The envelope of a sound signal is the curve describing the evolution of the signal’s maximum amplitude over time.
Discover FizziQ
How to measure it in class
Steps:
- Open FizziQ and select the Oscilloscope tool. Prepare several sound sources: a tuning fork, a metallic object, a hand clap.
- Record successively the sound of a struck tuning fork and a hand clap. Capture both oscillograms.
- Compare the envelopes: the tuning fork shows a slow, regular decay, while the hand clap has a very brief, intense envelope.
- Interpret: the envelope shape characterizes the sound type (percussive, sustained, resonant).
Scientific activities on this topic
Several experiments easily performed with a smartphone, tablet, or computer allow you to study the envelope of a sound signal.
1: The Sound of Bells - Harmonic and non-harmonic sounds through the study of bell sounds: https://www.fizziq.org/en/activities/the-sound-of-bells/
2: Instrument Timbre - Why does the same note sound different depending on the musical instrument that produces it?: https://www.fizziq.org/en/activities/the-tone-of-an-instrument/
3: Vowels - How our mouth pronounces vowels and creating a training tool for singers: https://www.fizziq.org/en/activities/vowels/
4: Acoustic Beats - How the acoustic beat effect is used in electronic music: https://www.fizziq.org/en/activities/acoustic-beats/
Learn more
Historical context:
The ADSR model was popularized in the 1960s by Robert Moog’s analog synthesizers. By enabling control of electronic sound envelopes, Moog paved the way for modern sound synthesis and new musical genres.
Envelope and perception:
Psychoacoustic studies have shown that if you play a piano sound backwards (reversing the temporal envelope), it becomes unrecognizable. The attack is a major perceptual cue for instrument identification.
Envelope and signal processing:
In signal processing, the envelope is mathematically obtained through the Hilbert transform. This technique is used in musical analysis, voice recognition, and seismology to characterize signals.
Additional experiments:
The experiment The Sound of Bells allows you to observe the distinctive envelope of a bell sound, with its beat phenomena.
Formula
The envelope can be modeled by decreasing exponential functions for the decay phase. In sound synthesis, each ADSR phase is parameterized by duration and level:
- Attack: Rise time from 0 to maximum amplitude
- Decay: Duration of descent to sustain level
- Sustain: Level maintained while the note is held
- Release: Duration of descent to silence after release
Application examples
- Piano sound: sharp attack then slow amplitude decay
- Flute sound: soft attack, constant sustain, then rapid decay when breath stops
- Door slam: very brief envelope with nearly instantaneous attack
- Synthesizers use ADSR parameters to sculpt each sound’s envelope
- Bell sound: strong attack then long decaying resonance with beats
FAQ
Q: What is the ADSR model? A: ADSR stands for Attack, Decay, Sustain, Release. These are the four phases of a sound’s envelope. Attack is the initial rise, decay is the descent to the sustain level, sustain is the stable level, and release is the descent to silence.
Q: Why is the envelope important for recognizing an instrument? A: The temporal envelope contributes to an instrument’s timbre. A piano has a sharp attack and a long decay. A flute has a soft attack and constant sustain. Our ear uses these cues to identify instruments.
Q: How do you visualize a sound’s envelope? A: With FizziQ, you record the sound and observe the oscillogram. The envelope is the curve that surrounds the oscillations by connecting successive peaks.
Q: Does a pure tone have an envelope? A: Yes. Even a pure (sinusoidal) tone has an envelope that describes how its amplitude varies over time. A continuous pure tone has a constant (rectangular) envelope. A pure tone that fades out has a decreasing envelope.
Q: Is the envelope the same thing as the spectrum? A: No. The spectrum shows the frequencies present in the sound at a given moment. The envelope shows how the sound’s overall amplitude evolves over time. They are two complementary descriptions.
Related concepts
Timbre - Amplitude - Oscillogram - Sound spectrum - Sound synthesis - ADSR - Harmonics