Musical Carbon Dating 🎵

A Statistical Feature Recognition Analysis (1960-2020)

“Can we timestamp a musical recording purely from its acoustic properties?”

This project implements a rigorous statistical pipeline to quantifiably “carbon date” music. By analyzing 13 physical and perceptual audio features (e.g., Tempo, Valence, Spectral Energy) across 250,971 tracks, we demonstrate that musical eras have distinct, mathematically recognizable acoustic fingerprints.

📊 Key Results (Verified)

1. Statistical Validity

Despite the complexity of artistic expression, our Weighted Least Squares (WLS) model ensures valid inference:

• $R^2$: 0.275. (27.5% of variance explained by acoustic physics alone).
• MAE: 9.30 years. (Average error < 1 decade).
• See output/figures/pred_vs_act_best_model_(wls)_predictions.png.

2. Statistical Rigor

We explicitly address the failures of standard OLS regression:

• Heteroscedasticity: Diagnosed via Breusch-Pagan Test ($\chi^2 \approx 19,567, p < 0.001$) and corrected with WLS weights ($w_i \propto 1/\sigma_i^2$).
• Non-Linearity: Confirmed via Partial F-Tests ($F \approx 4945$).
• Feature Selection: LASSO ($L_1$) regularization validated the use of all 13 acoustic features, confirming that even subtle markers (like Key and Mode) are essential for tracking harmonic evolution.

3. The “Nostalgia Index”

We define prediction error as a commercial metric: $\text{Index} = |\hat{y}_{pred} - y_{actual}|$.

• Insight: High index values identify songs that are “Time-Displaced” (Retro or Futuristic).
• Examples:
  • Uptown Funk (2015): Index 1.9 (Modern construction).
  • Physical (Dua Lipa, 2020): Index 11.0 (Strong 80s aesthetic).

🛠 Project Structure

├── data/                   # Dataset (Spotify 600k Tracks)
├── src/                    # Source Code
│   ├── analysis.py         # Regression Engine (OLS, WLS, Ridge, LASSO, Stepwise)
│   ├── config.py           # Configuration (Feature Definitions)
│   ├── data_loader.py      # Data Preprocessing
│   └── visualization.py    # Plotting Logic
├── report/                 # [FINAL] Formal LaTeX Report
│   ├── main.tex            # Comprehensive Academic Report
│   └── figures/            # Auto-generated Figures
├── slides/                 # Presentation Slides (Beamer)
│   ├── main.tex            # "No Hiding" Detailed Slides
│   └── speaker_notes.md    # 22-min Verbatim Script (5 Speakers)
├── output/                 # Generated Artifacts
│   ├── figures/            # Residual Plots, Q-Q Plots, Prediction Plots
│   ├── tables/             # CSV Results
│   └── pipeline_verified.log # Definitive Statistical Output
└── main.py                 # Main Execution Pipeline

🚀 Usage

1. Environment Setup

python3 -m venv venv
source venv/bin/activate
pip install -r requirements.txt

2. Run Main Analysis

Execute the full pipeline (Data Load -> Feature Selection -> WLS -> Diagnostics):

python3 main.py

This will generate all figures in output/figures/ and metrics in output/pipeline_verified.log.

3. Compile Documentation

To build the PDF report and slides:

# Compile Report
cd report
latexmk -pdf main.tex

# Compile Slides
cd ../slides
latexmk -pdf main.tex

📄 Methodology Summary

1. Phase I (SLR): The “Loudness War” analysis ($R^2=0.14$).
2. Phase II (MLR): Baseline multiple regression ($R^2=0.24$).
3. Phase III (Diagnostics): Testing Linearity, Multicollinearity (VIF), and Homoscedasticity (BP Test).
4. Phase IV (Model Selection): Comparison of Stepwise AIC vs LASSO.
5. Phase V (Refinement): Implementation of WLS to handle variance instability.

University Statistical Analysis Project | Term: Fall 2024