feat(mq_editor): Complete Phase 2 - JS synthesizer with STFT cache

Phase 2 - JS Synthesizer:
- Created mq_synth.js with replica oscillator bank
- Bezier curve evaluation (cubic De Casteljau algorithm)
- Replica synthesis: frequency spread, amplitude decay, phase jitter
- PCM buffer generation from extracted MQ partials
- Normalization to prevent clipping
- Key '1' plays synthesized audio, key '2' plays original
- Playback comparison with animated playhead

STFT Cache Optimization:
- Created STFTCache class in fft.js for pre-computed windowed FFT frames
- Clean interface: getFFT(t), getMagnitudeDB(t, freq), setHopSize()
- Pre-computes all frames on WAV load (eliminates redundant FFT calls)
- Dynamic cache update when hop size changes
- Shared across spectrogram, tooltip, and mini-spectrum viewer
- Significant performance improvement

Mini-Spectrum Viewer:
- Bottom-right overlay (200x100) matching spectral_editor style
- Real-time FFT display at playhead or mouse position
- 100-bar visualization with cyan-to-yellow gradient
- Updates during playback or mouse hover

Files:
- tools/mq_editor/mq_synth.js (new)
- tools/mq_editor/fft.js (STFTCache class added)
- tools/mq_editor/index.html (synthesis playback, cache integration)
- tools/mq_editor/viewer.js (cache-based rendering, spectrum viewer)

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

5 files changed, 354 insertions, 53 deletions

diff --git a/tools/mq_editor/README.md b/tools/mq_editor/README.md
index 35e414c..1f43c19 100644
--- a/tools/mq_editor/README.md
+++ b/tools/mq_editor/README.md
@@ -41,8 +41,14 @@ open tools/mq_editor/index.html
   - [x] Mouse tooltip (time/frequency/dB intensity)
   - [x] Improved partial tracking (frequency-dependent threshold, candidate system)
   - [x] Original WAV playback with animated playhead
-  - [x] Keyboard shortcuts ('2' for playback)
-- [ ] Phase 2: JS synthesizer (preview playback)
+  - [x] Keyboard shortcuts ('1' synthesized, '2' original)
+  - [x] Mini-spectrum viewer (bottom-right overlay)
+  - [x] STFT cache for optimized FFT access
+- [x] Phase 2: JS synthesizer (preview playback)
+  - [x] Bezier curve evaluation (cubic)
+  - [x] Replica oscillator bank with frequency spread and jitter
+  - [x] PCM synthesis from extracted partials
+  - [x] Playback via Web Audio API
 - [ ] Phase 3: Editing UI (drag control points, replicas)
 - [ ] Phase 4: Export (.txt + C++ code generation)
 
diff --git a/tools/mq_editor/fft.js b/tools/mq_editor/fft.js
index 8610222..0668906 100644
--- a/tools/mq_editor/fft.js
+++ b/tools/mq_editor/fft.js
@@ -101,3 +101,89 @@ function realFFT(signal) {
 
