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.
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.


== 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]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 702.9804, ~5/4 = 380.8399


[[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 (unchanged-intervals): 2, 3/2, 35/32
: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3.35


{{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }}
{{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }}
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== 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
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 703.4155, ~5/4 = 380.6973


{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}
{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}
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== Festival  ==
== Festival  ==
 
[[Subgroup]]: 2.3.5.7.11
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]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 693.6257, ~5/4 = 371.2658


{{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }}
{{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }}
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== 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
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 713.5853, ~5/4 = 397.6952


{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e }}
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e }}
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== Jamboree  ==
== Jamboree  ==
 
[[Subgroup]]: 2.3.5.7.11
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]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 706.6559, ~5/4 = 376.8308


{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22 }}
{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22 }}
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Jubilismic]]
[[Category:Jubilismic family| ]] <!-- main article -->
[[Category:Jubilismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 05:51, 5 August 2023

The jubilismic family contains temperaments that temper out the 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.

Jubilismic

Subgroup: 2.3.5.7

Comma list: 50/49

Mapping: [⟨2 0 0 1], ⟨0 1 0 0], ⟨0 0 1 1]]

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

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 702.9804, ~5/4 = 380.8399

Minimax tuning:

[[1 0 0 0⟩, [0 1 0 0⟩, [-1/4 0 1/2 1/2⟩, [1/4 0 1/2 1/2⟩]
eigenmonzo (unchanged-interval) basis: 2.3.35

Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48

Scales: jubilismic10, jubilismic12

Jubilee

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98

Mapping: [⟨2 0 0 1 4], ⟨0 1 0 0 -2], ⟨0 0 1 1 2]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 703.4155, ~5/4 = 380.6973

Optimal ET sequence: 4, 8d, 10e, 12, 22, 34d, 48

Badness: 0.600 × 10-3

Festival

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49

Mapping: [⟨2 0 0 1 -4], ⟨0 1 0 0 2], ⟨0 0 1 1 1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 693.6257, ~5/4 = 371.2658

Optimal ET sequence: 10, 12, 22e, 26

Badness: 0.689 × 10-3

Fiesta

Subgroup: 2.3.5.7.11

Comma list: 50/49, 56/55

Mapping: [⟨2 0 0 1 7], ⟨0 1 0 0 0], ⟨0 0 1 1 0]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 713.5853, ~5/4 = 397.6952

Optimal ET sequence: 8d, 10, 12, 22e

Badness: 0.717 × 10-3

Jamboree

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54

Mapping: [⟨2 0 0 1 2], ⟨0 1 0 0 3], ⟨0 0 1 1 -1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.6559, ~5/4 = 376.8308

Optimal ET sequence: 8d, 10, 12e, 14c, 22

Badness: 0.781 × 10-3

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