Real-time tonal self-adaptive tuning for electronic instruments

Abstract

A fixed tuning system cannot achieve just intonation on all intervals. A better approximation of just intonation is possible if the frequencies of notes are allowed to vary. Adaptive tuning is a class of methods that adjusts the frequencies of notes dynamically in order to maximize musical consonance. However, finding the optimal frequencies of notes directly based on some definition of consonance has shown to be difficult and computationally expensive. Instead, this paper proposes that the current key of the music is both a good summary of past notes and a good prediction of future notes, which can facilitate adaptive tuning. A method is proposed that uses a hidden Markov model to detect the current key of the music and compute optimal frequencies of notes based on the current key. In addition, a specialized online machine learning method that enforces symmetry among diatonic keys is presented, which can potentially adapt the model for different genres of music. The algorithm can operate in real time, is responsive to the notes played, and is applicable to various electronic instruments, such as MIDI pianos. This paper also presents comparisons between this proposed tuning system and conventional tuning systems.