Two tones inside one critical band (one Bark) mask each other and fuse; outside it they stay separate.
Roughness/dissonance peaks at ~0.25 Bark spacing; tones smooth out once past ~1 Bark apart.
Speed of sound in air = 343 m/s at 20 C (rises ~0.6 m/s per +1 C); wavelength = speed / frequency.
+6 dB = double sound pressure; +10 dB = perceived twice as loud; +3 dB = double power; -3 dB = half power.
0 dB SPL = 20 micropascals (2e-5 Pa); loudness model unit is the Sone, summed across all 24 Bark bands.
How it works
Take a frequency in Hz off your analyser.
Run it through the Zwicker arctan formula to convert Hz to a Bark number (1 to 24).
Now equal Bark steps equal equal 'ear distance', so the pitch axis is warped to match hearing.
Group energy into the 24 critical bands; each band is one masking bucket.
Inside a band, the loudest tone hides quieter ones (masking); the model marks them inaudible.
Sum the audible band loudness into Sones to predict real perceived loudness, not just raw dB.
Real examples
A loudness meter (Zwicker/DIN 45631) reads in Bark bands so its 'how loud' number matches what the crowd hears.
Codecs (MP3, AAC) drop sounds masked within a critical band, saving data with no audible loss.
Auto-Tune/Melodyne and spectral tools warp pitch on a Bark/Mel-like axis to match perceived pitch.
A 1/3-octave RTA roughly tracks critical bands above 500 Hz, so its bars mirror Bark resolution.
Speech tools use Bark/Mel filterbanks because vowels are defined by which Bark bands hold energy (formants).
How it helps in live sound
Think in critical bands when ringing out monitors: a feedback notch only needs to be ~1 Bark (band) wide, not an octave.
Below 500 Hz problem bands are ~100 Hz wide; above 500 Hz they widen to ~20% of frequency, so use wider EQ Q up high, tighter down low.
Two instruments fighting inside one critical band mask each other; pan or EQ-carve one band apart to unmask them.
Use a Bark/ERB-weighted loudness meter (LUFS-style or Zwicker) to judge mix balance the way the audience hears, not a flat RTA.
For vocal intelligibility, protect the 1.5 kHz to 4 kHz bands (Bark ~12 to 17) where consonant clarity lives.
Roughness peaks when tones sit ~0.25 Bark apart, so a slightly detuned pair sounds gritty; tune or spread them past 1 Bark.
Everyday analogy
It's like swapping a tape measure marked in even centimetres for one whose marks get wider as you go up, so each mark lands exactly where your ear feels one 'pitch zone' begins and ends.
Watch out
Myth: pitch buckets are a fixed width in Hz. Reality: critical bands stay ~100 Hz wide only below 500 Hz, then grow to ~20% of centre frequency, which is exactly what the Bark scale encodes.
Fun fact
The 24 Barks map almost one-to-one onto the cochlea: each Bark is about 1.3 mm of basilar membrane, so the scale is literally a ruler laid along the inside of your ear.
Key takeaways
1 Bark = 1 critical band = 1 ear filter; 24 of them cover all human hearing.
Equal Bark steps feel like equal pitch distance; Hz does not.
Critical bands are ~100 Hz wide below 500 Hz, then ~20% of centre frequency above.
Sounds inside one Bark mask and fuse; outside it they stay distinct.
Bark-based meters and codecs judge masking and loudness like real ears do.