What makes two instruments playing the same note sound different, and how does the harmonic series explain timbre?
The harmonic series and timbre: fundamental and harmonics, how the relative levels of harmonics shape tone, the waveform shapes of basic tones, the frequency spectrum and the phase relationships that create a sound's character.
A focused answer to the Edexcel 9MT0 harmonics content, covering the harmonic series, fundamental and harmonics, how relative harmonic levels shape timbre, the basic waveform shapes, the frequency spectrum and phase.
Reviewed by: AI editorial process; not yet individually human-reviewed
Have a quick question? Jump to the Q&A page
Jump to a section
What this dot point is asking
Edexcel wants you to explain why a trumpet and a flute playing the same note sound completely different, using the harmonic series. You must know that a periodic sound is built from a fundamental plus harmonics, that the relative levels of those harmonics create timbre, and that the basic waveform shapes (sine, sawtooth, square, triangle) have characteristic harmonic content. This idea connects the physics of sound directly to synthesis and EQ.
The answer
The harmonic series
The harmonic series is why notes an octave apart blend so well: the harmonics of the higher note line up exactly with the even harmonics of the lower one. It also explains why a missing fundamental can still be heard as the right pitch, because the spacing of the upper harmonics implies it.
Harmonics and timbre
The attack and decay of each harmonic over time also matter: a piano's bright attack comes from strong upper harmonics at the start that fade as the note sustains. Timbre is therefore both a spectral fingerprint (which harmonics) and a dynamic one (how they evolve).
The basic waveform shapes
These shapes are the raw material of subtractive synthesis: you pick a harmonically rich waveform such as a sawtooth, then carve away harmonics with a filter to shape the tone. Knowing which waveform carries which harmonics lets you predict and explain a synth sound by ear.
The frequency spectrum and phase
The frequency spectrum is a graph of amplitude against frequency: a snapshot of which harmonics are present and how loud each is. A spectrum analyser in a DAW shows it in real time, and a graphic or parametric EQ lets you reshape it. Phase describes the relative timing of the harmonics; for steady tones the ear is fairly insensitive to phase, but phase relationships matter greatly when two signals are combined, because out-of-phase components cancel.
Examples in context
When you boost kHz with an EQ to add "presence" to a vocal, you are raising the upper harmonics that the ear reads as clarity. When you choose a sawtooth oscillator for a bright synth lead, you are starting with a spectrum full of harmonics to filter. When you describe a recording as "warm" or "harsh", you are describing its harmonic balance: warmth from strong low harmonics, harshness from prominent upper ones. The harmonic series is the link between what you hear and what you can measure.
Try this
Q1. What sets the perceived pitch of a periodic sound? [1 mark]
- Cue. The fundamental frequency (the first harmonic).
Q2. List the harmonics present in a square wave. [2 marks]
- Cue. The odd harmonics only: , , , ...
Q3. Explain in one sentence why a flute and a violin playing the same note sound different. [2 marks]
- Cue. They have the same fundamental but different harmonic content, so the same pitch but different timbre.
Exam-style practice questions
Practice questions written in the style of Pearson Edexcel exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Edexcel 9MT0/03 20194 marksExplain what is meant by the harmonic series, and describe how the harmonics of a sound determine its timbre. Use the example of a sawtooth wave compared with a sine wave.Show worked answer →
The harmonic series is the set of frequencies present in a periodic sound: the fundamental frequency plus whole-number multiples , , and so on. The fundamental sets the perceived pitch; the harmonics above it are overtones.
Timbre (tone colour) is determined by which harmonics are present and at what relative levels. A sine wave contains only the fundamental, so it sounds pure and hollow. A sawtooth wave contains every harmonic (odd and even) with amplitudes falling off as , so it sounds bright and buzzy and is a rich starting point for subtractive synthesis. Two instruments playing the same note differ in timbre because their harmonic content differs.
Markers reward the fundamental plus integer-multiple harmonics, timbre defined by relative harmonic levels, and a correct contrast (sine = fundamental only; sawtooth = all harmonics, bright).
Edexcel 9MT0/03 20233 marksA square wave and a sawtooth wave are played at the same fundamental frequency and loudness. Describe how their harmonic content differs and how this affects the sound.Show worked answer →
A square wave contains only the odd harmonics (, , , ...) with amplitudes falling off as , giving a hollow, clarinet-like or reedy tone. A sawtooth wave contains all harmonics, both odd and even (, , , ...), also falling as , giving a brighter, fuller, brassier tone.
Because the sawtooth includes the even harmonics that the square wave lacks, it sounds fuller and richer; the square wave sounds more hollow and woody. Both are richer than a sine wave, which has only the fundamental.
Markers reward square = odd harmonics only, sawtooth = all harmonics, and a sensible description of the resulting tonal difference.
Related dot points
- Sound as a longitudinal pressure wave: amplitude and loudness, frequency and pitch, period, wavelength and the wave equation, and the audible frequency range.
A focused answer to the Edexcel 9MT0 principles of sound, covering sound as a longitudinal pressure wave, amplitude and loudness, frequency and pitch, period, wavelength, the wave equation and the audible range.
- Subtractive synthesis: oscillators and waveforms, the voltage-controlled signal path (VCO, VCF, VCA), the filter and resonance, the ADSR envelope, the LFO and modulation, and how these combine to design a synth sound.
A focused answer to the Edexcel 9MT0 subtractive synthesis content, covering oscillators and waveforms, the VCO, VCF and VCA signal path, the filter and resonance, the ADSR envelope, the LFO and sound design.
- Other synthesis methods: additive synthesis (building from sine waves), FM synthesis (carrier and modulator), wavetable synthesis, the characteristic sounds of each, and how they contrast with subtractive synthesis.
A focused answer to the Edexcel 9MT0 synthesis content, covering additive synthesis from sine waves, FM synthesis with carrier and modulator, wavetable synthesis, their characteristic sounds, and the contrast with subtractive synthesis.
- Equalisation: the frequency bands, high-pass and low-pass filters, shelving and parametric EQ, cut and boost, the Q (bandwidth) control, and using subtractive EQ to create space and corrective and creative EQ in a mix.
A focused answer to the Edexcel 9MT0 EQ content, covering the frequency bands, high-pass and low-pass filters, shelving and parametric EQ, cut and boost, the Q control, and subtractive, corrective and creative equalisation in a mix.
- The decibel as a logarithmic ratio: the power formula and the amplitude (voltage) formula, dBFS and headroom, the relationship between decibel change and perceived loudness, and dynamic range.
A focused answer to the Edexcel 9MT0 decibel content, covering the decibel as a logarithmic ratio, the power and amplitude formulae, dBFS and headroom, how decibel changes map to perceived loudness, and dynamic range.
Sources & how we know this
- Pearson Edexcel A-Level Music Technology (9MT0) specification — Pearson Edexcel (2017)