Math's Tuning Trick: East vs. West Notes

In July 1966, Ravi Shankar and Yehudi Menuhin recorded an album, yet their musical traditions, while harmonious culturally, were mathematically opposed. Indian classical music adheres to "just intonation," anchoring all notes to a pure home pitch, like Sa, creating deep but confined keys. This system ensures notes lock into place but prevents key changes.

Western music, however, employs "equal temperament." Faced with natural mathematical discrepancies, Europe chose to slightly bend every note. This allows for freer modulation between keys, a hallmark of Western composition, but sacrifices absolute purity in any single chord.

The clash becomes audible in intervals like the major third, where Western tuning is nearly 14 cents sharper than its pure counterpart. This slight, deliberate imperfection causes a perceptible beating or pulsing effect when played against pure Indian tuning.

Instruments that can bend notes, like violins or voices, can adapt to either system. Fixed-pitch instruments like pianos or harmoniums, however, maintain their predetermined tuning, meaning they approximate rather than perfectly join the other tradition's sound.

Ultimately, both traditions offer honest answers to an impossible mathematical problem: how to have every note in perfect tune across all keys. India chose purity and depth, while the West chose travel and flexibility, leading to their distinct sonic identities.