# Beat-Based Timing System

## Overview

The demo uses **beat-based timing** for visual effect sequences, ensuring musical synchronization regardless of BPM changes. All timeline sequences are authored in beats (musical time) and converted to physical seconds at runtime.

**Key Principle:** Variable tempo only affects audio sample triggering. Visual effects run at constant physical time with optional beat-synchronized animation.

---

## Quick Start

### Timeline Authoring
```seq
# BPM 120
SEQUENCE 0 0 "Intro"         # Beat 0 (bar 1)
  EFFECT + Flash 0 2         # Beats 0-2 (half bar)
  EFFECT + Fade 4 8          # Beats 4-8 (full bar)

SEQUENCE 16 1 "Drop"         # Beat 16 (bar 5)
  EFFECT + Heptagon 0 16     # 4 bars
```

**Conversion:** At 120 BPM, 1 beat = 0.5 seconds, 4 beats = 2 seconds

### Shader Animation
```wgsl
@group(0) @binding(2) var<uniform> uniforms: CommonUniforms;

// Use beat_time for musical animation
let bar_cycle = uniforms.beat_time / 4.0;  // Bars
let pulse = sin(bar_cycle * TAU);

// Use beat_phase for smooth per-beat effects
let wave = sin(uniforms.beat_phase * TAU);

// Use time for constant-speed physics
let rotation = uniforms.time * TAU;
```

---

## Uniform Structure

All effects receive `CommonPostProcessUniforms` with timing data:

```cpp
struct CommonPostProcessUniforms {
  vec2 resolution;        // Screen dimensions (pixels)
  float aspect_ratio;     // Width/height ratio
  float time;             // Physical seconds (constant, unaffected by tempo)
  float beat_time;        // Absolute beats (musical time from audio clock)
  float beat_phase;       // Fractional beat 0.0-1.0 (smooth oscillation)
  float audio_intensity;  // Audio peak for beat sync
  float _pad;            // Alignment padding
};  // 32 bytes
```

**Use Cases:**
- `time`: Physics animation, constant-speed rotation/movement
- `beat_time`: Bar-based patterns, musical synchronization
- `beat_phase`: Smooth per-beat pulse/wave effects

---

## Timeline Format

### Time Notation

**Default:** Beats (no suffix)
```seq
SEQUENCE 0 0      # Beat 0
  EFFECT + Flash 0 4    # Beats 0-4
```

**Explicit Seconds:** Use `s` suffix (rare)
```seq
SEQUENCE 2.5s 0   # 2.5 physical seconds
  EFFECT + Flash 0 4    # Still uses beats for duration
```

**Explicit Beats:** Use `b` suffix (optional clarity)
```seq
SEQUENCE 8b 0     # Same as "8"
  EFFECT + Flash 0b 4b  # Same as "0 4"
```

### BPM Declaration

**Required** in all timeline files:
```seq
# BPM 120
```

Specifies beats per minute for runtime conversion to seconds.

---

## Architecture

### Timing Flow

```
Platform Clock (physical seconds)
    │
    ├──► Physical Time ────────┐
    │    (constant)             │
    │                           │
    └──► Audio Time ────┐       │
         (playback)     │       │
                        ▼       │
                 Beat Calculation    │
                 (BPM * 60)          │
                        │            │
                        ▼            ▼
                   Visual Effects Rendering
                   (time + beat_time + beat_phase)
```

### Key Insight

**Variable tempo changes `music_time`** (used for audio event triggering), but **visual effects receive `time` (physical)** and **`beat_time` (from audio playback clock)**, not from tempo-scaled music time.

