Acoustic Pedagogy Lab — User Guide
Comprehensive demonstrations of 15 acoustic phenomena for teaching and research. Interactive auditory experiments in Praat.
Overview
This script provides 15 interactive acoustic demonstrations covering fundamental psychoacoustic and musical phenomena. Each demonstration generates and plays sounds with visual representations, making abstract concepts tangible through direct auditory experience.
📊 Demonstration Categories
| Category | Phenomena | Topics Covered |
|---|---|---|
| Tuning Systems | 1-4 | Just intonation, commas, wolf intervals |
| Perceptual Effects | 5-8, 12 | Roughness, combination tones, binaural beats |
| Auditory Illusions | 7, 10 | Missing fundamental, Shepard tone |
| Synthesis | 9, 11, 13 | Fourier, harmonic series, formants |
| Modulation | 14, 15 | AM/FM, phase cancellation |
- Hear abstract concepts: Convert mathematical ratios to audible experiences
- Visual reinforcement: ParamCurve plots show waveform relationships
- Interactive exploration: Adjust parameters and hear immediate changes
- Comparative listening: A/B comparisons between related phenomena
- Theory-to-practice: Connect acoustic theory with perceptual reality
Quick start
- Open Praat (no objects need to be selected)
- Run script:
acoustic_pedagogy_lab.praat - Select a phenomenon from the dropdown menu (1-15)
- Adjust playback controls if desired:
- Duration: 0.5-10.0 seconds
- Base frequency: 50-1000 Hz
- Amplitude: 0.1-1.0
- Enable Show info window for detailed explanations
- Enable Save sounds to list to keep generated sounds
- Click OK
- Listen to the demonstration and view the visual plot
- Check Info window for technical details (if enabled)
- Start with Just Intonation (1) for basic interval hearing
- Use Missing Fundamental (7) to demonstrate perceptual completion
- Binaural Beats (8) require headphones for proper effect
- Shepard Tone (10) creates compelling auditory illusions
- Compare AM vs FM (14) to hear modulation differences
- Enable info window for detailed explanations during lectures
Phenomena Guide
1. Just Intonation (Perfect Fifth)
🎵 Pure 3:2 Ratio
What you hear: Two pure sine waves at a perfect fifth interval (3:2 frequency ratio)
Key concept: Consonance from simple integer ratios
Frequency ratio: f2 = f1 × 3/2
Educational use: Introduction to tuning systems, consonance perception
2. Pythagorean Comma
📐 Tuning System Imperfection
What you hear: The small discrepancy between 12 perfect fifths and 7 octaves
Key concept: (3/2)¹² ≈ 129.746, 2⁷ = 128 → difference = ~23.5 cents
Educational use: Why equal temperament exists, historical tuning challenges
3. Syntonic Comma
🎼 Just vs Pythagorean Major Third
What you hear: Difference between pure 5:4 major third and Pythagorean 81:64 third
Key concept: 81/80 = 1.0125 ≈ 21.5 cents
Educational use: Meantone temperament, historical tuning compromises
4. The Wolf Fifth
🐺 Impure Temperament Interval
What you hear: A "howling" fifth with audible beats
Key concept: Imperfect fifth created by temperament compromises
Educational use: Temperament limitations, historical keyboard tuning
5. Critical Bands (Roughness)
🔊 Maximum Dissonance
What you hear: Two tones 25Hz apart creating maximum roughness
Key concept: Critical bandwidth ≈ 25Hz at low frequencies
Educational use: Dissonance perception, auditory masking
6. Tartini Tones (Difference Tone)
🎻 Perceptual Combination
What you hear: 440Hz + 660Hz, but perceive 220Hz difference tone
Key concept: f_diff = |f2 - f1| (nonlinear ear distortion)
Educational use: Auditory nonlinearity, combination tones in music
7. Missing Fundamental (Phantom Pitch)
👻 Perceptual Completion
What you hear: Harmonics 660, 880, 1100Hz (no 220Hz), but perceive 220Hz
Key concept: Brain reconstructs fundamental from harmonic series
Educational use: Pitch perception, telephone bandwidth, small speakers
8. Binaural Beats
🎧 Stereo Brain Effect
What you hear: Different frequencies in each ear create phantom "beat"
Key concept: f_beat = |f_right - f_left|, requires headphones
Educational use: Brain processing of spatial hearing, meditation apps
9. Fourier Square Wave
📈 Additive Synthesis
What you hear: Square wave approximated by odd harmonics
Key concept: Square = Σ[sin(nωt)/n] for odd n
Educational use: Fourier series, harmonic synthesis, timbre creation
10. Shepard Tone (Infinite Ascent)
♾️ Auditory Illusion
What you hear: Pitch seems to rise forever without getting higher
Key concept: Multiple octaves fading in/out create endless motion
Educational use: Auditory illusions, perceptual relativity, film scoring
11. Harmonic Series
🎹 Natural Overtone Series
What you hear: Complete harmonic series f, 2f, 3f, 4f...
