Jubilismic family: Difference between revisions
m Cleanup |
Databoxified; edo list reviewed |
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= Jubilismic = | = Jubilismic = | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generators: ~3/2 = 702.9804, ~5/4 = 380.8399 | |||
EDO generators: [[4edo|(2, 1)\4]], [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]] | |||
Scales: [[jubilismic10]], [[jubilismic12]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 50/49 | [[Comma list]]: 50/49 | ||
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| 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 }}] | ||
| Line 13: | Line 28: | ||
Mapping [[generator]]s: ~7/5, ~3, ~5 | Mapping [[generator]]s: ~7/5, ~3, ~5 | ||
{{Val list|legend=1| 10, 12, 22, | {{Val list|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }} | ||
</div></div> | |||
= Jubilee = | = Jubilee = | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generators: ~3/2 = 703.4155, ~5/4 = 380.6973 | |||
EDO generators: [[8edo|(5, 3)\8]], [[12edo|(7, 4)\12]], [[14edo|(8, 4)\14]] | |||
Scales: | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
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: [{{val| 2 0 0 1 4 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 1 2 }}] | ||
{{Val list|legend=1| 12, 22, 48 }} | {{Val list|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }} | ||
Badness: 0.600 × 10<sup>-3</sup> | Badness: 0.600 × 10<sup>-3</sup> | ||
</div></div> | |||
= Festival = | = Festival = | ||
Comma list: 50/49 | |||
Period: 1\2 | |||
Optimal ([[POTE]]) generators: ~3/2 = 693.6257, ~5/4 = 371.2658 | |||
EDO generators: [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]], [[14edo|(8, 4)\14]] | |||
Scales: | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
Subgroup: 2.3.5.7.11 | |||
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: [{{val| 2 0 0 1 -4 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 1 1 }}] | ||
{{Val list|legend=1| 10, 12, 26 }} | {{Val list|legend=1| 10, 12, 22e, 26 }} | ||
Badness: 0.689 × 10<sup>-3</sup> | Badness: 0.689 × 10<sup>-3</sup> | ||
</div></div> | |||
= Fiesta = | = Fiesta = | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generators: ~3/2 = 713.5853, ~5/4 = 397.6952 | |||
EDO generators: [[8edo|(5, 3)\8]], [[10edo|(6, 3)\10]], [[12edo|(7, 4)\12]] | |||
Scales: | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
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: [{{val| 2 0 0 1 7 }}, {{val| 0 1 0 0 0 }}, {{val| 0 0 1 1 0 }}] | ||
{{Val list|legend=1| 10, 12 }} | {{Val list|legend=1| 8d, 10, 12, 22e }} | ||
Badness: 0.717 × 10<sup>-3</sup> | Badness: 0.717 × 10<sup>-3</sup> | ||
</div></div> | |||
= Jamboree = | = Jamboree = | ||
Period: 1\2 | |||
Optimal ([[POTE]]) generators: ~3/2 = 706.6559, ~5/4 = 376.8308 | |||
EDO generators: [[8edo|(5, 3)\8]], [[10edo|(6, 3)\10]], [[14edo|(8, 4)\14]] | |||
Scales: | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
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: [{{val| 2 0 0 1 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 1 -1 }}] | ||
{{Val list|legend=1| 10, 22 }} | {{Val list|legend=1| 8d, 10, 12e, 14c, 22 }} | ||
Badness: 0.781 × 10<sup>-3</sup> | Badness: 0.781 × 10<sup>-3</sup> | ||
</div></div> | |||
[[Category:Theory]] | [[Category:Theory]] | ||
| Line 57: | Line 140: | ||
[[Category:Jubilismic]] | [[Category:Jubilismic]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 18:16, 18 March 2021
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
Period: 1\2
Optimal (POTE) generators: ~3/2 = 702.9804, ~5/4 = 380.8399
EDO generators: (2, 1)\4, (6, 3)\10, (7, 4)\12
Scales: jubilismic10, jubilismic12
Subgroup: 2.3.5.7
Comma list: 50/49
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [-1/4 0 1/2 1/2⟩, [1/4 0 1/2 1/2⟩]
- Eigenmonzos: 2, 3/2, 35/32
Mapping: [⟨2 0 0 1], ⟨0 1 0 0], ⟨0 0 1 1]]
Mapping generators: ~7/5, ~3, ~5
Jubilee
Period: 1\2
Optimal (POTE) generators: ~3/2 = 703.4155, ~5/4 = 380.6973
EDO generators: (5, 3)\8, (7, 4)\12, (8, 4)\14
Scales:
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]]
Badness: 0.600 × 10-3
Festival
Period: 1\2
Optimal (POTE) generators: ~3/2 = 693.6257, ~5/4 = 371.2658
EDO generators: (6, 3)\10, (7, 4)\12, (8, 4)\14
Scales:
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]]
Badness: 0.689 × 10-3
Fiesta
Period: 1\2
Optimal (POTE) generators: ~3/2 = 713.5853, ~5/4 = 397.6952
EDO generators: (5, 3)\8, (6, 3)\10, (7, 4)\12
Scales:
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]]
Badness: 0.717 × 10-3
Jamboree
Period: 1\2
Optimal (POTE) generators: ~3/2 = 706.6559, ~5/4 = 376.8308
EDO generators: (5, 3)\8, (6, 3)\10, (8, 4)\14
Scales:
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]]
Badness: 0.781 × 10-3