1848edo

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1848edo

1849edo →

Prime factorization	23 × 3 × 7 × 11
Step size	0.649351 ¢
Fifth	1081\1848 (701.948 ¢)
Semitones (A1:m2)	175:139 (113.6 ¢ : 90.26 ¢)
Consistency limit	15
Distinct consistency limit	15

Theory

1848edo is a super strong 11-limit division, having the lowest 11-limit relative error than any division until 6079. It tempers out the 11-limit commas 9801/9800, 151263/151250, 1771561/1771470 and 3294225/3294172. In the 5-limit it is an atomic system, tempering out the atom, [161 -84 -12⟩ and also the minortone comma, [-16 35 -17⟩. It also tempers out the 7-limit landscape comma, 250047/250000. It is distinctly consistent through the 15-odd-limit, and tempers out the 13-limit commas 4225/4224 and 6656/6655.

In the 7-limit, it supports domain and akjayland.

1848 factors as 2³ × 3 × 7 × 11. It is a superabundant number in the no-fives subgroup, that is, if only numbers not divisible by 5 are counted. Its divisors are 1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 42, 44, 56, 66, 77, 84, 88, 132, 154, 168, 231, 264, 308, 462, 616, 924.

Prime harmonics

Approximation of prime harmonics in 1848edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.007	+0.050	+0.005	-0.019	-0.268	+0.239	-0.110	+0.297	+0.293	-0.230
	Relative (%)	+0.0	-1.1	+7.7	+0.8	-3.0	-41.3	+36.9	-17.0	+45.8	+45.1	-35.5
Steps (reduced)		1848 (0)	2929 (1081)	4291 (595)	5188 (1492)	6393 (849)	6838 (1294)	7554 (162)	7850 (458)	8360 (968)	8978 (1586)	9155 (1763)

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-2929 1848⟩	[⟨1848 2929]]	0.002192	0.002192	0.338
2.3.5	[-16 35 -17⟩, [129 -14 -46⟩	[⟨1848 2929 4291]]	-0.005705	0.011311	1.742
2.3.5.7	250047/250000, 645700815/645657712, [43 -1 -13 -4⟩	[⟨1848 2929 4291 5188]]	-0.004748	0.009935	1.530
2.3.5.7.11	9801/9800, 250047/250000, 14348907/14348180, 67110351/67108864	[⟨1848 2929 4291 5188 6393]]	-0.002686	0.009797	1.509
2.3.5.7.11.13	4225/4224, 9801/9800, 67392/67375, 250047/250000, 4429568/4428675	[⟨1848 2929 4291 5188 6393 6838]]	0.009828	0.029378	4.524

Rank-2 temperaments

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
3	281\1848	182.467	10/9	Domain
12	3\1848	1.948	32805/32768	Atomic
21	901\1848 (21\1848)	585.065 (13.636)	91875/65536 (126/125)	Akjayland
44	767\1848 (11\1848)	498.052 (7.143)	4/3 (?)	Ruthenium
56	767\1848 (21\1848)	498.052 (13.636)	4/3 (126/125)	Barium