   return spectrum;
 }
+
+// STFT Cache - Pre-computes and caches windowed FFT frames
+class STFTCache {
+  constructor(signal, sampleRate, fftSize, hopSize) {
+    this.signal = signal;
+    this.sampleRate = sampleRate;
+    this.fftSize = fftSize;
+    this.hopSize = hopSize;
+    this.frames = []; // Array of {time, offset, spectrum}
+    this.compute();
+  }
+
+  compute() {
+    this.frames = [];
+    const numFrames = Math.floor((this.signal.length - this.fftSize) / this.hopSize);
+
+    for (let frameIdx = 0; frameIdx < numFrames; ++frameIdx) {
+      const offset = frameIdx * this.hopSize;
+      const time = offset / this.sampleRate;
+
+      // Extract frame
+      const frame = this.signal.slice(offset, offset + this.fftSize);
+
+      // Apply Hann window
+      const windowed = new Float32Array(this.fftSize);
+      for (let i = 0; i < this.fftSize; ++i) {
+        const w = 0.5 - 0.5 * Math.cos(2 * Math.PI * i / this.fftSize);
+        windowed[i] = frame[i] * w;
+      }
+
+      // Compute FFT
+      const spectrum = realFFT(windowed);
+
+      this.frames.push({time, offset, spectrum});
+    }
+  }
+
+  setHopSize(hopSize) {
+    if (hopSize === this.hopSize) return;
+    this.hopSize = hopSize;
+    this.compute();
+  }
+
+  setFFTSize(fftSize) {
+    if (fftSize === this.fftSize) return;
+    this.fftSize = fftSize;
+    this.compute();
+  }
+
+  getNumFrames() {
+    return this.frames.length;
+  }
+
+  getFrameAtIndex(frameIdx) {
+    if (frameIdx < 0 || frameIdx >= this.frames.length) return null;
+    return this.frames[frameIdx];
+  }
+
+  getFrameAtTime(t) {
+    if (this.frames.length === 0) return null;
+
+    // Find closest frame
+    const frameIdx = Math.floor(t * this.sampleRate / this.hopSize);
+    return this.getFrameAtIndex(frameIdx);
+  }
+
+  getFFT(t) {
+    const frame = this.getFrameAtTime(t);
+    return frame ? frame.spectrum : null;
+  }
+
+  // Get magnitude in dB at specific time and frequency
+  getMagnitudeDB(t, freq) {
+    const spectrum = this.getFFT(t);
+    if (!spectrum) return -80;
+
+    const bin = Math.round(freq * this.fftSize / this.sampleRate);
+    if (bin < 0 || bin >= this.fftSize / 2) return -80;
+
+    const re = spectrum[bin * 2];
+    const im = spectrum[bin * 2 + 1];
+    const mag = Math.sqrt(re * re + im * im);
+    return 20 * Math.log10(Math.max(mag, 1e-10));
+  }
+}
+
diff --git a/tools/mq_editor/index.html b/tools/mq_editor/index.html
index 1a07b61..84abd1c 100644
--- a/tools/mq_editor/index.html
+++ b/tools/mq_editor/index.html
@@ -86,7 +86,14 @@
     </div>
   </div>
 
-  <canvas id="canvas" width="1400" height="600"></canvas>
+  <div style="position: relative;">
+    <canvas id="canvas" width="1400" height="600"></canvas>
+
+    <!-- Mini spectrum viewer (bottom-right overlay) -->
+    <div id="spectrumViewer" style="position: absolute; bottom: 10px; right: 10px; width: 200px; height: 100px; background: rgba(30, 30, 30, 0.9); border: 1px solid #555; border-radius: 3px; pointer-events: none;">
+      <canvas id="spectrumCanvas" width="200" height="100"></canvas>
+    </div>
+  </div>
 
   <div id="tooltip" style="position: fixed; display: none; background: #2a2a2a; padding: 4px 8px; border: 1px solid #555; border-radius: 3px; pointer-events: none; font-size: 11px; z-index: 1000;"></div>
 
@@ -94,12 +101,15 @@
 
   <script src="fft.js"></script>
   <script src="mq_extract.js"></script>
+  <script src="mq_synth.js"></script>
   <script src="viewer.js"></script>
   <script>
     let audioBuffer = null;
     let viewer = null;
     let audioContext = null;
     let currentSource = null;
+    let extractedPartials = null;
+    let stftCache = null;
 
     const wavFile = document.getElementById('wavFile');
     const extractBtn = document.getElementById('extractBtn');
@@ -133,16 +143,36 @@
         initAudioContext();
         extractBtn.disabled = false;
         playBtn.disabled = false;
-        setStatus(`Loaded: ${audioBuffer.duration.toFixed(2)}s, ${audioBuffer.sampleRate}Hz, ${audioBuffer.numberOfChannels}ch`, 'info');
+        setStatus('Computing STFT cache...', 'info');
 
