Tempo-Pitch Curves (Accelerando & Ritardando) — User Guide
Advanced tempo manipulation: applies musical tempo curves (accelerando, ritardando, slow-fast-slow) with flexible pitch behavior using PSOLA resynthesis.
What this does
This script implements musical tempo curve manipulation — applying expressive tempo variations like accelerando (gradual speeding up) and ritardando (gradual slowing down) to audio using PSOLA (Pitch-Synchronous Overlap-Add) resynthesis. The tool provides two distinct processing modes: one that simulates tape-speed effects (pitch changes with tempo) and another that maintains constant pitch while altering duration only.
Key Features:
- Three Tempo Patterns — Accelerando, ritardando, and slow-fast-slow
- Dual Processing Modes — Pitch-changing vs pitch-preserving
- Adjustable Strength — Control intensity of tempo variations
- Flexible Duration Control — Preserve original duration or specify new duration
- PSOLA Resynthesis — High-quality time-stretching and pitch-shifting
- Real-time Preview — Optional automatic playback of results
What are tempo curves in audio processing? Traditional tempo changes: uniform time-stretching, simple speed changes. Advanced tempo curves: Smooth, musical acceleration/deceleration patterns that mimic human performance. Advantages: (1) Musical expressivity: Creates natural-sounding tempo variations. (2) Dual behavior options: Choose between tape-speed effect (pitch changes) or modern time-stretching (pitch constant). (3) Precise control: Adjustable strength and duration parameters. (4) High quality: PSOLA preserves audio quality better than simple resampling. (5) Creative possibilities: Enables effects impossible with analog tape. Use cases: Music production (adding expressivity to rigid performances), film scoring (matching music to visual pacing), sound design (creating tension/release), musicology (studying performance practice), audio restoration (correcting timing issues).
Technical Implementation: (1) PSOLA Analysis: Converts sound to Manipulation object with pitch and pulse markers. (2) Tempo Curve Generation: Creates DurationTier with 31 control points defining tempo pattern. (3) Mode A (Pitch Changes): Applies average pitch shift to simulate tape-speed effect while maintaining formant structure. (4) Mode B (Pitch Constant): Uses PSOLA duration manipulation only, preserving original pitch. (5) Duration Normalization: Optional adjustment to maintain original duration or achieve target duration. (6) Resynthesis: Overlap-add synthesis from modified Manipulation object. (7) Quality Control: Peak normalization and safe parameter limits ensure usable results.
Quick start
- In Praat, select exactly one Sound object.
- Run script… →
tempo_pitch_curves.praat. - Choose Pattern_type: Accelerando, ritardando, or slow-fast-slow.
- Select Pitch_behavior: Pitch changes (tape-speed) or keep pitch constant.
- Set Strength (1 = mild, 2 = medium, 3 = strong).
- Choose Duration_mode: Keep original or specify new duration.
- If specifying duration, enter Target_duration in seconds.
- Enable Play_result_when_finished for immediate preview.
- Click OK — processed sound appears as "originalname_pattern".
Quick tip: Start with Strength = 2.0 for noticeable but natural effects. Use Pitch changes with tempo for vintage tape-recorder effects or musical realism. Use Keep pitch constant for modern time-stretching applications. For speech, try ritardando with pitch constant for dramatic emphasis. For music, try accelerando with pitch changes for excitement buildup. Enable Play_result_when_finished to immediately hear the effect. The script automatically handles stereo-to-mono conversion and maintains audio quality through PSOLA resynthesis.
Important: PSOLA LIMITATIONS — PSOLA works best on monophonic sources with clear pitch (voice, solo instruments). Polyphonic music or noisy signals may produce artifacts. Extreme tempo factors (>3× speedup or <0.3× slowdown) can cause quality degradation. Pitch-changing mode affects formant frequencies — very strong effects may create "chipmunk" or "demon" voices. Duration normalization uses additional processing that may slightly affect quality. Original selection is preserved — new Sound object created with "_pattern" suffix. Processing time increases with audio length and complexity.