Key concept: Natural resonance pattern, amplitude ~ 1/n
Educational use: Acoustics of instruments, timbre theory, spectral analysis
12. Combination Tones
🔀 Sum and Difference
What you hear: 400Hz + 600Hz generates perceived 200Hz difference tone
Key concept: Nonlinear distortion creates f2±f1 combinations
Educational use: Ear physiology, pipe organ tuning issues
13. Formant Synthesis (Vowels)
🗣️ Vowel /a/ Synthesis
What you hear: Vowel-like sound created by formant filtering
Key concept: Formants = spectral peaks defining vowel quality
Educational use: Speech acoustics, vocal tract modeling, synthesis
14. AM vs FM Modulation
📻 Tremolo vs Vibrato
What you hear: AM = volume fluctuation, FM = pitch fluctuation
Key concept: AM: A(t) varies, FM: φ(t) varies
Educational use: Radio technology, synthesis techniques, musical effects
15. Phase Cancellation
⚡ Destructive Interference
What you hear: Two identical waves 180° out of phase cancel to silence
Key concept: sin(ωt) + sin(ωt+π) = 0
Educational use: Wave interference, noise-cancelling headphones, acoustics
Parameters
Playback Controls
| Parameter | Default | Range | Description |
|---|---|---|---|
| Duration (s) | 2.0 | 0.5-10.0 | Length of demonstration |
| Base Frequency (Hz) | 220 | 50-1000 | Reference frequency for demonstrations |
| Amplitude (0-1) | 0.5 | 0.1-1.0 | Loudness control |
Options
| Parameter | Default | Description |
|---|---|---|
| Show info window | ✓ enabled | Display technical details in Info window |
| Save sounds to list | ✗ disabled | Keep generated sounds in Objects window |
- Duration: 2-3 seconds for quick demos, 5+ for detailed listening
- Base frequency: 220Hz (A3) works for most demos
- Amplitude: 0.5-0.7 for comfortable listening
- Info window: Always enable for teaching sessions
- Save sounds: Enable for student exploration or analysis
Teaching Applications
🏫 Classroom Integration
Music Theory Courses:
- Tuning systems: Demos 1-4 show historical tuning challenges
- Interval quality: Compare just vs equal temperament intervals
- Harmonic analysis: Demo 11 shows harmonic series in action
Acoustics/Physics Courses:
- Wave interference: Demo 15 shows destructive interference
- Fourier analysis: Demo 9 demonstrates harmonic composition
- Modulation: Demo 14 compares AM and FM effects
Psychology/Neuroscience:
- Auditory illusions: Demos 7, 10 show perceptual completion
- Binaural processing: Demo 8 requires stereo headphones
- Perceptual limits: Demo 5 shows critical band roughness
Lesson Plan Ideas
- Introduction (5 min): What is sound? Frequency, amplitude, phase
- Simple intervals (10 min): Demo 1 - Just intonation fifth
- Tuning problems (10 min): Demos 2-3 - Pythagorean and syntonic commas
- Perceptual effects (15 min): Demos 5-6 - Roughness and combination tones
- Auditory illusions (10 min): Demos 7, 10 - Missing fundamental, Shepard tone
- Synthesis (10 min): Demo 9 - Fourier square wave synthesis
- Parameter exploration: Change base frequency and describe perceptual changes
- Comparative listening: Compare just vs equal temperament intervals
- Illusion testing: Test Shepard tone on different listeners
- Frequency measurement: Use Praat to measure beat frequencies
- Creative synthesis: Modify formulas to create new timbres