-        // Create viewer
-        viewer = new SpectrogramViewer(canvas, audioBuffer);
+        // Compute STFT cache
+        setTimeout(() => {
+          const signal = audioBuffer.getChannelData(0);
+          stftCache = new STFTCache(signal, audioBuffer.sampleRate, fftSize, parseInt(hopSize.value));
+
+          setStatus(`Loaded: ${audioBuffer.duration.toFixed(2)}s, ${audioBuffer.sampleRate}Hz, ${audioBuffer.numberOfChannels}ch (${stftCache.getNumFrames()} frames cached)`, 'info');
+
+          // Create viewer with cache
+          viewer = new SpectrogramViewer(canvas, audioBuffer, stftCache);
+        }, 10);
       } catch (err) {
         setStatus('Error loading WAV: ' + err.message, 'error');
         console.error(err);
       }
     });
 
+    // Update cache when hop size changes
+    hopSize.addEventListener('change', () => {
+      if (stftCache) {
+        setStatus('Updating STFT cache...', 'info');
+        setTimeout(() => {
+          stftCache.setHopSize(parseInt(hopSize.value));
+          setStatus(`Cache updated (${stftCache.getNumFrames()} frames)`, 'info');
+          if (viewer) viewer.render();
+        }, 10);
+      }
+    });
+
     // Extract partials
     extractBtn.addEventListener('click', () => {
       if (!audioBuffer) return;
@@ -161,6 +191,7 @@
 
           const partials = extractPartials(audioBuffer, params);
 
+          extractedPartials = partials;
           setStatus(`Extracted ${partials.length} partials`, 'info');
 