Tempo Patterns
Pattern 1: Accelerando (slow → fast)
🎵 Gradual Acceleration
Mathematical definition: Linear increase from minTempoFactor to maxTempoFactor
Musical effect: Building excitement, forward momentum, urgency
Best for: Climactic sections, action sequences, energetic passages
Tempo curve calculation:
For 31 control points (i = 0 to 30):
t = i × originalDuration / 30
x = i / 30 (normalized position 0→1)
Tempo factor at point x:
tempoFactor = minTempoFactor + (maxTempoFactor - minTempoFactor) × x
Duration factor (inverse):
durationFactor = 1.0 / tempoFactor
Strength scaling:
minTempoFactor = 1.0 - (0.25 × strength)
maxTempoFactor = 1.0 + (0.35 × strength)
Example (strength=2.0):
Start: tempoFactor = 0.5, durationFactor = 2.0
Middle: tempoFactor = 1.175, durationFactor = 0.85
End: tempoFactor = 1.7, durationFactor = 0.59
Pattern 2: Ritardando (fast → slow)
🎵 Gradual Deceleration
Mathematical definition: Linear decrease from maxTempoFactor to minTempoFactor
Musical effect: Relaxation, conclusion, finality, calmness
Best for: Endings, reflective passages, emotional resolution
Tempo curve calculation:
For 31 control points (i = 0 to 30):
t = i × originalDuration / 30
x = i / 30 (normalized position 0→1)
Tempo factor at point x:
tempoFactor = maxTempoFactor - (maxTempoFactor - minTempoFactor) × x
Duration factor (inverse):
durationFactor = 1.0 / tempoFactor
Strength scaling (same as accelerando):
minTempoFactor = 1.0 - (0.25 × strength)
maxTempoFactor = 1.0 + (0.35 × strength)
Example (strength=2.0):
Start: tempoFactor = 1.7, durationFactor = 0.59
Middle: tempoFactor = 1.175, durationFactor = 0.85
End: tempoFactor = 0.5, durationFactor = 2.0
Pattern 3: Slow-Fast-Slow
🎵 Arch Form
Mathematical definition: Quadratic curve with peak at center
Musical effect: Symmetric tension and release, balanced form
Best for: Musical phrases, poetic readings, dramatic arcs
Tempo curve calculation:
For 31 control points (i = 0 to 30):
t = i × originalDuration / 30
x = i / 30 (normalized position 0→1)
Centered coordinate:
centered = (x - 0.5) × 2 (range -1 to +1)
Tempo factor at point x:
tempoFactor = minTempoFactor + (maxTempoFactor - minTempoFactor) × (1 - centered²)
Duration factor (inverse):
durationFactor = 1.0 / tempoFactor
Strength scaling (same):
minTempoFactor = 1.0 - (0.25 × strength)
maxTempoFactor = 1.0 + (0.35 × strength)
Example (strength=2.0):
Start: tempoFactor = 0.5, durationFactor = 2.0
Middle: tempoFactor = 1.7, durationFactor = 0.59
End: tempoFactor = 0.5, durationFactor = 2.0
Strength Parameter Effects
| Strength | minTempoFactor | maxTempoFactor | Effect Character |
|---|---|---|---|
| 0.5 | 0.875 | 1.175 | Very subtle, barely noticeable |
| 1.0 | 0.75 | 1.35 | Gentle, natural expression |
| 2.0 | 0.5 | 1.7 | Clear, musical, recommended |
| 3.0 | 0.25 | 2.05 | Strong, dramatic effect |
| 4.0 | 0.0 → 0.4* | 2.4 → 3.0* | Extreme, potentially artificial |
| 5.0 | 0.0 → 0.4* | 2.75 → 3.0* | Maximum, use with caution |
*Script clamps factors to safe range 0.4-3.0
Processing Modes
Mode A: Pitch Changes with Tempo (Tape-Speed Effect)
⏩ Analog Tape Simulation
Behavior: Pitch rises with acceleration, falls with deceleration
Technical approach: PSOLA + average pitch shift
Sound character: Vintage, musical, physically realistic
Implementation details:
STEP 1: PSOLA analysis
workingSound → To Manipulation (0.01s, 75-600Hz)
Extract PitchTier and create DurationTier
STEP 2: Apply tempo curve to DurationTier
31 points with calculated duration factors
STEP 3: Calculate average pitch shift
avgTempoFactor = (minTempoFactor + maxTempoFactor) / 2
Apply to PitchTier: pitch = original_pitch × avgTempoFactor
STEP 4: Duration normalization (if keeping original duration)
Calculate mean duration factor across curve
Scale all points by inverse of mean factor
STEP 5: Resynthesis
Replace both tiers in Manipulation
Get resynthesis (overlap-add)
STEP 6: Final duration adjustment (if specified)
Use Change gender with formant scaling
Why Average Pitch Shift?
