A stepped acoustic structure having multiple degrees of acoustic freedom for reducing noise generated from a source. Acoustic septum caps are anchored at the same depth within the cells of the stepped acoustic structure. The multiple degrees of acoustic freedom that is usually provided by locating the septum portions of the septum caps at different depths within the cells is obtained by placing steps within the cells which reduce the cross-sectional area of the cell. Depth control portions are optionally included in the septum caps so that the septum portions of different septum caps are located at different depths within the stepped acoustic structure. Various combinations of steps and depth control portions are used to provide an acoustic structure having multiple degrees of acoustic freedom even though the acoustic septum caps are anchored at the same depth within the structure.
