Towards Schenkerian Analysis by Computer: a reductional Matrix

An approach to the implementation of Schenkerian analysis in a computer program is described. It would appear that a single piece of music has a number of possible analyses related exponentially to the size of the piece. The approach described differs from previous attempts at the computer implementation of Schenkerian analysis by not aiming to build an analysis directly from the notes of the score, but instead to construct a matrix which contains, in different paths through the matrix, all possible analyses. The size of the matrix is related to the square of the size of the piece, and the time-complexity of its generation to the cube. Generation of the matrix is therefore a tractable problem. An analysis can be derived from the matrix in time related to the square of the size of the piece, but the complexity of deriving analyses with particular properties has yet to be investigated.