Technical rationale:
Alternative approaches considered:
1. No pitch change: Wouldn't simulate tape effect
2. Continuous pitch curve: Too complex, potential artifacts
3. Average shift: Good compromise, preserves formant ratios
Formant preservation:
Original formant frequencies: F1, F2, F3...
After average shift: F1×avg, F2×avg, F3×avg...
Formant ratios maintained: (F2/F1), (F3/F1) unchanged
Result: Natural-sounding pitch change
Unlike simple resampling that preserves formants absolutely
Creates more musical, less "chipmunk" effect
Mode B: Keep Pitch Constant (Modern Time-Stretching)
⏱️ Pure Tempo Manipulation
Behavior: Pitch remains unchanged throughout tempo variations
Technical approach: PSOLA duration manipulation only
Sound character: Modern, clean, "impossible" effect
Implementation details:
STEP 1: PSOLA analysis
workingSound → To Manipulation (0.01s, 75-600Hz)
Create DurationTier only (keep original PitchTier)
STEP 2: Apply tempo curve to DurationTier
31 points with calculated duration factors
STEP 3: Duration normalization (if keeping original duration)
Calculate mean duration factor across curve
Scale all points by inverse of mean factor
STEP 4: Resynthesis
Replace DurationTier in Manipulation
Get resynthesis (overlap-add)
STEP 5: Final duration adjustment (if specified)
Use Change gender with formant scaling
Key difference: Original PitchTier preserved unchanged
No pitch multiplication applied
Pure duration manipulation
Duration Control Options
Option 1: Keep Original Duration
Normalization algorithm:
Calculation:
sumFactors = 0
FOR each of 31 points:
Calculate durationFactor for that point
sumFactors = sumFactors + durationFactor
END FOR
meanFactor = sumFactors / 31
Normalization:
FOR each of 31 points:
normalizedFactor = originalFactor / meanFactor
Update DurationTier point
END FOR
Effect:
Integrated duration change = 1.0
Result duration ≈ original duration
Tempo pattern shape preserved, overall scale adjusted
Option 2: Specify New Duration
Two-stage adjustment:
Stage 1: PSOLA with tempo curve
Apply tempo pattern without duration normalization
Result: duration determined by integral of tempo curve
Stage 2: Uniform scaling if needed
actualDuration = Get total duration
IF |actualDuration - targetDuration| > 0.01
scaleFactor = targetDuration / actualDuration
Change gender: 75, 600, 1.0, 0, scaleFactor, 1.0
Parameters for Change gender:
pitch floor: 75 Hz
pitch ceiling: 600 Hz
formant scale ratio: 1.0 (preserve formants)
pitch scale ratio: 1.0 (preserve pitch)
duration scale factor: scaleFactor
normalize amplitude: yes
Result: Target duration achieved with minimal quality loss
Mode Comparison
| Aspect | Mode A (Pitch Changes) | Mode B (Pitch Constant) |
|---|---|---|
| Sound character | Vintage, tape-like | Modern, clean |
| Musical realism | High (like real performance) | Low (impossible effect) |
| Formant behavior | Scaled with pitch | Preserved exactly |
| Best for music | Expressive performance | Technical applications |
| Best for speech | Dramatic reading | Timing correction |
| Artifact risk | Medium (pitch shift) | Low (pure PSOLA) |
| Processing time | Slightly longer | Standard |
PSOLA Technology
What is PSOLA?
