Jubilismic family: Difference between revisions

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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]].

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 [[octave]] in two. Related to this is the 2.5.7-subgroup {50/49} temperament [[jubilic]].

== Jubilismic ==

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

== ~~Jubilee~~ ==

== Undecimal jubilismic ==

Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[7/6]]'s or two [[5/3]]'s octave reduced. This then extends naturally to the 2.3.5.7.11.17 subgroup, which tempers out [[85/84]] and [[120/119]], and adds [[17/12]] and [[24/17]] to the semioctave.

[[Subgroup]]: 2.3.5.7.11

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[[Badness]] (Sintel): 0.673

=== 2.3.5.7.11.17 subgroup ===

Subgroup: 2.3.5.7.11.17

Comma list: 50/49, 85/84, 99/98

Subgroup-val mapping: {{Mapping| 2 0 0 1 4 5 | 0 1 0 0 -2 1 | 0 0 1 1 2 0 }}

Optimal tunings:

* WE: ~7/5 = 599.8463{{c}}, ~3/2 = 702.9469{{c}}, ~5/4 = 379.5011{{c}}

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9274{{c}}, ~5/4 = 379.2350{{c}}

{{Optimal ET sequence|legend=0| 4, 8d, 10e, 12, 14c, 22, 34d, 48 }}

Badness (Sintel): 0.578

== Festival ==

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[[Category:Temperament families]]

[[Category:Jubilismic family| ]]

~~[[Category:Jubilismic| ]] ~~

[[Category:Rank 3]]

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 {{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]].
+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 [[octave]] in two. Related to this is the 2.5.7-subgroup {50/49} temperament [[jubilic]].
 == Jubilismic ==
@@ Line 28: / Line 28: @@
 Scales: [[jubilismic10]], [[jubilismic12]]
-== Jubilee ==
+== Undecimal jubilismic ==
+Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[7/6]]'s or two [[5/3]]'s octave reduced. This then extends naturally to the 2.3.5.7.11.17 subgroup, which tempers out [[85/84]] and [[120/119]], and adds [[17/12]] and [[24/17]] to the semioctave.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 44: / Line 46: @@
 [[Badness]] (Sintel): 0.673
+=== 2.3.5.7.11.17 subgroup ===
+Subgroup: 2.3.5.7.11.17
+Comma list: 50/49, 85/84, 99/98
+Subgroup-val mapping: {{Mapping| 2 0 0 1 4 5 | 0 1 0 0 -2 1 | 0 0 1 1 2 0 }}
+Optimal tunings:
+* WE: ~7/5 = 599.8463{{c}}, ~3/2 = 702.9469{{c}}, ~5/4 = 379.5011{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9274{{c}}, ~5/4 = 379.2350{{c}}
+{{Optimal ET sequence|legend=0| 4, 8d, 10e, 12, 14c, 22, 34d, 48 }}
+Badness (Sintel): 0.578
 == Festival ==
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 [[Category:Temperament families]]
 [[Category:Jubilismic family| ]] <!-- main article -->
-[[Category:Jubilismic| ]] <!-- key article -->
 [[Category:Rank 3]]