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The 224 equal temperament divides the octave into 224 equal parts of 5.357 cents each. It is a very strong 13-limit system, tempering out 32805/32768 in the 5-limit; 4375/4374, 16875/16807 and 65625/65536 in the 7-limit; 540/530, 1375/1372 and 4000/3993 in the 11-limit; and 625/624, 729/728, 1575/1573 and 2200/2197 in the 13-limit, leading to an abundance of precisely-tuned essentially tempered chords. It defines the optimal patent val for octoid temperament in the 7-, 11- and 13-limit, and for mirkwai, the 7-limit planar temperament tempering out 16875/16807. It also provides an excellent tuning for indra and shibi temperaments. It is the twelfth zeta integral edo.

224 = 32 * 7, and has divisors 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112.

Music

Dreyfus play by Gene Ward Smith