}
-|1/4 0 1/2 1/2&gt;]
-[[Eigenmonzo|Eigenmonzos]]: 2, 3/2, 35/32
+: mapping generators: ~7/5, ~3, ~5
-Map: [&lt;2 0 0 1|, &lt;0 1 0 0|, &lt;0 0 1 1|]
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 599.6673{{c}}, ~3/2 = 702.5906{{c}}, ~5/4 = 380.6287{{c}}
+: [[error map]]: {{val| -0.665 -0.030 -7.016 +10.139 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.4574{{c}}, ~5/4 = 380.0086{{c}}
+: error map: {{val| 0.000 +0.502 -6.305 +11.183 }}
-[[generator|Generators]]: 7/5, 3, 5
+[[Minimax tuning]]:
+* 7- and [[9-odd-limit]]
+: {{monzo list| 1 0 0 0 | 0 1 0 0 | -1/4 0 1/2 1/2 | 1/4 0 1/2 1/2 }}
+: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.35
-[[EDO|Edos]]: [[10edo|10]], [[12edo|12]], [[22edo|22]], [[26edo|26]], [[38edo|38]], [[48edo|48]]
+{{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48, 60d }}
-Scales: [[jubilismic10|jubilismic10]]
+[[Badness]] (Sintel): 0.561
-==Jubilee==
+Scales: [[jubilismic10]], [[jubilismic12]]
-Commas: 50/49, 99/98
-Map: [&lt;2 0 0 1 4|, &lt;0 1 0 0 -2|, &lt;0 0 1 1 2|]
+== Jubilee ==
+[[Subgroup]]: 2.3.5.7.11
-EDOS: 12, 22, 48
+[[Comma list]]: 50/49, 99/98
-Badness: 0.000600
+{{Mapping|legend=1| 2 0 0 1 4 | 0 1 0 0 -2 | 0 0 1 1 2 }}
-==Festival==
+[[Optimal tuning]]s:
-Commas: 50/49, 45/44
+* [[WE]]: ~7/5 = 599.6219{{c}}, ~3/2 = 702.9722{{c}}, ~5/4 = 380.4574{{c}}
+: [[error map]]: {{val| -0.756 +0.261 -7.369 +9.741 +0.628 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9249{{c}}, ~5/4 = 379.6796{{c}}
+: error map: {{val| 0.000 +0.970 -6.634 +10.854 +2.192 }}
-Map: [&lt;2 0 0 1 -4|, &lt;0 1 0 0 2|, &lt;0 0 1 1 1|]
+{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}
-EDOs: 10, 12, 26
+[[Badness]] (Sintel): 0.673
-Badness: 0.000689
+== Festival ==
+[[Subgroup]]: 2.3.5.7.11
-==Fiesta==
+[[Comma list]]: 45/44, 50/49
-Commas: 50/49, 56/55
-Map: [&lt;2 0 0 1 7|, &lt;0 1 0 0 0|, &lt;0 0 1 1 0|]
+{{Mapping|legend=1| 2 0 0 1 -4 | 0 1 0 0 2 | 0 0 1 1 1 }}
-EDOs: 10, 12
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 600.8501{{c}}, ~3/2 = 694.6084{{c}}, ~5/4 = 371.7918{{c}}
+: [[error map]]: {{val| +1.700 -5.646 -11.121 +7.216 +13.091 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.5001{{c}}, ~5/4 = 372.9799{{c}}
+: error map: {{val| 0.000 -7.455 -13.334 +4.154 +10.662 }}
-Badness: 0.000717
+{{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }}
-==Jamboree==
+[[Badness]] (Sintel): 0.827
-Commas: 50/49, 55/54
-Map: [&lt;2 0 0 1 2|, &lt;0 1 0 0 3|, &lt;0 0 1 1 -1|]
+== Fiesta ==
+[[Subgroup]]: 2.3.5.7.11
-EDOs: 10, 22
+[[Comma list]]: 50/49, 56/55
-Badness: 0.000781
+{{Mapping|legend=1| 2 0 0 1 7 | 0 1 0 0 0 | 0 0 1 1 0 }}
-[[Category:Theory]]
+[[Optimal tuning]]:
-[[Category:Temperament family]]
+* [[WE]]: ~7/5 = 596.3068{{c}}, ~3/2 = 709.1930{{c}}, ~5/4 = 395.2472{{c}}
-[[Category:Jubilismic]]
+: [[error map]]: {{val| -7.386 -0.148 -5.839 +7.955 +22.830 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.6819{{c}}, ~5/4 = 391.4911{{c}}
+: error map: {{val| 0.000 +7.727 +5.177 +22.665 +48.682 }}
-[[Category:Todo:cleanup]]
+{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e, 30dee, 42ddeee }}
+[[Badness]] (Sintel): 0.861
+== Jamboree ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 50/49, 55/54
+{{Mapping|legend=1| 2 0 0 1 2 | 0 1 0 0 3 | 0 0 1 1 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 600.0436{{c}}, ~3/2 = 706.7073{{c}}, ~5/4 = 376.8582{{c}}
+: [[error map]]: {{val| +0.087 +4.839 -9.281 +8.250 -7.880 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.7334{{c}}, ~5/4 = 376.9332{{c}}
+: error map: {{val| 0.000 +4.778 -9.381 +8.107 -8.051 }}
+{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22, 58ce }}
+[[Badness]] (Sintel): 0.938
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Jubilismic family| ]] <!-- main article -->
+[[Category:Jubilismic| ]] <!-- key article -->
+[[Category:Rank 3]]