Pitch-Synchronous Overlap-Add synthesis:
PSOLA = Analysis + Modification + Resynthesis
Analysis phase:
1. Detect fundamental frequency (pitch)
2. Identify pitch pulses (glottal closures)
3. Extract short segments around each pulse
Modification phase:
1. Adjust timing of pulses (duration changes)
2. Adjust pulse spacing (pitch changes)
3. Apply overlap-add with new timing
Resynthesis phase:
1. Overlap and add modified segments
2. Apply smoothing at segment boundaries
3. Output modified signal
Advantages over simple resampling:
- Preserves formant structure
- Handles pitch and duration separately
- Higher quality for vocal sounds
- Natural-sounding modifications
PSOLA in Praat
Manipulation Objects
Praat's implementation:
Conversion to Manipulation:
sound → To Manipulation: timeStep, pitchFloor, pitchCeiling
Contains:
- Original sound
- PitchTier (continuous pitch contour)
- DurationTier (time scaling factors)
- PulseTier (analysis markers)
Key parameters:
timeStep = 0.01 (10 ms analysis frames)
pitchFloor = 75 Hz (minimum expected F0)
pitchCeiling = 600 Hz (maximum expected F0)
Resynthesis options:
Overlap-add (higher quality)
Pitch-synchronous (faster)
This script uses overlap-add for best quality
DurationTier Manipulation
How DurationTier affects timing:
DurationTier defines local time scaling:
Points: (time, durationFactor)
durationFactor > 1.0: time stretches (slower)
durationFactor < 1.0: time compresses (faster)
Interpolation between points:
Linear interpolation between specified points
Default factor = 1.0 between defined regions
Example with 3 points:
(0.0, 2.0) - first second stretched to 2 seconds
(1.0, 0.5) - next section compressed to half time
(2.0, 1.0) -恢复正常速度
This script uses 31 points for smooth curves
Quality Considerations
Safe Parameter Ranges
Script-enforced limits:
Strength clipping:
IF strength < 0.5: strength = 0.5
IF strength > 5: strength = 5
Tempo factor limits:
IF durationFactor < 0.3: durationFactor = 0.3
IF durationFactor > 3.0: durationFactor = 3.0
Rationale:
<0.3×: Extreme stretching causes artifacts
>3.0×: Extreme compression loses information
0.3-3.0×: PSOLA works reasonably well
Target duration validation:
IF targetDuration ≤ 0.01: exit with error
Prevents impossible processing requests
Mono Conversion
Stereo handling:
IF numberOfChannels > 1:
workingSound = Convert to mono
ELSE:
workingSound = Copy: soundName$ + "_working"
Why convert to mono?
- PSOLA designed for monophonic signals
- Stereo processing would require channel separation
- Most applications involve mono sources (voice)
- Preserves original stereo sound unchanged
Processing chain:
Original (possibly stereo) → Working (mono) → PSOLA → Result (mono)
Original remains available for comparison
Advanced Technical Details
📊 Duration Normalization Mathematics
Continuous integral approach:
Theoretical basis:
Total duration = ∫₀ᵀ durationFactor(t) dt
Discrete approximation:
totalDuration ≈ Σᵢ durationFactor(tᵢ) × Δtᵢ
Normalization:
Let meanFactor = (1/T) × ∫₀ᵀ durationFactor(t) dt
Normalized curve: durationFactor_normalized(t) = durationFactor(t) / meanFactor
Then: ∫₀ᵀ durationFactor_normalized(t) dt = T
Implementation:
31-point Riemann sum approximation
Linear interpolation between points
Preserves curve shape while fixing total duration
Pitch Shift Formant Behavior:
In Mode A (pitch changes):
Original formants: F₁, F₂, F₃, ...
After pitch shift: αF₁, αF₂, αF₃, ...
Where α = avgTempoFactor
Formant ratios preserved:
F₂/F₁ → (αF₂)/(αF₁) = F₂/F₁
F₃/F₁ → (αF₃)/(αF₁) = F₃/F₁
Unlike simple resampling:
Resampling: F₁, F₂, F₃ preserved absolutely
PSOLA+pitch: F₁, F₂, F₃ scaled equally
Result: More natural vocal character
Applications
Music Production
Use case: Adding expressivity to quantized performances
Technique: Apply ritardando at phrase endings, accelerando for buildups
Settings: Pitch changes with tempo, strength 1.5-2.5, keep original duration
Film and Media Scoring
Use case: Synchronizing music with visual pacing
Technique: Use slow-fast-slow pattern for scene transitions
Settings: Pitch constant, specify target duration to match scene length
Voice Acting and Drama
Use case: Enhancing dramatic readings and storytelling
Technique: Accelerando for excitement, ritardando for emphasis
Settings: Pitch changes for vintage radio effect, strength 2.0-3.0
Audio Restoration
Use case: Correcting inconsistent tempo in old recordings
Technique: Apply inverse tempo patterns to stabilize timing
Settings: Pitch constant, mild strength (0.8-1.2)
Sound Design
Use case: Creating tension and release effects
Technique: Extreme accelerando/ritardando on sound effects
Settings: Experiment with both modes, high strength values
Practical Workflow Examples
🎹 Piano Phrase Expression
Goal: Add musical rubato to mechanical piano recording
