Very high accuracy temperaments: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
document francium |
||
| Line 270: | Line 270: | ||
{{Optimal ET sequence|legend=1|135, 571, 706, 1277, 1848, 3125}}, ... | {{Optimal ET sequence|legend=1|135, 571, 706, 1277, 1848, 3125}}, ... | ||
== Francium == | |||
Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit, hereby dividing the octave into 87 parts. | |||
Subgroup: 2.3.5.7 | |||
Comma list: 78125000/78121827, {{monzo|152 -112 -41 43}} | |||
Mapping: [[{{val|87 1 -106 -406}}, {{val|0 4 9 19}}] | |||
Mapping generators: ~126/125 = 1\87, ~{{monzo|37 -25 -12 11}} = 472.043 | |||
Optimal tuning (CTE): ~{{monzo|37 -25 -12 11}} = 472.043 | |||
[[Support]]ing [[ET]]s: {{EDOs|783, 1566, 2349, 8178, 8961, 9744, 10527, 12093, 18705}} | |||
TE Error: 0.003103 cents/octave | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 78125000/78121827, 199297406/199290375, {{monzo|74 -17 -5 -4 -7}} | |||
Mapping: [[{{val|87 1 -106 -406 1225}}, {{val|0 4 9 19 -27}}] | |||
Mapping generators: ~126/125 = 1\87, ~103079215104/78466609375 = 472.043 | |||
Optimal tuning (CTE): ~103079215104/78466609375 = 472.043 | |||
[[Support]]ing [[ET]]s: {{EDOs|783, 8178, 8961, 9744, 18705}} | |||
TE Error: 0.003587 cents/octave | |||
= Rank-3 temperaments = | = Rank-3 temperaments = | ||