Harmonics and Overtones

• Harmonics and overtones are components of complex sound waves that contribute to the timbre, or tonal color, of a sound

Harmonics

• Harmonics are frequencies that are integer multiples of the fundamental frequency
• The fundamental frequency is the lowest frequency in a complex sound and determines the perceived pitch
• If the fundamental frequency is f, then the harmonics are 2f, 3f, 4f, and so on
• Harmonics are also known as "harmonic partials" or "harmonic overtones"
• The first harmonic is the same as the fundamental frequency
• The second harmonic is twice the frequency of the fundamental and is one octave higher
• The third harmonic is three times the frequency of the fundamental
• The fourth harmonic is four times the frequency of the fundamental, and so on
• The presence and relative strength of different harmonics determine the timbre of a sound and are perceived as a richer, more complex tone

Overtones

• Overtones are any frequencies above the fundamental frequency in a complex sound
• This includes both harmonics and non-harmonic partials
• Non-harmonic partials are frequencies that are not integer multiples of the fundamental frequency
• In many musical instruments, the overtones are close to being harmonics, but not perfectly so
• The inharmonicity of overtones affects the timbre of the sound
• Instruments like bells and some percussion instruments have overtones that are significantly non-harmonic
• The specific set of overtones present in a sound, along with their amplitudes, gives each instrument its unique sound

Relationship between Harmonics and Overtones

• Harmonics are a subset of overtones
• All harmonics are overtones, but not all overtones are harmonics
• The term "overtone" is more general and includes all partials above the fundamental, whether they are integer multiples or not
• In ideal string or air column instruments, the overtones are very close to being harmonics

Timbre

• Timbre is the quality of a sound that distinguishes it from other sounds of the same pitch and loudness
• Harmonics and overtones are primary contributors to timbre
• Different instruments have different sets of harmonics and overtones, as well as different amplitudes
• Even the same note played on the same instrument can have a different timbre depending on how it is played and the acoustics of the environment
• The attack, sustain, and decay of a sound also contribute to its timbre

Examples in Music

• In string instruments (guitar, violin, piano), the strings vibrate not only at the fundamental frequency but also at various harmonics
• The relative amplitudes of these harmonics are determined by where the string is plucked, bowed, or struck, and this affects the timbre
• In wind instruments (flute, clarinet, trumpet), the air column inside the instrument vibrates at the fundamental frequency and various harmonics
• The shape and dimensions of the air column, as well as the way the instrument is played, determine which harmonics are present and their amplitudes

Synthesis

• Understanding harmonics and overtones is important in audio and music synthesis
• Synthesis techniques like additive synthesis involve creating sounds by adding together sine waves at the desired harmonic frequencies and amplitudes
• By carefully controlling the frequencies and amplitudes of the harmonics, it is possible to create a wide variety of sounds, from simple tones to complex instrument sounds

Explore harmonics and overtones as components of complex sound waves. Learn about frequencies that are integer multiples of the fundamental frequency. Understand how the presence and strength of different harmonics determine the timbre of a sound.