Harmonics Calculator

The concept of musical harmonics dates to Pythagoras (~500 BCE), who discovered that strings whose lengths form simple integer ratios (1:2, 2:3, 3:4) produce consonant intervals. Joseph Fourier's 1807 heat-conduction theory formalized the mathematical framework: any periodic function decomposes into a sum of sinusoids at integer multiples of a fundamental frequency. This unified musical, mechanical, and electrical periodic phenomena into a single mathematical language.

Power-system harmonics became a critical engineering concern in the 1970s-80s as nonlinear loads (SCR-controlled motor drives, arc furnaces, then SMPS-based consumer electronics) injected large 5th, 7th, 11th, and 13th harmonic currents into utility feeders. The IEEE 519 standard (first published 1981) codified harmonic voltage and current distortion limits: THD < 5% at the point of common coupling on low-voltage systems, with tighter limits on stiffer feeders.

Audio harmonic measurement gave rise to THD (total harmonic distortion) as a quality metric in the 1930s-40s. A perfect sine-wave input through a linear amplifier produces a perfect sine-wave output; nonlinearity creates harmonics at 2f, 3f, 4f... Audiophile-grade power amps specify THD+N below 0.01%; budget consumer gear often exceeds 1%. Tube amplifiers and the warmth of analog tape trade on specific even-harmonic signatures that listeners find musically pleasing.

Enter the fundamental frequency f₀, the number of harmonics to compute (up to 30), and whether you want all integer multiples, odd-only (1, 3, 5, 7...), or even-only (2, 4, 6...). The tool returns a table of nth harmonic = n × f₀ with labels indicating odd/even status. Spectrum visualization shows relative amplitude (1/n for square/sawtooth, 1/n² for triangle) alongside frequency.

Common references: 60 Hz line → 120, 180, 240... Hz harmonics dominate utility measurement; 50 Hz line → 100, 150, 200... Hz in Europe. Musical "octave" is the 2nd harmonic; "perfect fifth" is the ratio 3:2. Clock signals radiate every odd harmonic of the fundamental — a 25 MHz crystal's EMI spectrum shows 25, 75, 125, 175... MHz tones. Everything runs client-side; no values leave your browser.