Just Intonation
Tuning by simple integer ratios sounds pure, but makes free modulation difficult.
Related
Divide a string by 2:1, 3:2 or 5:4 and you get an octave, a pure fifth or a pure third. The simpler the ratio, the more the sound fuses. That is the promise of just intonation, but a twelve-key keyboard cannot keep every interval pure.
The question
Just intonation defines intervals by whole-number ratios. Its thirds sound sweeter. But pure fifths and thirds cannot coexist in every key, and the comma must go somewhere. A tuned keyboard cannot adjust.
Historical arc
Pythagoreans stacked fifths at 3:2, and medieval theory built modes on the ratios. Zarlino made the 5:4 third the centre; choirs and strings still slide toward pure intervals by ear. Meantone compromised for keyboards, and equal temperament won after 1700. Partch built a 43-tone just scale; Johnston wrote it into string quartets.
The turning point
The pivot is the syntonic comma of 81/80. Keep the third pure and the cycle of fifths leaves a gap; spread it over twelve semitones and you get equal temperament. It is not purer, only free to modulate. Singers and strings still lean toward pure thirds, so it never vanished.
What to listen for
Begin with a Palestrina mass, where voices fuse the thirds. Then Tallis's forty-voice Spem in alium, chords standing on pure intervals. Finally a Josquin motet, its cadential third like a shaft of light. The library often uses synth timbres; listen for beating.
Related
The mathematics is Interval, the judgement of sweetness Consonance and Dissonance; the sound is clearest in Renaissance vocal music, and strings carry it into intonation on the Violin.
Listen in the library
All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).
Sources
- The New Grove Dictionary of Music and Musicians, 2nd ed., entry "Just intonation" — definitions checked, not quoted
- J. Murray Barbour, Tuning and Temperament, A Historical Survey (Michigan State College Press) — historical outline checked, not quoted
Used for fact-checking only; all prose is original.