389edo

← 388edo

389edo

390edo →

Prime factorization	389 (prime)
Step size	3.08483¢
Fifth	228\389 (703.342¢)
Semitones (A1:m2)	40:27 (123.4¢ : 83.29¢)
Dual sharp fifth	228\389 (703.342¢)
Dual flat fifth	227\389 (700.257¢)
Dual major 2nd	66\389 (203.599¢)
Consistency limit	3
Distinct consistency limit	3

389edo divides the octave into parts of 3.0848c each.

Theory

Approximation of prime intervals in 389 EDO

Prime number		2	3	5	7	11	13	17	19
Error	absolute (¢)	+0.00	+1.39	-0.71	-0.19	+0.87	-1.45	-0.07	-1.37
	relative (%)	+0	+45	-23	-6	+28	-47	-2	-44
Steps (reduced)		389 (0)	617 (228)	903 (125)	1092 (314)	1346 (179)	1439 (272)	1590 (34)	1652 (96)

389edo has two mappings for 3, which makes it a dual-fifth system. The best approach to this tuning is through a 2.5.7.11.17 subgroup.

Relation to a calendar reform

389edo represents the north solstice (summer in the northern hemisphere) leap year cycle 69/389 as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a maximum evenness scale, temperament can be generated by simply merging the numerator and the denominator.

Solstice Leap Day (94 & 295)

295 seems to precede 389.

Subgroup: 2.5.7.11.17

POTE generator: 370.1796c

Comma list: 250000/248897, 2100875/2097152, 4096000/4092529

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	[20 -17 3⟩, [-39 -12 25⟩	[⟨389 617 903]]	-0.19	0.500	16.2
2.3.5	2109375/2097152, [-7, 44, -27⟩	[⟨389 616 903]] (389b)	0.46	0.451	14.6
2.5.7	2100875/2097152, [0, 52, -43⟩	[⟨389 903 1092]]	0.12	0.131	4.2
2.5.7.11.17	6664/6655, 156250/155771, 180625/180224, 184960/184877	[⟨389 903 1092 1346 1590]]	0.03	0.177	5.7

Scales

• Solstice[69]
• SolsticeDay[94]

Links

https://individual.utoronto.ca/kalendis/leap/index.htm#mod