Timbre and overtones

A sound has more than one component

A complex musical sound can be analysed as a combination of frequency components, or partials. For a periodic sound, the fundamental frequency is the repetition rate of the whole waveform; a component at that frequency can be weak or absent. An overtone is a component above that fundamental. Harmonics are components at whole-number multiples of a fundamental frequency. These words overlap in many instrumental sounds, but they are not interchangeable: an overtone need not be exactly harmonic.

For a 120 Hz fundamental, an ideal harmonic series begins 120, 240, 360, 480 and 600 Hz. The fundamental is the first harmonic, so the second harmonic is the first overtone. Stating which numbering system you use prevents a common confusion. The figures identify possible component positions; they do not tell us how strong each component is, or how it changes after the note begins.

References: [1]

Spectral balance contributes to colour

A spectrum shows the distribution of a signal across frequency. Two sounds can have the same fundamental and different strengths of higher components. This contributes to differences described as dark, bright, hollow or buzzy. Such words are listening descriptions, not precise substitutes for a measurement. Ask what changed and test the description against an actual sound rather than treating an adjective as an acoustic law.

Try playing the same guitar note near the bridge and nearer the middle of the vibrating string. Keep the pitch and overall effort similar. Listen for a change in the balance of the attack and sustained sound. You have changed how the string is excited, not simply selected another note. Recording the experiment can help you compare it repeatedly, provided microphone position and recording gain remain steady.

References: [1]

The beginning matters

A note's attack, decay, sustained portion and release are often described as its envelope. The crisp beginning of a pluck and the slower growth of a bowed tone provide strong identity cues. Frequency components can also evolve at different rates: a bright attack may give way to a darker tail. Looking at one frozen spectrum therefore misses part of the sound's character.

To listen for this, make a short recording of one sustained note and compare the first moment with a later segment. Do not assume a short cropped segment represents the whole instrument. In composition, changing the onset can make familiar material feel unfamiliar. A slowly swelling sound may merge with another sustained line, while a sharp attack can separate the same pitch into an obvious new event.

References: [2]

Real instruments do not follow one recipe

The harmonic series is a useful model, not a requirement for musical value. Real strings can deviate from exact harmonic relationships, and bells and other resonating objects can have prominent components that are not integer multiples of one fundamental. A sound can still be musically recognisable without fitting a simple pitched-instrument template. Analyse its behaviour before deciding which model is helpful.

Instrument labels also hide variety. A voice changes colour with vowel, register and articulation; a drum changes with stroke position and damping. If you are arranging a piece, ask which part of the sound you need: its sustained weight, breath, transient or roughness. That question may suggest a more useful musical choice than assigning every instrument a permanent adjective such as warm or bright.

References: [3]

What to remember

• Harmonics are a special case of frequency components.
• Spectral balance and time evolution both shape timbre.
• Compare sounds under similar conditions before attributing a difference.