Two vibrations with an irrational frequency ratio never exactly repeat their combined pattern

Evidence

By way of contrast and to complete the story, sounds that have no definite musical pitch (but a pitch nevertheless—see what follows) associated with them, such as the “ss” in sea (Figure 3.9 later in the chapter), have an acoustic pressure waveform that does not repeat regularly, and is often random in its variation with time and is therefore not periodic. Such a waveform is referred to as being “aperiodic” (see Chapter 1). The spectrum of such sounds contains frequency components that are not related as integer multiples of some frequency, and there are no harmonic components. The spectrum will often contain all frequencies, in which case it is known as a “continuous” spectrum. An example of an acoustic pressure waveform and spectrum for a nonperiodic sound is illustrated in Figure 3.6 for a snare drum being brushed. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822 (#expands, via linked claim)

Categorization

• XREF: connects to: Linear superposition lets separate vibrations coexist independently while interfering in shared space; Periodic sounds give line spectra while aperiodic sounds give continuous spectra — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822

Related

• Periodic sounds give line spectra while aperiodic sounds give continuous spectra (similarity 0.90)
• Noise-like sounds have non-repeating waveforms and continuous, inharmonic spectra (similarity 0.89)
• Signals with autocorrelations that decay to zero need continuous spectra (similarity 0.87)
• Superposed sinusoids with incommensurate frequencies yield nonperiodic motion (similarity 0.81)
• Periodic and aperiodic spectra differ in discrete versus continuous partials (similarity 0.81)
• Aperiodic sounds emerge when continuous in-between frequencies cancel periodic repeats (similarity 0.81)
• Linear superposition lets separate vibrations coexist independently while interfering in shared space (similarity 0.80)
• Waveforms become non-periodic because higher normal-mode frequencies are not equally spaced (similarity 0.80)
• Pairs of tones with irrational frequency ratios never exactly repeat their combined shape. (similarity 0.79)
• Continuous-spectrum noises like ‘ss’ and ‘sh’ still convey pitch sensations. (similarity 0.79)
• Small-integer frequency ratios yield short periodic traces while irrational ratios never repeat (similarity 0.79)
• Noise-based sounds like ss and sh can carry pitch despite nonperiodic waveforms. (similarity 0.79)
• Periodic pressure waves are perceived as pitched while nonperiodic ones are not (similarity 0.79)
• Non-periodic continuous-spectrum sounds like fricatives can still evoke pitch sensations (similarity 0.79)
• Superposed vibrations with unrelated frequencies never repeat their overall shape (similarity 0.79)

Broader Connections

• Periodic sounds give line spectra while aperiodic sounds give continuous spectra #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 822