A harmonic spectrum has partials at exact integer multiples of a fundamental frequency

When a string, air column, or other one-dimensional resonator vibrates, it can only sustain modes at integer multiples of its fundamental frequency f₀: the partials occur at f₀, 2f₀, 3f₀, 4f₀, and so on. This is called a harmonic spectrum. The fundamental is the first partial; 2f₀ is the second partial (one octave up); 3f₀ is the third partial (an octave plus a fifth up); etc. Harmonic spectra are the basis of most Western instrument timbres — strings (guitar, violin, piano), winds (flute, trumpet, clarinet), and voice. In contrast, membranes, metal bars, and bells vibrate with inharmonic partials at non-integer-multiple ratios. The harmonicity of a spectrum determines which scales will sound most consonant when the instrument is played.

Examples

A guitar string vibrating at 100 Hz produces partials at 100, 200, 300, 400, 500 Hz. A marimba bar does not — its partials are at inharmonic ratios like 1:2.76:5.40 (not 1:2:3:4:5).

Assessment

State whether each instrument produces a harmonic or inharmonic spectrum, and explain why: (a) violin, (b) xylophone bar, (c) orchestral flute, (d) bell. Then state which type of spectrum supports conventional Western 12-tet tuning and why.