449edo

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449edo

450edo →

Prime factorization	449 (prime)
Step size	2.67261 ¢
Fifth	263\449 (702.895 ¢)
Semitones (A1:m2)	45:32 (120.3 ¢ : 85.52 ¢)
Dual sharp fifth	263\449 (702.895 ¢)
Dual flat fifth	262\449 (700.223 ¢)
Dual major 2nd	76\449 (203.118 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

449edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, giving us the option of treating it as a full 7-limit temperament, or a 2.9.15.21.11.13 subgroup temperament.

Using the patent val, the equal temperament tempers out 4375/4374 and 26873856/26796875 in the 7-limit; 41503/41472, 160083/160000, 539055/537824, 805255/802816, and 825000/823543 in the 11-limit.

Odd harmonics

Approximation of odd harmonics in 449edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.94	+1.21	+1.33	-0.79	-0.76	-1.33	-0.52	-0.72	-0.85	-0.40	-0.21
	Relative (%)	+35.2	+45.4	+49.8	-29.6	-28.5	-49.7	-19.4	-27.1	-31.9	-15.1	-7.9
Steps (reduced)		712 (263)	1043 (145)	1261 (363)	1423 (76)	1553 (206)	1661 (314)	1754 (407)	1835 (39)	1907 (111)	1972 (176)	2031 (235)

Subsets and supersets

449edo is the 87th prime edo. 898edo, which doubles it, gives a good correction to the harmonic 3, 5 and 7.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-1423 449⟩	[⟨449 1423]]	0.1249	0.1249	4.67

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	127\449	339.421	243\200	Amity (7-limit)

Music

Francium

• Little Victorious Dance (2023)