This separation ensures:
- ✅ Visual effects run at constant frame rate
- ✅ Beat-synced animations track actual audio playback
- ✅ Tempo changes don't cause visual stuttering

---

## Implementation

### Beat Calculation (Runtime)

```cpp
// main.cc - Calculate from audio playback time
const float absolute_beat_time = current_audio_time * g_tracker_score.bpm / 60.0f;
const float beat_phase = fmodf(absolute_beat_time, 1.0f);

// Pass to GPU rendering
gpu_draw(visual_peak, aspect_ratio, physical_time, absolute_beat_time, beat_phase);
```

### Timeline Compilation

```cpp
// seq_compiler.cc - Convert beats to seconds at compile time
std::string convert_to_time(const std::string& value, float bpm) {
  if (value.back() == 's') return explicit_seconds;  // Pass through

  // Default: treat as beats
  float beat = std::stof(value);
  float time = beat * 60.0f / bpm;
  return time;
}
```

**Result:** Generated `timeline.cc` contains physical seconds for effect activation.

---

## Migration

### Existing Timelines

Already migrated with explicit `s` suffix to preserve timing:
```seq
SEQUENCE 2.50s 0          # Physical seconds preserved
  EFFECT + Flash 0.00s 1.00s
```

### New Content

Use beat notation (recommended):
```seq
# BPM 140
SEQUENCE 0 0 "Intro"
  EFFECT + Flash 0 4      # 4 beats = 1.71s @ 140 BPM
  EFFECT + Fade 4 8       # 4 beats = 1.71s
```

**Benefits:**
- Natural musical alignment (bars/beats)
- BPM changes don't break timing
- Easier to author to music

---

## Examples

### Four-Bar Pattern
```seq
# BPM 120
SEQUENCE 0 0 "Verse 1"
  EFFECT - Background 0 16    # 4 bars background
  EFFECT + Flash 0 1          # First beat flash
  EFFECT + Pulse 4 5          # Second bar pulse
  EFFECT + Fade 15 16         # Final beat fade
```

### Multi-Bar Sequence
```seq
SEQUENCE 16 0 "Chorus"        # Bar 5
  EFFECT + Heptagon 0 32      # 8 bars (full chorus)
  EFFECT + Particles 8 24     # Bars 7-11 (middle)
```

### Beat-Synced Shader
```wgsl
fn fragment_main(@location(0) uv: vec2<f32>) -> @location(0) vec4<f32> {
  // Pulse every bar (4 beats)
  let bar_phase = fract(uniforms.beat_time / 4.0);
  let bar_pulse = smoothstep(0.0, 0.1, bar_phase) *
                  (1.0 - smoothstep(0.9, 1.0, bar_phase));

  // Smooth per-beat wave
  let beat_wave = sin(uniforms.beat_phase * TAU);

  // Combine
  let intensity = bar_pulse * 0.5 + beat_wave * 0.3;
  return vec4<f32>(color * intensity, 1.0);
}
```

---

## Troubleshooting

### Shader Compilation Error: "invalid accessor 'beat'"

**Cause:** Old shader using `uniforms.beat` (deprecated field)

**Fix:** Use `uniforms.beat_phase` or `uniforms.beat_time`

```wgsl
// OLD (error):
let x = uniforms.beat;

// NEW:
let x = uniforms.beat_phase;  // For 0-1 fractional
let y = uniforms.beat_time;   // For absolute beats
```

### Timeline Parse Error

**Cause:** Missing BPM declaration

**Fix:** Add BPM at top of file
```seq
# BPM 120    ← Required
SEQUENCE 0 0
```

### Effects Start at Wrong Time

**Cause:** Mixing beats and seconds without explicit suffixes

**Fix:** Be explicit
```seq
SEQUENCE 8 0      # 8 beats (not 8 seconds)
SEQUENCE 8s 0     # 8 seconds (explicit)
SEQUENCE 8b 0     # 8 beats (explicit, same as first)
```

---

## See Also

- **Format Reference:** `doc/SEQUENCE.md` - Complete .seq syntax
- **Implementation:** `BEAT_TIMING_SUMMARY.md` - Technical details
- **Effect Creation:** `doc/EFFECT_WORKFLOW.md` - Adding new effects
- **Timeline Editor:** `tools/timeline_editor/README.md` - Visual editing