User:Eliora/Proposed concept names

Prequartismic

Named because 3125edo was the only one confirmed for tempering out the quartisma before it's discovery as significance of the difference between 5 33/32s and 7/6. Defined as the 1259e & 3125 temperament, but in terms of patent vals it can also be described as 3125 & 4991 or 3125 & 1866.

Subgroup: 2.3.5.7.11

Comma list: [24, -6, 0, 1, -5⟩, [-1, 4, 11, -11, 0⟩, [-19 -25 14  13 -3⟩

Mapping: to be filled in

Optimal tuning (CTE): ~64/33 = 1146.624

Vals: 1259e, 1866, 3125, 4384e, 4991, 6250e, 8116d, 7509ee, 9375e, 11241de

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1990656/1990625, 14236560/14235529, 117440512/117406179, 1181640625/1181599328

Mapping: to be filled in

Optimal tuning (CTE): ~64/33 = 1146.624

test

← 3577edo

3578edo

3579edo →

Prime factorization	2 × 1789
Step size	0.335383 ¢
Fifth	2093\3578 (701.956 ¢)
Semitones (A1:m2)	339:269 (113.7 ¢ : 90.22 ¢)
Consistency limit	21
Distinct consistency limit	21

← 2117edo

2118edo

2119edo →

Prime factorization	2 × 3 × 353
Step size	0.566572 ¢
Fifth	1239\2118 (701.983 ¢) (→ 413\706)
Semitones (A1:m2)	201:159 (113.9 ¢ : 90.08 ¢)
Consistency limit	11
Distinct consistency limit	11

← 705edo

706edo

707edo →

Prime factorization	2 × 353
Step size	1.69972 ¢
Fifth	413\706 (701.983 ¢)
Semitones (A1:m2)	67:53 (113.9 ¢ : 90.08 ¢)
Consistency limit	11
Distinct consistency limit	11

← 292edo

293edo

294edo →

Prime factorization	293 (prime)
Step size	4.09556 ¢
Fifth	171\293 (700.341 ¢)
Semitones (A1:m2)	25:24 (102.4 ¢ : 98.29 ¢)
Dual sharp fifth	172\293 (704.437 ¢)
Dual flat fifth	171\293 (700.341 ¢)
Dual major 2nd	50\293 (204.778 ¢)
Consistency limit	5
Distinct consistency limit	5

← 1775edo

1776edo

1777edo →

Prime factorization	24 × 3 × 37
Step size	0.675676 ¢
Fifth	1039\1776 (702.027 ¢)
Semitones (A1:m2)	169:133 (114.2 ¢ : 89.86 ¢)
Consistency limit	15
Distinct consistency limit	15