           // Update viewer
@@ -235,12 +266,60 @@
       status.className = type;
     }
 
+    // Play synthesized audio
+    function playSynthesized() {
+      if (!extractedPartials || extractedPartials.length === 0) {
+        setStatus('No partials extracted yet', 'warn');
+        return;
+      }
+      if (!audioBuffer || !audioContext) return;
+
+      stopAudio();
+
+      setStatus('Synthesizing...', 'info');
+
+      // Synthesize PCM from partials
+      const sampleRate = audioBuffer.sampleRate;
+      const duration = audioBuffer.duration;
+      const pcm = synthesizeMQ(extractedPartials, sampleRate, duration);
+
+      // Create audio buffer
+      const synthBuffer = audioContext.createBuffer(1, pcm.length, sampleRate);
+      synthBuffer.getChannelData(0).set(pcm);
+
+      const startTime = audioContext.currentTime;
+      currentSource = audioContext.createBufferSource();
+      currentSource.buffer = synthBuffer;
+      currentSource.connect(audioContext.destination);
+      currentSource.start();
+
+      currentSource.onended = () => {
+        currentSource = null;
+        playBtn.disabled = false;
+        stopBtn.disabled = true;
+        viewer.setPlayheadTime(-1);
+        setStatus('Stopped', 'info');
+      };
+
+      playBtn.disabled = true;
+      stopBtn.disabled = false;
+      setStatus('Playing synthesized...', 'info');
+
+      // Animate playhead
+      function updatePlayhead() {
+        if (!currentSource) return;
+        const elapsed = audioContext.currentTime - startTime;
+        viewer.setPlayheadTime(elapsed);
+        requestAnimationFrame(updatePlayhead);
+      }
+      updatePlayhead();
+    }
+
     // Keyboard shortcuts
     document.addEventListener('keydown', (e) => {
       if (e.code === 'Digit1') {
         e.preventDefault();
-        // TODO: Play synthesized (Phase 2)
-        setStatus('Synthesized playback not yet implemented', 'warn');
+        playSynthesized();
       } else if (e.code === 'Digit2') {
         e.preventDefault();
         if (!playBtn.disabled) {
diff --git a/tools/mq_editor/mq_synth.js b/tools/mq_editor/mq_synth.js
new file mode 100644
index 0000000..f1c7f73
--- /dev/null
+++ b/tools/mq_editor/mq_synth.js
@@ -0,0 +1,107 @@
+// MQ Synthesizer
+// Replica oscillator bank for sinusoidal synthesis
+
+// Evaluate cubic bezier curve at time t
+function evalBezier(curve, t) {
+  // Normalize t to [0, 1]
+  let u = (t - curve.t0) / (curve.t3 - curve.t0);
+  u = Math.max(0, Math.min(1, u));
+
+  // Cubic interpolation
+  const u1 = 1.0 - u;
+  return u1*u1*u1 * curve.v0 +
+         3*u1*u1*u * curve.v1 +
+         3*u1*u*u * curve.v2 +
+         u*u*u * curve.v3;
+}
+
+// Simple deterministic PRNG (for frequency spread and jitter)
+function randFloat(seed, min, max) {
+  // LCG parameters
+  const a = 1664525;
+  const c = 1013904223;
+  const m = 0x100000000; // 2^32
+
+  seed = (a * seed + c) % m;
+  const normalized = seed / m;
+  return min + normalized * (max - min);
+}
+
+// Synthesize audio from MQ partials
+// partials: array of {freqCurve, ampCurve, replicas: {offsets, decay_alpha, jitter, spread_above, spread_below}}
+// sampleRate: output sample rate (Hz)
+// duration: output duration (seconds)
+// Returns: Float32Array of PCM samples
+function synthesizeMQ(partials, sampleRate, duration) {
+  const numSamples = Math.floor(sampleRate * duration);
+  const pcm = new Float32Array(numSamples);
+
+  // Default replica config
+  const defaultReplicas = {
+    offsets: [1.0], // Just fundamental
+    decay_alpha: 0.1,
+    jitter: 0.05,
+    spread_above: 0.02,
+    spread_below: 0.02
+  };
+
+  for (let i = 0; i < numSamples; ++i) {
+    const t = i / sampleRate;
+    let sample = 0.0;
+
+    for (let p = 0; p < partials.length; ++p) {
+      const partial = partials[p];
+      const freqCurve = partial.freqCurve;
+      const ampCurve = partial.ampCurve;
+
+      // Skip if outside curve time range
+      if (t < freqCurve.t0 || t > freqCurve.t3) continue;
+
+      const f0 = evalBezier(freqCurve, t);
+      const A0 = evalBezier(ampCurve, t);
+
+      // Use default replicas if not specified
+      const replicas = partial.replicas || defaultReplicas;
+      const offsets = replicas.offsets || [1.0];
+      const decay_alpha = replicas.decay_alpha || 0.1;
+      const jitter = replicas.jitter || 0.05;
+      const spread_above = replicas.spread_above || 0.02;
+      const spread_below = replicas.spread_below || 0.02;
+
+      // For each replica offset
+      for (let r = 0; r < offsets.length; ++r) {
+        const ratio = offsets[r];
+
+        // Frequency spread (asymmetric randomization)
+        const seed1 = i * 12345 + p * 67890 + r;
+        const spread = randFloat(seed1, -spread_below, spread_above);
+        const f = f0 * ratio * (1.0 + spread);
+
+        // Amplitude decay
+        const A = A0 * Math.exp(-decay_alpha * Math.abs(f - f0));
+
+        // Phase with jitter
+        const seed2 = seed1 + 1;
+        const jitterPhase = randFloat(seed2, 0.0, 1.0) * jitter * 2.0 * Math.PI;
+        const phase = 2.0 * Math.PI * f * t + jitterPhase;
+
+        sample += A * Math.sin(phase);
+      }
+    }
+
+    pcm[i] = sample;
+  }
+
+  // Normalize to prevent clipping
+  let maxAbs = 0;
+  for (let i = 0; i < numSamples; ++i) {
+    maxAbs = Math.max(maxAbs, Math.abs(pcm[i]));
+  }
+  if (maxAbs > 1.0) {
+    for (let i = 0; i < numSamples; ++i) {
+      pcm[i] /= maxAbs;
+    }
+  }
+
+  return pcm;
+}
diff --git a/tools/mq_editor/viewer.js b/tools/mq_editor/viewer.js
index 459cd9e..451421d 100644
--- a/tools/mq_editor/viewer.js
+++ b/tools/mq_editor/viewer.js
@@ -2,10 +2,11 @@
 // Handles all visualization: spectrogram, partials, zoom, mouse interaction
 
