146edo

← 145edo

146edo

147edo →

Prime factorization	2 × 73
Step size	8.21918 ¢
Fifth	85\146 (698.63 ¢)
Semitones (A1:m2)	11:13 (90.41 ¢ : 106.8 ¢)
Dual sharp fifth	86\146 (706.849 ¢) (→ 43\73)
Dual flat fifth	85\146 (698.63 ¢)
Dual major 2nd	25\146 (205.479 ¢)
Consistency limit	5
Distinct consistency limit	5

Template:EDO intro 146edo has an accurate major third, only 0.012344 cents compressed from just 5/4 interval. 146edo is the denominator of a convergent to log₂5, after 3, 28 and 59, and before 643.

However, it also provides the optimal patent val for the 11-limit newspeak temperament. It tempers out the 2109375/2097152 (semicomma), and [-6 17 -9⟩ in the 5-limit; 225/224, 1728/1715, and 100442349/97656250 in the 7-limit; 441/440, 1375/1372, 1944/1925, and 43923/43750 in the 11-limit; 1001/1000, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 146edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-3.32	-0.01	+1.04	+1.57	-0.63	-2.17	-3.34	+1.89	-1.62	-2.29	-3.62
	Relative (%)	-40.5	-0.2	+12.6	+19.1	-7.7	-26.4	-40.6	+23.0	-19.7	-27.8	-44.0
Steps (reduced)		231 (85)	339 (47)	410 (118)	463 (25)	505 (67)	540 (102)	570 (132)	597 (13)	620 (36)	641 (57)	660 (76)

Subsets and supersets

Since 146 factors into 2 × 73, 146edo contains 2edo and 73edo as its subsets.