Tuning Invariance

The TransformSynth presents several examples of tuning continua - parameterized families of tunings where each specific tuning corresponds to a particular value of the parameter. These tuning continua are tuning invariant as described here (where all intervals and chords within a specified set have the same geometric shape in all of the tunings of the continuum) as well as transpositionally invariant (where each interval, chord, and scale type has the same geometric shape in every key). For example, in the syntonic continuum, a major chord can be played like this on a hexagonal keyboard (lattice).




The pattern shown in green always plays a major chord. But there can be variety in the exact tuning of the various tones. For example, the intervals could be tuned to 12-tone equal tempered fourths and fifths. Or they could be tuned to just fourths and fifths. Or they could be tuned so that the major third was an exact 5/4 and the fifth was 3/2. Or they might be tuned to 19-tone equal tempered intervals. Whatever the exact tuning, here is the diatonic scale under the same mapping.




The fascinating thing about the TransFormSynth's keyboard layouts is that any given interval is fingered the same across all of these tunings -- and many more! This is how the vertical sliders (labeled 'width of generators') can change the tuning while leaving the fingerings unchanged. This uniformity makes it much easier to play in a wide variety of tunings -- learn one fingering, play in many tunings.