87th-octave temperaments: Difference between revisions
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{{Infobox fractional-octave|87}} | |||
One step of 87edo is in direct proximity to starling comma, [[126/125]]. | One step of 87edo is in direct proximity to starling comma, [[126/125]]. | ||
==Francium== | == Francium == | ||
Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit, hereby dividing the octave into 87 parts. | Francium tempers out the [[euzenius comma]] and the 87-126/125 comma in the 7-limit, hereby dividing the octave into 87 parts. | ||
| Line 15: | Line 16: | ||
Badness: 0.762 | Badness: 0.762 | ||
===11-limit=== | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 27: | Line 29: | ||
Badness: 0.352 | Badness: 0.352 | ||
{{Navbox fractional-octave}} | |||
[[Category:87edo]] | [[Category:87edo]] | ||
Latest revision as of 03:46, 14 February 2025
One step of 87edo is in direct proximity to starling comma, 126/125.
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, [152 -112 -41 43⟩
Mapping: [⟨87 1 -106 -406], ⟨0 4 9 19]]
- mapping generators: ~126/125, ~[37 -25 -12 11⟩
Optimal tuning (CTE): ~126/125 = 1\87, ~[37 -25 -12 11⟩ = 472.043
Optimal ET sequence: 783, …, 8178, 8961, 9744, 10527, 20271, 30798
Badness: 0.762
11-limit
Subgroup: 2.3.5.7.11
Comma list: 78125000/78121827, 199297406/199290375, [74 -17 -5 -4 -7⟩
Mapping: [⟨87 1 -106 -406 1225], ⟨0 4 9 19 -27]]
- mapping generators: ~126/125, ~[35 1 -6 -3 -4⟩
Optimal tuning (CTE): ~126/125 = 1\87, ~[35 1 -6 -3 -4⟩ = 472.043
Optimal ET sequence: 783, 8178, 8961, 9744, 28449de, 38193bcde, 47937bcdee
Badness: 0.352