Settings:
- Pattern: Slow-fast-slow
- Pitch behavior: Pitch changes with tempo
- Strength: 2.0
- Duration: Keep original
Result: Natural-sounding phrase shaping with authentic pitch variations
🎬 Film Scene Sync
Goal: Match music duration to specific scene length
Settings:
- Pattern: Ritardando
- Pitch behavior: Keep pitch constant
- Strength: 1.5
- Duration: Specify target duration
Result: Music naturally slows to fill required time without pitch artifacts
🎭 Dramatic Monologue
Goal: Enhance emotional impact of spoken word
Settings:
- Pattern: Accelerando → ritardando (run twice)
- Pitch behavior: Pitch changes with tempo
- Strength: 2.5
- Duration: Keep original
Result: Vintage radio drama effect with heightened expressivity
Creative Techniques
Layered processing:
- Multiple passes: Apply different patterns sequentially
- Sectional treatment: Process different song sections separately
- Extreme effects: Use maximum strength for special effects
- Combination with other effects: Add reverb, EQ after tempo processing
- Experimental patterns: Manual editing of DurationTier for custom curves
Quality optimization:
- Source quality: Start with clean, well-recorded audio
- Appropriate parameters: Match pitch range to source material
- Progressive adjustment: Make small changes and preview frequently
- Alternative approaches: For problematic sources, try different pitch floor/ceiling
- Final touch: Always use peak normalization (already included)
Troubleshooting Common Issues
Problem: Artifacts or glitches in output
Cause: PSOLA analysis errors, extreme parameters, or noisy source
Solution: Reduce strength, try different pitch floor/ceiling, use cleaner source
Cause: PSOLA analysis errors, extreme parameters, or noisy source
Solution: Reduce strength, try different pitch floor/ceiling, use cleaner source
Problem: Output duration not as expected
Cause: Complex tempo curve integration, normalization issues
Solution: Check duration mode setting, use specified duration for exact control
Cause: Complex tempo curve integration, normalization issues
Solution: Check duration mode setting, use specified duration for exact control
Problem: Unnatural "chipmunk" or "robot" effect
Cause: Extreme pitch shifting or formant distortion
Solution: Use pitch constant mode, reduce strength, try different source material
Cause: Extreme pitch shifting or formant distortion
Solution: Use pitch constant mode, reduce strength, try different source material
Problem: Processing very slow
Cause: Long audio files, complex PSOLA analysis
Solution: Process shorter segments, use faster computer, be patient for long files
Cause: Long audio files, complex PSOLA analysis
Solution: Process shorter segments, use faster computer, be patient for long files
Technical Reference
Complete Parameter Reference
| Parameter | Type | Default | Description |
|---|---|---|---|
| Pattern_type | optionmenu | 1 | Tempo variation pattern |
| Pitch_behavior | optionmenu | 1 | Pitch change behavior |
| Strength | real | 2.0 | Intensity of tempo variation |
| Duration_mode | optionmenu | 1 | Duration control method |
| Target_duration | real | 5.0 | Desired output duration (seconds) |
| Play_result_when_finished | boolean | 1 | Auto-play after processing |
Output Naming Convention
Automatic output naming:
Input: "mysound"
Pattern 1 + Mode A: "mysound_accel_pitched"
Pattern 1 + Mode B: "mysound_accel_PSOLA"
Pattern 2 + Mode A: "mysound_ritard_pitched"
Pattern 2 + Mode B: "mysound_ritard_PSOLA"
Pattern 3 + Mode A: "mysound_slowFastSlow_pitched"
Pattern 3 + Mode B: "mysound_slowFastSlow_PSOLA"
Purpose:
- Clear identification of processing type
- Easy comparison between different settings
- Prevents overwriting original
- Systematic and predictable
Performance Characteristics
Processing Time Factors
Major time consumers:
1. PSOLA analysis: O(n) with audio length
- Pitch tracking complexity
- Pulse detection
2. DurationTier manipulation: O(1) constant
- 31 points regardless of length
3. Resynthesis: O(n) with audio length
- Overlap-add algorithm
4. Final scaling (if needed): O(n) with audio length
- Change gender processing
Typical performance:
1-minute audio: 10-20 seconds
5-minute audio: 1-2 minutes
30-minute audio: 5-10 minutes
Mode A slightly slower due to pitch tier processing
Memory Usage
Storage requirements:
Major objects:
Original sound: n samples × channels
Working sound: n samples (mono)
Manipulation: ~3× original size
PitchTier: 31 points × 8 bytes
DurationTier: 31 points × 8 bytes
Result sound: m samples (variable duration)
Peak memory ≈ 4-5× original audio size
Typical usage:
1-minute mono 44.1kHz: ~10 MB original → ~50 MB peak
5-minute mono 44.1kHz: ~50 MB original → ~250 MB peak
Efficient for most practical applications