Isomorphic controllers and dynamic tuning : invariant fingering over a tuning continuum

The tuning invariance is where the relationship among the intervals of a given scale remain the same over a range of tunings but requires that the frequency differences are glossed over to expose the similarities. Tuning invariance can be a musically useful property by enabling dynamic tuning which is the real-time changes to the tuning of all sounded notes as a tuning variable changes along a smooth continuum. The mathematical and perceptual abstractions that are the prerequisite of this dynamic tuning are greatly discussed. Other topics being discussed include the identification of the note layouts that are tuning invariant, the meaning of the "same" across a range of tunings for a given interval and the definition of "range of tunings" for a given temperament.