Mel, MFCC, and Timbre
Some questions are not about which notes but about what the sound is like — bright or dark, smooth or noisy, a flute or a distorted guitar. That is timbre, and the features here describe it. They build on the spectrogram from Spectrogram and STFT.
Timbre: the "color" of a sound
Timbre (pronounced "TAM-ber") is what makes a piano and a guitar sound different even on the same note at the same loudness. It comes from the relative strengths of a sound's overtones and how they evolve. Pitch tells you the note; timbre tells you the voice.
The mel scale: frequency the way we hear it
Humans do not hear frequency linearly. The jump from 100 Hz to 200 Hz feels large, while 5000 Hz to 5100 Hz feels like almost nothing.
The mel scale is a perceptual frequency scale that matches this behavior: fine resolution in the low range, coarser resolution in the high range.
A mel spectrogram re-maps the STFT onto that scale. Its detail is concentrated where our ears can actually discriminate, which is why it is the default front-end for many audio machine-learning systems.
- triangular mel filters
- evenly spaced
MFCC: a compact timbre fingerprint
MFCCs (Mel-Frequency Cepstral Coefficients) compress a mel spectrogram into a small set of numbers.
They are designed to capture the spectral envelope: the overall shape of the spectrum, while ignoring fine pitch detail.
The calculation has three main steps:
- Build a mel spectrogram.
- Take the log of the mel energies.
- Apply a DCT (discrete cosine transform), a cosine-basis transform that concentrates information into the first few coefficients.
The result is a compact timbre "fingerprint" used to classify instruments, voices, and sound types.
Single-number brightness: centroid and flatness
Two scalars summarize spectral shape per frame:
| Feature | Measures | High value means |
|---|---|---|
| Spectral centroid | The "center of mass" of the spectrum (Hz) | Brighter, more high-frequency energy |
| Spectral flatness | How noise-like vs. tonal (0–1) | Closer to noise (1) rather than a clear pitch (0) |
These are cheap brightness/noisiness proxies — useful for UI meters, thresholds, and quick descriptors when a full MFCC vector is more than you need.
Silence reads as flatness 1.0, not 0
Flatness is the geometric mean of the power spectrum divided by its arithmetic mean, with every bin floored at amin (1e-10) before the means are taken. A digitally silent frame therefore has a perfectly constant floored spectrum, and the ratio comes back as 1.0 — "maximally noise-like", the opposite of what the silence suggests. libsonare matches librosa.feature.spectral_flatness here and deliberately does not special-case silence.
Gate on level first: check RMS or peak for the frame and ignore the flatness reading below your noise floor. A UI meter or noise gate driven straight off flatness will light up during the quiet parts.
How libsonare computes these
libsonare builds the mel spectrogram with a mel filterbank applied to STFT power, then derives MFCCs via log compression and a DCT-style step, following librosa conventions closely enough for reference comparison. mfcc accepts a trailing lifter parameter (cepstral liftering, default 0 = no liftering) that matches librosa's lifter argument. Spectral centroid and flatness are computed directly from the magnitude spectrum per frame. These features are exposed through the feature-extraction APIs and reused by higher-level timbre and section descriptors; mel and MFCC can also be inverted to approximate audio for previews (see Inverse Features).
Related: MIR Overview, Spectrogram and STFT, Section and Structure, Chroma Features