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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
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  1. ↑ Souvignier, Todd (2003). Loops and Grooves, p.12. Hal Leonard. ISBN 9780634048135. "Pulse waves are often used to create bass sounds...Pulse width modulation has become a familiar, slightly clichéd sound within electronic dance music."
  2. ↑ Cann, Simon (2011). How to Make a Noise, [unpaginated]. BookBaby. ISBN 9780955495540.
  3. ↑ Pejrolo, Andrea and Metcalfe, Scott B. (2017). Creating Sounds from Scratch, p.56. Oxford University Press. ISBN 9780199921881. "A pulse-wave shape is colorful on its own but can really stand out when the duty cycle percentage is shifted over time by an envelope generator or LFO using what is called pulse-width modulation."
  4. ↑ a b Holmes, Thom (2015). Electronic and Experimental Music, p.230. Routledge. ISBN 9781317410232. "The harmonic content of the pulse wave is determined by the duty cycle...The harmonic content of a pulse wave can be changed dramatically merely by altering its duty cycle."
  5. ↑ Aikin, Jim (2004). Power Tools for Synthesizer Programming, p.55-56. Hal Leonard. ISBN 9781617745089.
  6. ↑ a b Reid, Gordon (February 2000). "Synth Secrets: Modulation", SoundOnSound.com. Retrieved May 4, 2018.
  7. ↑ a b Hurtig, Brent (1988). Synthesizer Basics, p.23. Hal Leonard. ISBN 9780881887143. "There is a general rule of thumb that applies [to pulse wave harmonic spectra]: For every pulse wave with a width of , every th harmonic will be absent or weak in proportion to the other harmonics.
  8. ↑ Johnston, Ian (2009). Measured Tones: The Interplay of Physics and Music, p.203 CRC Press. 3rd edition. ISBN 9781439894675. "A double reed would probably have the gap open for longer than it is closed."
  9. ↑ Snoman, Rick (2013). Dance Music Manual, p.11. Taylor & Francis. ISBN 9781136115745. "A pulse wave allows the width of the high and low states to be adjusted, therby varying the harmonic content of the sound."
  10. ↑ Skiadas, Christos H. and Skiadas, Charilaos; eds. (2017). Handbook of Applications of Chaos Theory, [unpaginated]. CRC Press. ISBN 9781315356549. "For example, if a rectangle wave has a duty cycle of 25%, or 1/4, every fourth harmonic is missing. If the duty cycle is 20%, or 1/5, every fifth harmonic would be missing."
  11. ↑ "Electronic Music Interactive: 14. Square and Rectangle Waves", UOregon.edu. A pulse wave's, "harmonic spectrum is related to its duty cycle. For example, if a rectangle wave has a duty cycle of 25%, or 1/4, every fourth harmonic is missing. If the duty cycle is 20%, or 1/5, every fifth harmonic would be missing. Given a duty cycle of 12.5%, or 1/8, then every eighth harmonic would be missing."
  12. ↑ Hartmann, William M. (2004). Signals, Sound, and Sensation, p.109. Springer Science & Business Media. ISBN 9781563962837. "Duty factors of the precise form , where is an integer, can be achieved by nulling the -th harmonic."

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