Description

English: Pulse wave 33 percent Fourier series 50 of 50 harmonics. A 1/3 wave includes all harmonics in the harmonic series except those divisible by 3/1. Sum of the harmonics in red. "Pulse waves with short positive [duty] cycles (10% to 20%) have more harmonics and take on more of a thin, nasal character; longer positive [duty] cycles (30% to 40%) sound richer and rounder."^[1] "The tone varies according to the width of the pulse, giving a range of tones going from sounding similar to square wave, through becoming increasingly thinner and more nasal, to ending with noise."^[2] "The shift away from the symmetrical square wave [to the asymmetrical pulse wave] adds variation to the harmonic content, most notably as a comb filter in the higher harmonics."^[3] "Pulse waves have a clear, resonant sound."^[4] "As the pulse becomes narrower..., the wave acquires a thinner, more biting character. A thin pulse wave is good for synthesizing Clavinet sounds."^[5] "Pulse waves with different duty cycles have quite different audible characteristics. Narrow cycles (usually in the range 5 to 10 percent) are thin and nasal, and are often used to create sounds such as oboes. As the duty cycle becomes closer to 50 percent the sound thickens considerably, but at exactly 50 percent it has a distinctively hollow character that is ideal for simulating clarinets," and similar sounding instruments.^[6] "In general, pulse waves are bright and buzzy, almost reed-like. The narrower the width, the thinner the sound. The wider the width, the rounder and richer the sound."^[7] Double reed instruments, such as the oboe, may approximate an almost square pulse wave.^[8] The duty cycle determines the spectrum or timbre of a pulse wave,^[4][9] suppressing or "leaving out" (nullifying) the harmonics which are divisible by the inverse of the duty cycle. Thus for a ratio of 50% (1/2) then all even harmonics (those divisible by 2/1) are suppressed, leaving only odd harmonics; for 33.% (1/3), then every third harmonic is suppressed (those divisible by 3/1); and for 25% (1/4) then every fourth harmonic is suppressed (those divisible by 4/1), and so on.^{[7][10][11][12]} If the duty cycle denominator is not a whole number (the numerator being 1) then harmonics are quieted but not eliminated: "Because 28.5 percent [57:200] lies somewhere between the 1:3 [33.%] and 1:4 [25%] duty cycles, every third harmonic is somewhat attenuated, as is every fourth, but no harmonics are completely eliminated from the signal."^[6]0