fix(audio): Scale procedural note generation for orthonormal DCT

Fixed procedural notes (NOTE_*) being inaudible by adding scaling
compensation in gen.cc.

Root Cause:
- Old non-orthonormal DCT produced values ~16x larger (no sqrt scaling)
- New orthonormal DCT: output *= sqrt(1/N) or sqrt(2/N)
- Procedural note generation in gen.cc now produces 16x smaller spectrograms
- IDCT expects same magnitude as .spec files -> notes too quiet

Solution:
- Added scale_factor = sqrt(DCT_SIZE / 2) = sqrt(256) = 16
- Multiply DCT output by 16 to match old magnitude
- Procedural notes now have same loudness as sample-based notes

Verification:
- Checked spectral_editor: does not use DCT for procedural
- Checked editor tools: no procedural generation with DCT
- All 23 tests pass

Procedural notes should now be audible at correct volume.

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

1 files changed, 7 insertions, 2 deletions

diff --git a/src/audio/gen.cc b/src/audio/gen.cc
index 148fc68..5604457 100644
--- a/src/audio/gen.cc
+++ b/src/audio/gen.cc
@@ -69,9 +69,14 @@ std::vector<float> generate_note_spectrogram(const NoteParams& params,
     float dct_chunk[DCT_SIZE];
     fdct_512(pcm_chunk, dct_chunk);
 
-    // Copy to buffer
+    // Scale up to compensate for orthonormal normalization
+    // Old non-orthonormal DCT had no sqrt scaling, so output was ~sqrt(N/2) larger
+    // Scale factor: sqrt(DCT_SIZE / 2) = sqrt(256) = 16
+    const float scale_factor = sqrtf(DCT_SIZE / 2.0f);
+
+    // Copy to buffer with scaling
     for (int i = 0; i < DCT_SIZE; ++i) {
-      spec_data[f * DCT_SIZE + i] = dct_chunk[i];
+      spec_data[f * DCT_SIZE + i] = dct_chunk[i] * scale_factor;
     }
   }