 class SpectrogramViewer {
-  constructor(canvas, audioBuffer) {
+  constructor(canvas, audioBuffer, stftCache) {
     this.canvas = canvas;
     this.ctx = canvas.getContext('2d');
     this.audioBuffer = audioBuffer;
+    this.stftCache = stftCache;
     this.partials = [];
 
     // Fixed time bounds
@@ -30,6 +31,11 @@ class SpectrogramViewer {
     // Playhead
     this.playheadTime = -1; // -1 = not playing
 
+    // Spectrum viewer
+    this.spectrumCanvas = document.getElementById('spectrumCanvas');
+    this.spectrumCtx = this.spectrumCanvas ? this.spectrumCanvas.getContext('2d') : null;
+    this.spectrumTime = 0; // Time to display spectrum for
+
     // Setup event handlers
     this.setupMouseHandlers();
 
@@ -40,6 +46,9 @@ class SpectrogramViewer {
 
   setPlayheadTime(time) {
     this.playheadTime = time;
+    if (time >= 0) {
+      this.spectrumTime = time;
+    }
     this.render();
   }
 
@@ -88,6 +97,7 @@ class SpectrogramViewer {
     this.renderPartials();
     this.drawAxes();
     this.drawPlayhead();
+    this.renderSpectrum();
   }
 
   drawPlayhead() {
@@ -108,46 +118,36 @@ class SpectrogramViewer {
 
   // Render spectrogram background
   renderSpectrogram() {
-    const {canvas, ctx, audioBuffer} = this;
+    const {canvas, ctx, stftCache} = this;
     const width = canvas.width;
     const height = canvas.height;
 
     ctx.fillStyle = '#000';
     ctx.fillRect(0, 0, width, height);
 
-    const signal = getMono(audioBuffer);
-    const fftSize = 1024;
-    const hopSize = 256;
-    const sampleRate = audioBuffer.sampleRate;
+    if (!stftCache) return;
 
-    const numFrames = Math.floor((signal.length - fftSize) / hopSize);
+    const sampleRate = this.audioBuffer.sampleRate;
+    const hopSize = stftCache.hopSize;
+    const fftSize = stftCache.fftSize;
     const frameDuration = hopSize / sampleRate;
     const viewDuration = this.t_view_max - this.t_view_min;
 
     // Map view bounds to frame indices
     const startFrameIdx = Math.floor(this.t_view_min * sampleRate / hopSize);
     const endFrameIdx = Math.ceil(this.t_view_max * sampleRate / hopSize);
+    const numFrames = stftCache.getNumFrames();
 
     for (let frameIdx = startFrameIdx; frameIdx < endFrameIdx; ++frameIdx) {
       if (frameIdx < 0 || frameIdx >= numFrames) continue;
 
-      const offset = frameIdx * hopSize;
-      if (offset + fftSize > signal.length) break;
+      const frame = stftCache.getFrameAtIndex(frameIdx);
+      if (!frame) continue;
 
-      const frame = signal.slice(offset, offset + fftSize);
-
-      // Windowing
-      const windowed = new Float32Array(fftSize);
-      for (let i = 0; i < fftSize; ++i) {
-        const w = 0.5 - 0.5 * Math.cos(2 * Math.PI * i / fftSize);
-        windowed[i] = frame[i] * w;
-      }
-
-      // FFT
-      const spectrum = realFFT(windowed);
+      const spectrum = frame.spectrum;
 
