A new generalized unsupervised competitive learning rule is introduced for adaptive scalar quantization. The rule, called the generalized boundary adaptation rule (BAR(r)), minimizes the rth power law distortion D-r in the high resolution case. It ir shown by simulations that a fast version of BAR(r) outperforms generalized Lloyd I in minimizing D-1 (mean absolute error) and D-2 (mean squared error) distortion with substantially less iterations. In addition. since BAR(r) does not require generalized centroid estimation, as in Lloyd I, it is much simpler to implement.