Adaptive tunings for musical scales

A fixed, octave‐based musical scale cannot remain faithful to the consonant simple integer ratio intervals and simultaneously be modulated to all keys. It is possible to reconcile these competing criteria, however, if the notes of the scale are allowed to vary. This paper presents a method of adjusting the pitches of notes dynamically, an adaptive tuning, that maintains fidelity to a desired set of intervals and can be modulated to any key. The adaptive tuning algorithm changes the pitches of notes in a musical performance so as to maximize consonance, which is calculated based on recent perceptual work. The algorithm can operate in real time, is responsive to the notes played, and can be readily tailored to the timbre (or spectrum) of the sound. This can be viewed as a generalization of the methods of just intonation, but it can operate without specifically musical knowledge such as key and tonal center and is applicable to timbres with nonharmonic spectra as well as the more common harmonic timbres.