Equal temperament versus just intonation

A four-octave electronic organ has been extensively revised for comparing the equally tempered scale with just intonation. As in usual tempered tuning, this equal-ratio scale is generated from alternate fifths and fourths, but the error is only one part in ten million, or within 0.0001 cent. Any note from this scale may be selected as a reference for the just-intonation intervals, whose ratios are absolute, not approximations. Progressive modulation may be performed in all 15 tonalities, i.e., to signature keys in seven sharps and seven flats. The black keys of an added keyboard are split for separate sharps and flats, and adjacent key tabs are used for augmented thirds and sevenths, as well as for three syntonic commas, or mutable notes. Thus there are 22 notes to the octave in a keyboard that in appearance does not differ too much from the standard 12-note keyboard. Through the use of a “movable Do” for modulation, 330 “theoretical” notes are obtained within an octave, and 1335 such notes are available to the four-octave just-intonation keyboard. [A demonstration is planned.]