222edt

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← 221edt222edt223edt →
Prime factorization 2 × 3 × 37
Step size 8.56736¢ 
Octave 140\222edt (1199.43¢) (→70\111edt)
Consistency limit 10
Distinct consistency limit 10

222 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 222edt or 222ed3), is a nonoctave tuning system that divides the interval of 3/1 into 222 equal parts of about 8.57 ¢ each. Each step represents a frequency ratio of 31/222, or the 222nd root of 3.

Harmonics

Approximation of harmonics in 222edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -0.57 +0.00 -1.14 -1.92 -0.57 -1.85 -1.71 +0.00 -2.49 +3.85 -1.14
Relative (%) -6.6 +0.0 -13.3 -22.4 -6.6 -21.6 -19.9 +0.0 -29.1 +45.0 -13.3
Steps
(reduced)
140
(140)
222
(0)
280
(58)
325
(103)
362
(140)
393
(171)
420
(198)
444
(0)
465
(21)
485
(41)
502
(58)
Approximation of harmonics in 222edt
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -2.63 -2.42 -1.92 -2.28 +4.14 -0.57 +0.07 -3.06 -1.85 +3.29 +3.43
Relative (%) -30.7 -28.3 -22.4 -26.6 +48.4 -6.6 +0.8 -35.7 -21.6 +38.3 +40.1
Steps
(reduced)
518
(74)
533
(89)
547
(103)
560
(116)
573
(129)
584
(140)
595
(151)
605
(161)
615
(171)
625
(181)
634
(190)