Audio Measurement·7 min read·

Understanding Total Harmonic Distortion (THD): Measurement, Linearity, and Audible Thresholds

Master audio fidelity metrics: how Total Harmonic Distortion (THD) and THD+N are calculated, even vs odd order harmonics, and real-world audibility limits.

By Audio Tests Online Editorial Team

Safety First: Testing equipment distortion limits at maximum amplifier output can clip speakers. Increase volume gradually.

In high-fidelity audio, total harmonic distortion (THD) is the standard number used to grade the linearity of a component, from a smartphone headphone jack to a studio subwoofer. It is a ratio, not a sound: the RMS sum of the harmonic energy a device adds, divided by the fundamental it was fed.

A perfect amplifier multiplies its input by a constant. Real electronics and real drivers bend the transfer curve, and any bend generates energy at integer multiples of the input frequency. THD compresses that spectrum into one number, which is both its convenience and its main weakness.

1. How THD and THD+N are Calculated

To measure THD, a pure sine wave at fundamental frequency f1 (traditionally 1 kHz) is fed into the device under test. The output is analysed with a notch filter or a fast Fourier transform to isolate the harmonic peaks:

THD = √(V2² + V3² + V4² + … + Vn²) / V1 × 100%

where V1 is the RMS amplitude of the fundamental and V2, V3, V4 and so on are the RMS amplitudes of the 2nd, 3rd, 4th and higher harmonics.

Worked example: feed a device 1.000 V RMS at 1 kHz, and suppose it outputs 0.010 V RMS at 2 kHz, its second harmonic. THD = 0.010 / 1.000 = 1%.

Converting a THD percentage to decibels

The dB form is referenced to the fundamental, so it is always negative:

THD (dB) = 20 × log10(THD ratio)

  • 1% THD = 20 × log10(0.01) = -40 dB
  • 0.1% THD = -60 dB
  • 0.001% THD = -100 dB

A THD figure is meaningless without the test frequency, the output level, and the measurement bandwidth, because distortion rises as a device approaches its limits.

THD+N: distortion plus noise

Filtering every harmonic individually is slow on a bench. Practical analysers instead notch out the fundamental and measure everything that remains: all harmonics, mains hum, thermal noise, and interference. That figure is THD+N, and because it counts noise it must always be quoted with the bandwidth over which it was measured. SINAD is its reciprocal.

The THD Test works this way in the browser: an FFT runs over a synthetic or captured buffer at 100 Hz, 440 Hz, or 1000 Hz. Mode A plays a clean sine; Mode B plays a tone with a deliberate 2nd harmonic at 4% and a 3rd at 2%, which is √(0.04² + 0.02²) = 4.47% THD. A self-test buffer with the 2nd at 3% and the 3rd at 1.5% should read 3.354%, or -29.5 dB, which verifies the analyser path without touching your speakers.

2. Even-Order vs. Odd-Order Harmonics: Musical Timbre

The shape of the transfer curve decides which harmonics appear, and the ear does not treat them equally.

Even-order harmonics (2nd, 4th, 6th)

  • Multiples of 440 Hz: 880 Hz, 1760 Hz, 2640 Hz.
  • Musical interval: the 2nd harmonic is exactly one octave above the fundamental; the 4th is two octaves.
  • Perception: even harmonics blend with the fundamental, adding fullness and body. Single-ended triode stages with an asymmetric transfer curve are the classic source, which is where the association between tubes and “warmth” comes from.

Odd-order harmonics (3rd, 5th, 7th)

  • Multiples of 440 Hz: 1320 Hz, 2200 Hz, 3080 Hz.
  • Musical interval: the 3rd harmonic is an octave plus a perfect fifth above the fundamental; the 5th is two octaves plus a major third. Higher odd orders (7th, 9th, 11th) do not land on clean intervals in 12-tone equal temperament.
  • Perception: odd-order distortion is the harsh kind. Symmetrical clipping pushes energy into high orders, which are the least masked part of the spectrum.

Device type does not guarantee harmonic order; what matters is the symmetry of the transfer curve. A symmetric nonlinearity generates only odd harmonics, while an asymmetric one generates both.

3. What are the Audible Thresholds of THD?

THD is not a perceptual metric, and the listening research is unusually clear about it. In a study at the AES 115th Convention in 2003, Geddes and Lee compared listener ratings of 21 nonlinear distortion stimuli against three objective measures. THD correlated poorly with the subjective ratings (r = -0.42, p = 0.06), as did intermodulation distortion, while a masking-based metric correlated strongly (r = 0.68, p < 0.001).

Masking explains most of the gap. A harmonic sitting just above the fundamental is partly masked by it; a high-order harmonic an octave or two up is not. In a headphone study presented at the AES 133rd Convention in 2012, Temme, Brunet and Qarabaqi played a 100 Hz tone through the same driver at levels from 75 to 95 dB SPL:

  • At 75 dB SPL, the 2nd harmonic sat 14 dB below the fundamental and the 3rd sat 36 dB below, for 20% THD. Listeners rated the distortion almost inaudible.
  • At 95 dB SPL, hundreds of harmonics produced 60% THD, and the spectrum was rated as clearly distorted.

The same low-order spectrum can be inaudible at one level and obvious at another, so 20% THD made of low-order harmonics is not automatically audible.

Device class Typical measured THD What the number reflects
DACs and preamps 0.0001% to 0.005% (-120 to -86 dB) Converter and op-amp linearity, usually below the noise floor in normal use
Solid-state power amps 0.01% to 0.1% Output-stage linearity and negative feedback; rises near clipping
Tube amps 0.5% to 3%, mostly low order Asymmetric transfer; often masked on music
Headphones and subwoofers 0.1% to 15% Driver excursion, in the bands where masking is strongest

These are approximate engineering ranges, not thresholds of audibility; spec sheets use 1% and 0.1% as reporting lines because they are easy to quote.

Accuracy, limits and troubleshooting

  • Bandwidth caps the harmonic count. At 44.1 kHz nothing above 22,050 Hz exists, so a 440 Hz fundamental exposes at most its 50th harmonic; a 100 Hz fundamental could theoretically show 200, though windowing hides all but the first dozen.
  • FFT resolution is set by window length. Bin spacing equals 1 / duration, so a 0.5 second buffer resolves to 2 Hz. A 100 Hz fundamental with tightly packed harmonics needs a longer capture than 440 Hz.
  • The browser test is dBFS, not dB SPL. There is no calibrated microphone and no loopback, so the results describe the digital domain and cannot grade your speakers or headphones.
  • Rub and buzz is not harmonic. A loose part or a buzzing grille produces noise rather than integer multiples of the test tone.
  • THD Test — hear a clean and a deliberately distorted tone, then read the harmonic table.
  • IMD Test — the non-harmonic cousin of THD, measured with two-tone stimuli.
  • Spectrum Analyzer — watch a harmonic comb build above a live fundamental.
  • Understanding ABX Testing — how to run a level-matched listening test before you trust any audibility claim.

Academic & Scientific References