Smoothed Curves and the Spectral Envelope

A spectrum is naturally jagged: every harmonic of the sung note shows up as a sharp peak, with deep valleys between them. Most of the time, what we want to see is not the individual harmonics but the envelope underneath them — the gentle hills and valleys that reflect the resonances of the vocal tract. The smoothed curve makes that envelope visible.

What the Smoothed Curve Shows

The vocal-tract filter shapes the source by amplifying frequencies near each resonance and attenuating frequencies away from them. The harmonics riding on this filter inherit its shape: a harmonic that lands close to a resonance frequency comes out loud; one that lands between resonances comes out quiet.

The unsmoothed Spectrum shows both the harmonics and the filter response, mixed together. The smoothed curve hides the harmonics and leaves the filter response — the spectral envelope. Reading a smoothed curve is therefore much closer to reading the vocal tract directly:

  • A bump in the smoothed curve is a formant, regardless of which harmonic happens to fall on it.

  • The shape of the curve between formants reflects the overall balance of the voice — bright, warm, breathy, ringing.

  • Two singers producing the same vowel produce smoothed curves whose major bumps are in similar places, even if the two are at different pitches.

How the Smoothing Works

VoceVista produces the smoothed curve by low-pass filtering the spectrum: at each frequency, the displayed value is averaged over a small window of nearby frequencies. The width of that window — the radius — determines how much detail is preserved:

  • A narrow radius leaves much of the harmonic detail intact and only smooths over very local jaggedness.

  • A wide radius smooths through the harmonics entirely, leaving only the slow envelope.

The right radius depends on what you want to see. To follow formants reliably across a sung phrase, the smoothing has to adapt to the pitch: at higher pitches harmonics are spaced further apart, so the smoothing window must be correspondingly wider. VoceVista therefore lets you express the radius as a percentage of the current pitch; this is the right setting for most pedagogical and analytical work. A radius expressed as a fixed number of Hertz is also available, useful when you want consistent smoothing within a fixed frequency band.

When Smoothing Helps and When It Hides

Smoothing is most useful when you are looking for the vocal-tract part of the signal — formants, vowel identity, timbre. It is less useful when you want to see individual harmonics — pitch, intonation, register transitions in detail. A common workflow is to keep both views available and switch between them, or display the smoothed curve as an overlay on the unsmoothed Spectrum.

In VoceVista

The smoothed curve is enabled in Display Settings, separately for the short-term Spectrum and for the LTAS or marker-averaged spectra. The smoothing radius and its interpretation (relative to pitch, or absolute Hz) are configured in the same place; see Radius.