Since bedrock river morphology is a key element in landform development, quantification of riverbed morphology is an important issue in geomorphology. Here we examine not only stream gradient but also its changes with measuring scales in order to quantify bedrock river morphology and to extract knickzones, i.e., relatively steep reaches. The method uses a simple slope calculation at every point along stream lines having a regular horizontal spacing, with variable measurement stick as a horizontal scale, revealing the local relative steepness of rivers, showing how a river reach is steeper than adjacent reaches. Fluctuations in the local relative steepness indicate step-pool or riffle-pool-like morphology of bedrock rivers, which occur in differing spatial scales. Portions with high local relative steepness can be regarded as knickzones, which are numerously found across the Japanese mountain bedrock rivers from 50-m resolution DEM. If such a coarse DEM such as 50-m resolution is used to do this analysis, large scale fluctuations with hundreds of meters in horizontal scale are found, and the large knickzones can be related to hydraulic factors such as variations in flow velocity to cause local oversteepening along rivers and/or flow perturbation around major stream confluences. When a finer DEM such as airborne LiDAR at 1-m resolution is used, much smaller-scale (on the order of 10-m horizontal scale) fluctuations in bedrock river morphology are found and they correspond to small knickpoints, waterfalls or step-pools found in the field.