User:Francium/Miscellaneous rank-2 temperaments: Difference between revisions

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{{Optimal ET sequence|legend=1|6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749 }}
{{Optimal ET sequence|legend=1|6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749 }}


TE error: 0.057032 cents/octave
Badness: 0.100


Possible temperament family: Schismatic
Possible temperament family: Schismatic
Line 29: Line 29:
{{Optimal ET sequence|legend=1|7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636 }}
{{Optimal ET sequence|legend=1|7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636 }}


TE error: 0.000570 cents/octave
Badness: 0.015


===11-limit===
===11-limit===
Line 41: Line 41:
POTE generator: ~11/9 = 348.2809
POTE generator: ~11/9 = 348.2809


TE error: 0.021291 cents/octave
Badness: 0.811


==31 & 449==
==31 & 449==
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{{Optimal ET sequence|legend=1| 31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd }}
{{Optimal ET sequence|legend=1| 31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd }}


TE error: 0.189700 cents/octave
Badness: 8.502


Possible temperament family: Porwell
Possible temperament family: Porwell

Revision as of 12:45, 30 August 2023

In this page I explore some unnamed rank-2 temperaments, that catched my interest.

53 & 307

Subgroup: 2.9.5

Comma list: 32805/32768

Mapping: [⟨1 0 15], ⟨0 7 -28]]

POTE generator: ~512/375 = 543.3531

Optimal ET sequence: 6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749

Badness: 0.100

Possible temperament family: Schismatic

31 & 317

Subgroup: 2.5.7

Comma list: 281484423828125/281474976710656

Mapping: [⟨1 0 6], ⟨0 8 -11]

POTE generator: ~49/40 = 348.2889

Optimal ET sequence: 7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636

Badness: 0.015

11-limit

Subgroup: 2.5.7.11

Comma list: 5767168/5764801, 537109375/536870912

Mapping: [⟨1 0 6 29], ⟨0 8 -11 -88]]

POTE generator: ~11/9 = 348.2809

Badness: 0.811

31 & 449

Subgroup: 2.3.5.7

Comma list: 6144/6125, [-4 -5 -13 15⟩, [7 -4 -16 13⟩, [15 6 10 -17⟩

Mapping: [⟨1 -3 2 1], ⟨0 71 5 28]]

POTE generator: ~256/245 = 77.498

Optimal ET sequence: 31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd

Badness: 8.502

Possible temperament family: Porwell

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