View source for 91st-octave temperaments

{{Infobox fractional-octave|91}}
{{todo|intro}}

== Protactinium ==
Protactinium is described as the 364 & 1547 temperament and named after the 91st element. Coincidentally, it reaches [[91/64]] in 1 generator.

Subgroup: 2.3.5.7

Comma list: {{monzo|47 -7 -7 -7}}, {{monzo|-2 -25 1 14}}

Mapping: [{{val| 91 0 644 -33 1036}}, {{val| 0 1 -3 -2 -5}}]
:mapping generators: ~1728/1715, ~3
Optimal tuning (CTE): ~3/2 = 701.991

[[Support]]ing [[ET]]s: {{EDOs|364, 819, 1183, 1547, 1911, 2730, 3094, 3913, 4277}}

==== 11-limit ====
Subgroup: 2.3.5.7.11

Comma list: 234375/234256, 26214400/26198073, 514714375/514434888

Mapping: [{{val| 91 0 644 -33 1036}}, {{val| 0 1 -3 -2 -5}}]
:mapping generators: ~1728/1715, ~3
Optimal tuning (CTE): ~3/2 = 702.015

[[Support]]ing [[ET]]s: {{EDOs|364, 819e, 1183, 1547, 1911, 2275, 2730e, 3458}}

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 4096/4095, 91125/91091, 369754/369603, 2912000/2910897

Mapping: [{{val| 91 0 644 -33 1036 481 }}, {{val| 0 1 -3 -2 -5 -1 }}]
:mapping generators: ~1728/1715, ~3
Optimal tuning (CTE): ~3/2 = 702.0195

{{Optimal ET sequence|legend=1| 364, 819e, 1183, 1547 }}

Badness: 0.0777

==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17

Comma list: 4096/4095, 14400/14399, 42500/42471, 75735/75712, 2100875/2100384

Mapping: [{{val| 91 0 644 -33 1036 481 -205 }}, {{val| 0 1 -3 -2 -5 -1 4 }}]

Optimal tuning (CTE): ~3/2 = 702.0269

{{Optimal ET sequence|legend=1| 364, 1183, 1547, 1911 }}

Badness: 0.0582

{{Navbox fractional-octave}}