An algorithm for spelling the pitches of any musical scale

In this paper, we propose a method for the fundamental task of optimally spelling the pitches of any given musical scale. The input, given as a sequence of pitch-class numbers, can be any randomly compiled subset of the chromatic scale, resulting in either a traditional/known scale or a novel/unknown one. The method consists of generating all potential solutions containing all possible spellings for the pitch classes in a given input sequence, and subjecting them to five filtering stages to find the correct solution. We present an algorithm to accomplish this task, and demonstrate some exemplary outputs. Constructing also a modified version of the algorithm to retrieve and execute all possible input sequences, we also present distributions of various outcomes of the procedure over the input universe to exhibit an overall view of results to be produced by the algorithm, along with some findings obtained by this process.