Jubilismic family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
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''' 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 ==
Line 11: Line 11:
: mapping generators: ~7/5, ~3, ~5
: mapping generators: ~7/5, ~3, ~5


[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~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 list| 1 0 0 0 | 0 1 0 0 | -1/4 0 1/2 1/2 | 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 basis|unchanged-interval (eigenmonzo) basis]]: 2.3.35
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) 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, 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


Line 29: Line 35:
{{Mapping|legend=1| 2 0 0 1 4 | 0 1 0 0 -2 | 0 0 1 1 2 }}
{{Mapping|legend=1| 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 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 }}


{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}
{{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }}


[[Badness]]: 0.600 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.673


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


Line 42: Line 52:
{{Mapping|legend=1| 2 0 0 1 -4 | 0 1 0 0 2 | 0 0 1 1 1 }}
{{Mapping|legend=1| 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 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 }}


{{Optimal ET sequence|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


Line 55: Line 69:
{{Mapping|legend=1| 2 0 0 1 7 | 0 1 0 0 0 | 0 0 1 1 0 }}
{{Mapping|legend=1| 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 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 }}


{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e }}
{{Optimal ET sequence|legend=1| 8d, 10, 12, 22e, 30dee, 42ddeee }}


[[Badness]]: 0.717 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.861


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


Line 68: Line 86:
{{Mapping|legend=1| 2 0 0 1 2 | 0 1 0 0 3 | 0 0 1 1 -1 }}
{{Mapping|legend=1| 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 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 }}
{{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22, 58ce }}


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


[[Category:Temperament families]]
[[Category:Temperament families]]

Latest revision as of 14:18, 22 July 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The jubilismic family of rank-3 temperaments 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

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 tunings:

  • WE: ~7/5 = 599.6673 ¢, ~3/2 = 702.5906 ¢, ~5/4 = 380.6287 ¢
error map: ⟨-0.665 -0.030 -7.016 +10.139]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.4574 ¢, ~5/4 = 380.0086 ¢
error map: ⟨0.000 +0.502 -6.305 +11.183]

Minimax tuning:

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

Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48, 60d

Badness (Sintel): 0.561

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 tunings:

  • WE: ~7/5 = 599.6219 ¢, ~3/2 = 702.9722 ¢, ~5/4 = 380.4574 ¢
error map: ⟨-0.756 +0.261 -7.369 +9.741 +0.628]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 702.9249 ¢, ~5/4 = 379.6796 ¢
error map: ⟨0.000 +0.970 -6.634 +10.854 +2.192]

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

Badness (Sintel): 0.673

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 tunings:

  • WE: ~7/5 = 600.8501 ¢, ~3/2 = 694.6084 ¢, ~5/4 = 371.7918 ¢
error map: ⟨+1.700 -5.646 -11.121 +7.216 +13.091]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 694.5001 ¢, ~5/4 = 372.9799 ¢
error map: ⟨0.000 -7.455 -13.334 +4.154 +10.662]

Optimal ET sequence: 10, 12, 22e, 26

Badness (Sintel): 0.827

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:

  • WE: ~7/5 = 596.3068 ¢, ~3/2 = 709.1930 ¢, ~5/4 = 395.2472 ¢
error map: ⟨-7.386 -0.148 -5.839 +7.955 +22.830]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 709.6819 ¢, ~5/4 = 391.4911 ¢
error map: ⟨0.000 +7.727 +5.177 +22.665 +48.682]

Optimal ET sequence: 8d, 10, 12, 22e, 30dee, 42ddeee

Badness (Sintel): 0.861

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 tunings:

  • WE: ~7/5 = 600.0436 ¢, ~3/2 = 706.7073 ¢, ~5/4 = 376.8582 ¢
error map: ⟨+0.087 +4.839 -9.281 +8.250 -7.880]
  • CWE: ~7/5 = 600.0000 ¢, ~3/2 = 706.7334 ¢, ~5/4 = 376.9332 ¢
error map: ⟨0.000 +4.778 -9.381 +8.107 -8.051]

Optimal ET sequence: 8d, 10, 12e, 14c, 22, 58ce

Badness (Sintel): 0.938

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