This paper proposes variable band-pass/band-stop infinite impulse response (IIR) state-space digital filters with high tuning accuracy and reduced computational complexity. We derive our proposed variable filters from the Gramian-preserving frequency transformation based on the normalized lattice structure of second-order all-pass functions. This approach gives a simple algorithm for control of the frequency characteristics of our proposed variable filters. In addition, we show that our proposed variable filters have smaller number of additions and multiplications than general state-space filters. Furthermore, it is shown that our proposed variable filters have the same controllability/observability Gramians as those of the prototype filters, regardless of the value of the tuning parameter. This property shows the high accuracy of our proposed filters with respect to quantization effects for all tunable frequency characteristics.