834edo

← 833edo

834edo

835edo →

Prime factorization	2 × 3 × 139
Step size	1.43885 ¢
Fifth	488\834 (702.158 ¢) (→ 244\417)
Semitones (A1:m2)	80:62 (115.1 ¢ : 89.21 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

834et is only consistent to the 3-odd-limit, with three mappings possible for the 7-limit:

• ⟨834 1322 1936 2341] (patent val),
• ⟨834 1322 1937 2341] (834c),
• ⟨834 1322 1937 2342] (834cd).

Using the patent val, it tempers out 1600000/1594323 and [-71 -5 34⟩ in the 5-limit; 2401/2400, 4802000/4782969 and [-28 -1 20 -6⟩ in the 7-limit.

Using the 834c val, it tempers out [40 7 -22⟩ and [-31 43 -16⟩ in the 5-limit; 823543/820125, 1959552/1953125 and 1640558367/1638400000 in the 7-limit.

Using the 834cd val, it tempers out [40 7 -22⟩ and [-31 43 -16⟩ in the 5-limit; 250047/250000, 283435200/282475249 and 102760448/102515625 in the 7-limit.

Prime harmonics

Approximation of prime harmonics in 834edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.203	-0.702	-0.481	-0.239	-0.240	+0.081	+0.329	+0.503	+0.639	+0.288
	Relative (%)	+0.0	+14.1	-48.8	-33.4	-16.6	-16.7	+5.6	+22.8	+34.9	+44.4	+20.0
Steps (reduced)		834 (0)	1322 (488)	1936 (268)	2341 (673)	2885 (383)	3086 (584)	3409 (73)	3543 (207)	3773 (437)	4052 (716)	4132 (796)

Subsets and supersets

834 factors into 2 × 3 × 139, with subset edos 2, 3, 6, 139, 278, and 417. 1668edo, which doubles it, gives a good correction to the harmonic 5.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[661 -417⟩	[⟨834 1322]]	-0.0641	0.0641	4.45

Music

JUMBLE

• Lullaby For A Dead Planet (2024)