Beauty of physics mathematics music
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2026
7 articles- How Close Can Two Beats Come Without Meeting? Nancarrow’s Study No. 33 puts an irrational number between two musical tempos. Exact recurrence disappears in an ideal pulse model, while rational approximations, near-coincidences and composed convergence remain.
- The Bell That Needed a Bulge Moving a bell’s tierce from a minor third to a major third required a new profile. The design reveals why an instrument’s partials cannot be adjusted as independent knobs.
- A Melody That Contains Its Own Mirror A melody-generating sequence survives systematic thinning as a reflection or a transposition of itself. Its parity is Thue–Morse, but the mathematics still leaves the composer substantial work to do.
- When Consonance Changes with the Instrument A frequency ratio describes two notes, but their upper partials determine many of the interactions the ear receives. A worked spectral example, Sethares’s local-consonance model and recent listening experiments show why changing a sound can change which intervals listeners prefer.
- Two Chords, One Interval Fingerprint Two different four-note collections contain precisely the same intervals. Their shared mathematics explains an ambiguity in diffraction, but does not make the chords acoustically identical.
- Why a Saw Needs an S to Sing An S-shaped blade traps a flexural vibration near its inflection point. The explanation connects ordinary shell mechanics to a carefully qualified topological mode.
- The Beauty of Physics, Mathematics, and Music (and Maybe Cats) Eight independent investigations of musical objects and mathematical structures: a singing saw, ambiguous interval fingerprints, changing consonance, frozen lakes, recursive melodies, redesigned bells, irrational tempos and music intended for cats.