2100edo

← 2099edo

2100edo

2101edo →

Prime factorization	22 × 3 × 52 × 7
Step size	0.571429 ¢
Fifth	1228\2100 (701.714 ¢) (→ 307\525)
Semitones (A1:m2)	196:160 (112 ¢ : 91.43 ¢)
Dual sharp fifth	1229\2100 (702.286 ¢)
Dual flat fifth	1228\2100 (701.714 ¢) (→ 307\525)
Dual major 2nd	357\2100 (204 ¢) (→ 17\100)
Consistency limit	7
Distinct consistency limit	7

The patent val tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, and thereby provides an excellent tuning for 5-limit schismatic aka helmholtz temperament, and the 7-limit sesquiquartififths temperament. As with any equal division of this size, it supports a number of possible meantone tunings, but the 1219\2100 fifth is notable for being an extremely close approximation to quarter-comma meantone.

Odd harmonics

Approximation of odd harmonics in 2100edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.241	-0.028	-0.254	+0.090	+0.111	+0.044	-0.269	+0.187	+0.201	+0.076	-0.274
	Relative (%)	-42.1	-4.9	-44.5	+15.7	+19.4	+7.7	-47.0	+32.8	+35.2	+13.3	-48.0
Steps (reduced)		3328 (1228)	4876 (676)	5895 (1695)	6657 (357)	7265 (965)	7771 (1471)	8204 (1904)	8584 (184)	8921 (521)	9224 (824)	9499 (1099)

Subsets and supersets

Since 2100 factors into 2² × 3 × 5² × 7, 2100edo has subset edos 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, and 1050.