       // Compute frame time range
-      const frameTime = frameIdx * hopSize / sampleRate;
+      const frameTime = frame.time;
       const frameTimeEnd = frameTime + frameDuration;
 
       const xStart = Math.floor((frameTime - this.t_view_min) / viewDuration * width);
@@ -350,6 +350,12 @@ class SpectrogramViewer {
       const freq = this.canvasToFreq(y);
       const intensity = this.getIntensityAt(time, freq);
 
+      // Update spectrum time when not playing
+      if (this.playheadTime < 0) {
+        this.spectrumTime = time;
+        this.renderSpectrum();
+      }
+
       tooltip.style.left = (e.clientX + 10) + 'px';
       tooltip.style.top = (e.clientY + 10) + 'px';
       tooltip.style.display = 'block';
@@ -408,38 +414,55 @@ class SpectrogramViewer {
   }
 
   getIntensityAt(time, freq) {
-    const signal = getMono(this.audioBuffer);
-    const fftSize = 1024;
-    const hopSize = 256;
-    const sampleRate = this.audioBuffer.sampleRate;
+    if (!this.stftCache) return -80;
+    return this.stftCache.getMagnitudeDB(time, freq);
+  }
 
-    const frameIdx = Math.floor(time * sampleRate / hopSize);
-    const offset = frameIdx * hopSize;
+  renderSpectrum() {
+    if (!this.spectrumCtx || !this.stftCache) return;
 
-    if (offset < 0 || offset + fftSize > signal.length) return -80;
+    const canvas = this.spectrumCanvas;
+    const ctx = this.spectrumCtx;
+    const width = canvas.width;
+    const height = canvas.height;
 
-    const frame = signal.slice(offset, offset + fftSize);
+    // Clear
+    ctx.fillStyle = '#1e1e1e';
+    ctx.fillRect(0, 0, width, height);
 
-    // Apply Hann window
-    const windowed = new Float32Array(fftSize);
-    for (let i = 0; i < fftSize; ++i) {
-      const w = 0.5 - 0.5 * Math.cos(2 * Math.PI * i / fftSize);
-      windowed[i] = frame[i] * w;
-    }
+    const spectrum = this.stftCache.getFFT(this.spectrumTime);
+    if (!spectrum) return;
 
-    // FFT
-    const spectrum = realFFT(windowed);
+    const fftSize = this.stftCache.fftSize;
 
-    // Find closest bin
-    const bin = Math.round(freq * fftSize / sampleRate);
-    if (bin < 0 || bin >= fftSize / 2) return -80;
+    // Draw bars
+    const numBars = 100;
+    const barWidth = width / numBars;
+    const numBins = fftSize / 2;
 
-    const re = spectrum[bin * 2];
-    const im = spectrum[bin * 2 + 1];
-    const mag = Math.sqrt(re * re + im * im);
-    const magDB = 20 * Math.log10(Math.max(mag, 1e-10));
+    for (let i = 0; i < numBars; ++i) {
+      const binIdx = Math.floor(i * numBins / numBars);
+      const re = spectrum[binIdx * 2];
+      const im = spectrum[binIdx * 2 + 1];
+      const mag = Math.sqrt(re * re + im * im);
+      const magDB = 20 * Math.log10(Math.max(mag, 1e-10));
 
-    return magDB;
+      // Normalize to [0, 1]
+      const normalized = (magDB + 80) / 80;
+      const clamped = Math.max(0, Math.min(1, normalized));
+      const intensity = Math.pow(clamped, 0.3);
+
+      const barHeight = intensity * height;
+      const x = i * barWidth;
+
+      // Gradient from bottom (cyan) to top (yellow)
+      const gradient = ctx.createLinearGradient(0, height - barHeight, 0, height);
+      gradient.addColorStop(0, '#4af');
+      gradient.addColorStop(1, '#fa4');
+
+      ctx.fillStyle = gradient;
+      ctx.fillRect(x, height - barHeight, barWidth - 1, barHeight);
+    }
   }
 
   // Utilities