2100edo

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← 2099edo2100edo2101edo →
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

2100 equal divisions of the octave (abbreviated 2100edo), or 2100-tone equal temperament (2100tet), 2100 equal temperament (2100et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2100 equal parts of about 0.571 ¢ each. Each step of 2100edo represents a frequency ratio of 21/2100, or the 2100th root of 2.

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 -5 -45 +16 +19 +8 -47 +33 +35 +13 -48
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.