2711edo

← 2710edo

2711edo

2712edo →

Prime factorization	2711 (prime)
Step size	0.442641 ¢
Fifth	1586\2711 (702.029 ¢)
Semitones (A1:m2)	258:203 (114.2 ¢ : 89.86 ¢)
Consistency limit	15
Distinct consistency limit	15

Theory

2711edo is distinctly consistent to the 15-odd-limit, or the no-11 19-odd-limit. The equal temperament tempers out 78125000/78121827 in the 7-limit; 35156250/35153041, 14348907/14348180, 21437500/21434787, 151263/151250, 2359296/2358125, 5767168/5764801 and 199297406/199290375 in the 11-limit.

Prime harmonics

Approximation of prime harmonics in 2711edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.074	+0.112	+0.115	+0.213	+0.048	-0.049	-0.058	-0.167	+0.006	+0.077
	Relative (%)	+0.0	+16.7	+25.3	+26.1	+48.1	+10.8	-11.2	-13.1	-37.6	+1.4	+17.4
Steps (reduced)		2711 (0)	4297 (1586)	6295 (873)	7611 (2189)	9379 (1246)	10032 (1899)	11081 (237)	11516 (672)	12263 (1419)	13170 (2326)	13431 (2587)

Subsets and supersets

2711edo is the 395th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[4297 -2711⟩	[⟨2711 4297]]	-0.0233	0.0233	5.26
2.3.5	[77 -31 -12⟩, [18 -89 53⟩	[⟨2711 4297 6295]]	-0.0316	0.0223	5.04
2.3.5.7	[3 -13 10 -2⟩, [37 -9 -11 1⟩, [0 -11 -7 12⟩	[⟨2711 4297 6295 7611]]	-0.0340	0.0198	4.47
2.3.5.7.11	151263/151250, 14348907/14348180, 2359296/2358125, 21437500/21434787	[⟨2711 4297 6295 7611 9379]]	-0.0395	0.0209	4.72
2.3.5.7.11.13	4096/4095, 43940/43923, 67392/67375, 151263/151250, 4429568/4428675	[⟨2711 4297 6295 7611 9379 10032]]	-0.0351	0.0215	4.86

Music

Francium

• "Ballad From A Broken Record" from HemischisMatic EP (2023) – Spotify | Bandcamp | YouTube – hemischis in 2711edo tuning