1955edo

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1955edo

1956edo →

Prime factorization	5 × 17 × 23
Step size	0.613811 ¢
Fifth	1144\1955 (702.199 ¢)
Semitones (A1:m2)	188:145 (115.4 ¢ : 89 ¢)
Dual sharp fifth	1144\1955 (702.199 ¢)
Dual flat fifth	1143\1955 (701.586 ¢)
Dual major 2nd	332\1955 (203.785 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

Approximation of odd harmonics in 1955edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.244	-0.227	-0.233	-0.125	-0.116	-0.221	+0.018	+0.006	+0.185	+0.012	+0.268
	Relative (%)	+39.8	-36.9	-37.9	-20.3	-18.9	-36.0	+2.9	+1.0	+30.2	+1.9	+43.6
Steps (reduced)		3099 (1144)	4539 (629)	5488 (1578)	6197 (332)	6763 (898)	7234 (1369)	7638 (1773)	7991 (171)	8305 (485)	8587 (767)	8844 (1024)

1955edo represents well the 2.9.11.15.17.21 subgroup, with a comma basis {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.

In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 [80 -8 -13 1⟩, and 2.15.17.21 [73 -15 4 -7⟩}.

The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 [-101 -12 48 -11⟩}.

Miscellany

1955 factors as 5 x 17 x 23, and has divisors 1, 5, 17, 23, 85, 115, 391.