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]]

~~=== Jubilife ===~~

~~There is a natural extension of jubilismic to the 2.3.5.7.17 subgroup, which tempers out [[85/84]] and [[120/119]], and identifies 7/5 with 10/7, 17/12 and 24/17 as the semioctave.~~

~~Subgroup: 2.3.5.7.17~~

~~Comma list: 50/49, 85/84~~

~~Mapping: {{Mapping| 2 0 0 1 5 | 0 1 0 0 1 | 0 0 1 1 0 }}~~

~~Optimal tunings:~~

* WE: ~7/5 = 599.8903{{c}}, ~3/2 = 702.6008{{c}}, ~5/4 = 379.6441{{c}}

* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.5503{{c}}, ~5/4 = 379.4777{{c}}

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

~~Badness (Sintel): 0.357~~

== 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.

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

=== ~~Jubilee~~ ===

=== 2.3.5.7.11.17 subgroup ===

~~Jubilismic temperament works on the [[No-thirteens subgroup temperaments|no-13s]] 17-limit subgroup very well, where the semioctave stands in for ~7/5, ~17/12, ~99/70 and their [[octave complement]]s.~~

Subgroup: 2.3.5.7.11.17

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

~~Mapping~~: {{Mapping| 2 0 0 1 4 5 | 0 1 0 0 -2 1 | 0 0 1 1 2 0 }}

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

Optimal tunings:

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* 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

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[[Badness]] (Sintel): 0.938

[[Category:Jubilismic family| ]]

[[Category:Temperament families]]

[[Category:~~Jubilismic family| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-3 temperaments]]

~~[[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 27: / Line 27: @@
 Scales: [[jubilismic10]], [[jubilismic12]]
-=== Jubilife ===
-There is a natural extension of jubilismic to the 2.3.5.7.17 subgroup, which tempers out [[85/84]] and [[120/119]], and identifies 7/5 with 10/7, 17/12 and 24/17 as the semioctave.
-Subgroup: 2.3.5.7.17
-Comma list: 50/49, 85/84
-Mapping: {{Mapping| 2 0 0 1 5 | 0 1 0 0 1 | 0 0 1 1 0 }}
-Optimal tunings:
-* WE: ~7/5 = 599.8903{{c}}, ~3/2 = 702.6008{{c}}, ~5/4 = 379.6441{{c}}
-* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.5503{{c}}, ~5/4 = 379.4777{{c}}
-{{Optimal ET sequence|legend=0| 4, 8d, 10, 12, 22, 34d, 48 }}
-Badness (Sintel): 0.357
 == 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.
+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 64: / Line 47: @@
 [[Badness]] (Sintel): 0.673
-=== Jubilee ===
+=== 2.3.5.7.11.17 subgroup ===
-Jubilismic temperament works on the [[No-thirteens subgroup temperaments|no-13s]] 17-limit subgroup very well, where the semioctave stands in for ~7/5, ~17/12, ~99/70 and their [[octave complement]]s.
 Subgroup: 2.3.5.7.11.17
 Comma list: 50/49, 85/84, 99/98
-Mapping: {{Mapping| 2 0 0 1 4 5 | 0 1 0 0 -2 1 | 0 0 1 1 2 0 }}
+Subgroup-val mapping: {{Mapping| 2 0 0 1 4 5 | 0 1 0 0 -2 1 | 0 0 1 1 2 0 }}
 Optimal tunings:
@@ Line 77: / Line 58: @@
 * 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, 22, 34d, 48 }}
+{{Optimal ET sequence|legend=0| 4, 8d, 10e, 12, 14c, 22, 34d, 48 }}
 Badness (Sintel): 0.578
@@ Line 132: / Line 113: @@
 [[Badness]] (Sintel): 0.938
+[[Category:Jubilismic family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Jubilismic family| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]