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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]].  


= Jubilismic =
== Jubilismic ==
 
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7


[[Comma list]]: 50/49
[[Comma list]]: 50/49


[[Mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 1 0 0 }}, {{val| 0 0 1 1 }}]
{{Mapping|legend=1| 2 0 0 1 | 0 1 0 0 | 0 0 1 1 }}


Mapping generators: ~7/5, ~3, ~5
: mapping generators: ~7/5, ~3, ~5


[[POTE generator]]s: ~3/2 = 702.9804, ~5/4 = 380.8399
[[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 }}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]
* 7- and [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| -1/4 0 1/2 1/2 }}, {{monzo| 1/4 0 1/2 1/2 }}]
: {{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]]s: 2, 3/2, 35/32
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.35


{{Val list|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }}
{{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48, 60d }}
 
[[Badness]] (Sintel): 0.561


Scales: [[jubilismic10]], [[jubilismic12]]
Scales: [[jubilismic10]], [[jubilismic12]]


= Jubilee =
== Jubilee ==
 
[[Subgroup]]: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 50/49, 99/98
[[Comma list]]: 50/49, 99/98


[[Mapping]]: [{{val| 2 0 0 1 4 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 1 2 }}]
{{Mapping|legend=1| 2 0 0 1 4 | 0 1 0 0 -2 | 0 0 1 1 2 }}
 
[[POTE generator]]s: ~3/2 = 703.4155, ~5/4 = 380.6973


{{Val list|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}
[[Optimal tuning]]s:
* [[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 }}


[[Badness]]: 0.600 × 10<sup>-3</sup>
{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}


= Festival =
[[Badness]] (Sintel): 0.673


Subgroup: 2.3.5.7.11
== Festival ==
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 45/44, 50/49
[[Comma list]]: 45/44, 50/49


[[Mapping]]: [{{val| 2 0 0 1 -4 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 1 1 }}]
{{Mapping|legend=1| 2 0 0 1 -4 | 0 1 0 0 2 | 0 0 1 1 1 }}


[[POTE generator]]s: ~3/2 = 693.6257, ~5/4 = 371.2658
[[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 }}


{{Val list|legend=1| 10, 12, 22e, 26 }}
{{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }}


[[Badness]]: 0.689 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.827


= Fiesta =
== Fiesta ==
 
[[Subgroup]]: 2.3.5.7.11
Subgroup: 2.3.5.7.11


[[Comma list]]: 50/49, 56/55
[[Comma list]]: 50/49, 56/55


[[Mapping]]: [{{val| 2 0 0 1 7 }}, {{val| 0 1 0 0 0 }}, {{val| 0 0 1 1 0 }}]
{{Mapping|legend=1| 2 0 0 1 7 | 0 1 0 0 0 | 0 0 1 1 0 }}
 
[[POTE generator]]s: ~3/2 = 713.5853, ~5/4 = 397.6952


{{Val list|legend=1| 8d, 10, 12, 22e }}
[[Optimal tuning]]:
* [[WE]]: ~7/5 = 596.3068{{c}}, ~3/2 = 709.1930{{c}}, ~5/4 = 395.2472{{c}}
: [[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 }}


[[Badness]]: 0.717 × 10<sup>-3</sup>
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e, 30dee, 42ddeee }}


= Jamboree =
[[Badness]] (Sintel): 0.861


Subgroup: 2.3.5.7.11
== Jamboree ==
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 50/49, 55/54
[[Comma list]]: 50/49, 55/54


[[Mapping]]: [{{val| 2 0 0 1 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 1 -1 }}]
{{Mapping|legend=1| 2 0 0 1 2 | 0 1 0 0 3 | 0 0 1 1 -1 }}


[[POTE generator]]s: ~3/2 = 706.6559, ~5/4 = 376.8308
[[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 }}


{{Val list|legend=1| 8d, 10, 12e, 14c, 22 }}
{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22, 58ce }}


[[Badness]]: 0.781 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.938


[[Category:Regular temperament theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Jubilismic]]
[[Category:Jubilismic family| ]] <!-- main article -->
[[Category:Jubilismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Jubilismic_family"