Just intonation tunes intervals to small-integer frequency ratios to eliminate beats with harmonic timbres

Just intonation (JI) tunes musical intervals to exact small-integer ratios: the perfect fifth is 3:2, the major third is 5:4, the minor third is 6:5, the perfect fourth is 4:3. These ratios cause partials to align exactly with no beats, producing maximum sensory consonance for harmonic timbres. The downside: JI is key-centered. A JI scale tuned for C major will have slightly off intervals when transposed to G major — some fifths become wolves with poor consonance. JI also cannot support equal division of the octave, making modulation problematic. Harry Partch extended JI to 43 tones per octave using ratios up to the 11-limit. JI is optimal for static harmonic music with a fixed tonal center and harmonic timbres.

Examples

A just fifth (3:2 = 702 cents) vs. equal-tempered fifth (700 cents): the 2-cent difference causes slow beating (~0.5 Hz at A440). A just major third (5:4 = 386 cents) vs. ET major third (400 cents): the 14-cent error causes fast beating (~7 Hz), producing the characteristic brightness of ET thirds.

Assessment

Why does just intonation produce more sensory consonance than equal temperament for a sustained harmonic major triad? Why does it fail when the key changes? What property of the timbres makes JI optimal, and what would happen if the timbres were inharmonic?