Zwicker Loudness Model

Sound is split into 24 ear-modelled Bark bands, masked, weighted by frequency, then summed into perceived loudness in sones.

What it is

A standardised model that converts a sound into how loud it actually feels to a human ear, in sones, not just dB.

Key facts

• Output unit = SONE: 1 sone = a 1 kHz tone at 40 dB SPL (the '40 phon' reference); 2 sones feels twice as loud, 0.5 sones half as loud.
• PHON = loudness level; X phon means 'as loud as an X dB, 1 kHz tone'. Loudness doubles roughly every +10 phon (~+10 dB at 1 kHz).
• The ear is split into 24 CRITICAL BANDS (Zwicker's BARK scale): Bark 1-24, each band sums energy like a separate frequency 'bucket'.
• Critical bandwidth = ~100 Hz below 500 Hz, then widens to ~20% of centre frequency above 500 Hz.
• Steps: spectrum to EXCITATION pattern, excitation to SPECIFIC LOUDNESS N' (sones/Bark), then INTEGRATE N' across all 24 Barks to get total loudness N (sones).
• Two main standards: Zwicker (ISO 532-1, free + diffuse field) and Moore-Glasberg (ISO 532-2); ISO 532-1 superseded the old DIN 45631 / ISO 532 B.
• Stevens' power law underneath: perceived loudness is proportional to (sound intensity)^0.3, i.e. it grows slower than raw energy.
• Equal-loudness contours (ISO 226): a 20 Hz tone needs ~+50 to +70 dB MORE SPL to sound as loud as a 1 kHz tone at 40 dB.
• Masking is built in: a loud tone raises the hearing threshold of nearby bands, so masked content adds little or nothing to perceived loudness.
• Reference anchors: speed of sound 343 m/s at 20 C; +6 dB = double the SPL (pressure x2); -3 dB = half the power; 0 dB SPL = 20 micropascals.

How it works

1. Filter the sound into 24 critical bands (Bark scale) the way the cochlea does.
2. Convert each band's energy to an EXCITATION level, including spreading into neighbouring bands (masking).
3. Turn excitation into SPECIFIC LOUDNESS N' (sones per Bark) using a compressive power law.
4. Sum (integrate) N' across all 24 bands to get total loudness N in sones.
5. Convert sones to phons if you want a single 'loudness level' number.

Real examples

• A 100 Hz tone and a 1 kHz tone both at 60 dB SPL: the 1 kHz one sounds clearly louder because the ear is more sensitive there.
• Pink noise and a sine wave at the same RMS dB can read identical on a meter but the noise feels louder (energy spread over more critical bands).
• Two mastered tracks both at -14 LUFS can still feel uneven; a Zwicker-style loudness meter exposes which one is harsher/louder.
• A thin 4 kHz hiss feels louder than a fat 80 Hz sub at the same dB, because 2-5 kHz sits in the ear's most sensitive zone.
• Add a quiet hi-hat under a loud cymbal: masking means the hat barely raises total loudness even though it adds dB energy.

How it helps in live sound

• Trust loudness/LUFS meters over peak meters for set-to-set balance; aim for consistent perceived level, not matching dB peaks.
• Tame 2-5 kHz first: that band drives perceived loudness and listener fatigue most per dB cut.
• A small HPF (e.g. 80-100 Hz) frees headroom with little perceived-loudness loss, since lows add few sones per dB.
• When a support act 'sounds quieter' at the same SPL, check spectral balance (often missing 2-4 kHz), not just the meter.
• Use C-weighting/Leq for SPL compliance limits, but judge mix 'feel' with a loudness model; they disagree on bass-heavy music.
• Match playback tracks by ear AND a LUFS meter before doors; raw normalising to peak dB will leave them feeling uneven.