2048edo

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← 2047edo

2048edo

2049edo →

Prime factorization	211
Step size	0.585938 ¢
Fifth	1198\2048 (701.953 ¢) (→ 599\1024)
Semitones (A1:m2)	194:154 (113.7 ¢ : 90.23 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

Approximation of prime harmonics in 2048edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.002	-0.181	-0.271	+0.049	+0.293	-0.073	+0.143	-0.149	-0.085	-0.114
	Relative (%)	+0.0	-0.3	-30.9	-46.3	+8.4	+49.9	-12.4	+24.4	-25.5	-14.5	-19.4
Steps (reduced)		2048 (0)	3246 (1198)	4755 (659)	5749 (1653)	7085 (941)	7579 (1435)	8371 (179)	8700 (508)	9264 (1072)	9949 (1757)	10146 (1954)

2048edo has an excellent perfect fifth, which derives from 1024edo. It tempers out the breedsma (2401/2400) in the 7-limit, and supports the rank 3 breed temperament.

2048edo is usable as high as 43-limit, with the 2048f val regular temperament having an error of 0.023 cents (0.04 edosteps) per octave, and the no-13s limit patent val is unambiguous and has an error of only 0.019 cents/octave.

2048edo is the 11th power of two EDO.

In the 5-limit, it supports monzismic temperament.

In the 11-limit, 2048edo tempers out the quartisma.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	[54, -37, 2⟩,[-111, -12, 56⟩	[⟨2048 3246 4755]]	0.0264	0.0364	6.22
2.3.5.7	2401/2400, [-18, -13, 13, 3⟩, [49, -38, 0, 4⟩	[⟨2048 3246 4755 5749]]	0.0439	0.0438	7.48
2.3.5.7.11	2401/2400, 1890625/1889568, 1953125/1951488, 117440512/117406179	[⟨2048 3246 4755 5749 7085]]	0.0323	0.0456	7.78