Accurate square waves require infinitely many harmonics

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; Real signals contain smooth distributions of infinite frequencies; Any complex waveform can be decomposed into simple sine waves (+7 more)

Related

• A waveform’s sharpness dictates how many high-frequency sine waves it contains (similarity 0.94)
• Harmonics are integer-related partials while partials need not be harmonic (similarity 0.90)
• Most everyday sounds are harmonic complex tones, not pure tones (similarity 0.89)
• Harmonic tones are integer multiples of a fundamental frequency (similarity 0.89)
• The harmonic overtone series of strings is a lucky gift, not a fixable property (similarity 0.86)
• Harmonic complex tones dominate daily life through speech and music (similarity 0.85)
• Spectrum components are partials and only integer-related ones are harmonics (similarity 0.85)
• Individual harmonics relate to each other as musical intervals, not just numeric frequency ratios. (similarity 0.84)
• Any complex tone is decomposable into sine wave components displayed as a spectrum (similarity 0.83)
• Sinusoidal vibration is the fundamental atom of all sound (similarity 0.83)
• Partials become harmonics only when integer-related to the fundamental (similarity 0.82)
• Any waveform can be exactly modeled by combining sine waves (similarity 0.82)
• Pitch perception depends on harmonics being integer multiples of the fundamental (similarity 0.81)
• Pitch of harmonic sounds is determined by the fundamental frequency. (similarity 0.81)
• Any waveform can be approximated by summing orthogonal sine waves (similarity 0.81)

Broader Connections

• Harmonic tones are integer multiples of a fundamental frequency #expands (0.85) — Jennifer Lentz, Psychoacoustics- Perception of Normal…, 1180