A waveform’s sharpness dictates how many high-frequency sine waves it contains

Evidence

Complex tones containing frequencies that are related to each other by integer multiples are called harmonic sounds or harmonic tones. The lowest frequency of a complex tone is the fundamental frequency (f0), and the harmonics occur at integer multiples of the fundamental frequency. There are numerous examples of harmonic sounds in our daily lives, such as vowels and sounds typically generated by stringed, woodwind, and brass musical instruments. — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1180 (#expands, via linked claim)

Categorization

• XREF: connects to: Only a sinusoid has a single frequency; every other shape contains multiple frequencies; Any complex waveform can be decomposed into simple sine waves; Superposition lets complex waveforms be solved as sums of sine wave solutions — David Howard, Jamie Angus, coustics and Psychoacoustics, 439 (+6 more)

Related

• Accurate square waves require infinitely many harmonics (similarity 0.94)
• Harmonic tones are integer multiples of a fundamental frequency (similarity 0.87)
• Harmonics are integer-related partials while partials need not be harmonic (similarity 0.87)
• Any complex tone is decomposable into sine wave components displayed as a spectrum (similarity 0.87)
• Most everyday sounds are harmonic complex tones, not pure tones (similarity 0.86)
• Any complex waveform can be built from independent orthogonal sine waves (similarity 0.85)
• Spectrum components are partials and only integer-related ones are harmonics (similarity 0.85)
• Any complex waveform can be decomposed into simple sine waves (similarity 0.85)
• Any waveform can be exactly modeled by combining sine waves (similarity 0.84)
• Any waveform can be approximated by summing orthogonal sine waves (similarity 0.84)
• Sine waves are fully described by amplitude, frequency, and phase (similarity 0.84)
• Only a sinusoid has a single frequency; every other shape contains multiple frequencies (similarity 0.83)
• All complex sounds, including noise, are superpositions of pure sinusoids (similarity 0.83)
• Harmonic complex tones dominate daily life through speech and music (similarity 0.83)
• Sinusoidal vibration is the fundamental atom of all sound (similarity 0.83)

Broader Connections

• Accurate square waves require infinitely many harmonics #expands (0.95)
• Any waveform can be approximated by summing orthogonal sine waves #corroborates (0.92)
• Harmonic tones are integer multiples of a fundamental frequency #expands (0.72) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1180