----------------------------------------------------------------- 2009.02.12 It's easy to see that the maximum error of an equal-step tuning for an arbitrary dyad target is 1/2 the step size. The average error over a large enough set of dyads is 1/4 the step size. But for chords, dyadic errors can add, up to the full step size. For instance, if I want a 4:5:6 triad and the error of 4:5 in my temperament is -0.49 steps and the error of 5:6 is +0.49 steps, then the error of 4:6 will be 0.98 steps. Alternatively, I can choose a different approximation of 4:5, the one with a +0.51 steps error. Then the error of 4:6 will only be 0.02 steps and the total error of the chord will be lower than when I used the best available approximations of 4:5 and 5:6. Calling the 4:5 error x and the 5:6 error y, the 4:6 error is then x-y, and the total error of the chord is |x| + |y| + |x - y| How big can any one term of this expression be when the value of the total expression is minimized? The answer appears to be 2/3 of a step.