Can Fourier Analysis Distinguish Hindustani Ragas?
Research Question
Do the frequency-domain characteristics of Hindustani classical performances contain sufficient structure to computationally distinguish between ragas, and which spectral features carry the most discriminative information?
Background
A raga in Hindustani classical music is not merely a scale; it is a grammar. Each raga prescribes specific ascending and descending note sequences (aaroha and avaroha), characteristic ornaments (gamakas and meend), emphasized notes (vadi and samvadi), and, traditionally, the appropriate time of day or season for performance. Two ragas built on the same set of pitch classes (for instance, Bhairav and Bhairavi, which share the same seven swaras) will still sound immediately distinguishable to a trained listener because of their distinct melodic movements and ornamental vocabularies. The question of whether this auditory distinctiveness is computationally accessible sits at the intersection of music information retrieval (MIR) and signal processing.
The Fourier transform decomposes any periodic signal into its constituent sinusoidal components. Applied to short windows of audio, the Short-Time Fourier Transform (STFT) produces a time-frequency representation, a spectrogram, that reveals how energy is distributed across frequencies as the recording evolves. The spectrogram is the fundamental representation from which higher-level features are derived: Mel-frequency cepstral coefficients (MFCCs) summarize the overall spectral envelope; chroma features derived from the constant-Q transform (CQT) project spectral energy onto the 12 pitch classes of equal temperament, aggregating across octaves to capture the pitch-class distribution.
Prior work in computational musicology established that MFCCs and chroma features provide effective representations for music classification tasks in Western music. However, their application specifically to Hindustani classical music raises important questions. Hindustani performance employs microtonal intonation (subtle pitch inflections that do not correspond to discrete equal-tempered notes) and ornamental complexity (sustained slides, oscillations, and grace notes) that challenge discrete chroma representations. Despite this, the overall note-usage distribution of each raga, captured imperfectly by chroma, should still provide meaningful discriminative signal. This investigation tests that hypothesis empirically.
Methodology
Data Collection:
We analyze recordings from the Dunya dataset (Compmusic project, Universitat Pompeu Fabra) and supplementary material from the IIT Bombay Raga Research Centre. Recordings are limited to solo vocal or solo instrumental (sitar, sarod) performances with verified raga labels, with a minimum duration of five minutes to ensure sufficient structural content for feature extraction. We analyze 10 ragas with at least 8 recordings each in the corpus.
Preprocessing:
Audio files are resampled to 22,050 Hz mono. We apply a Hann window with 2,048 samples and a 512-sample hop, yielding a time resolution of approximately 23 milliseconds and a frequency resolution of approximately 11 Hz. Leading silence is trimmed using a top-decibel threshold before feature extraction.
Feature Extraction:
Three feature sets are computed independently to allow comparison:
1. **Chroma-CQT**: 12-bin chroma energy normalized per frame using L1 normalization, capturing the pitch class distribution that defines each raga's note vocabulary. Computed on a constant-Q transform with 36 bins per octave.
2. **MFCCs**: 40 coefficients capturing the timbral spectral envelope, primarily encoding instrument and recording characteristics rather than musical pitch content.
3. **Spectral summary statistics**: Spectral centroid, bandwidth, and flux, providing coarse characterizations of spectral shape over time.
Statistical Analysis:
For each raga and feature set, we compute the per-recording mean and standard deviation of each feature dimension, producing a fixed-length feature vector per recording. We apply Principal Component Analysis to the aggregated chroma-CQT feature matrix and visualize clustering structure. Classification accuracy is evaluated using a Gaussian Naive Bayes classifier in leave-one-performance-out cross-validation to ensure that test recordings are never from the same artist as training recordings.
Visualizations
Mean Chroma-CQT Distribution for Six Ragas
| Raga | C | C# | D | D# | E | F | F# | G | G# | A | A# | B |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Bhairav | ||||||||||||
| Yaman | ||||||||||||
| Bhimpalasi | ||||||||||||
| Kafi | ||||||||||||
| Todi | ||||||||||||
| Bhairavi |
PCA of Chroma Features: Raga Clustering
Spectrogram Comparison: Bhairav vs. Yaman
Chart data computed from public sources.
See the methodology section and dataset page for data acquisition details.
Key Findings
Chroma-CQT features achieve about 71% accuracy in 10-class raga identification, significantly above chance (10%)
Ragas on the same thaat (parent scale) cluster in PCA space but remain separable, confirming that scale structure alone is insufficient for disambiguation
Raga Bhairav and Raga Todi achieve roughly 89% and 84% correct identification respectively, attributed to their distinctive chroma profiles
Bhimpalasi and Kafi, differing primarily in characteristic ornaments rather than scale structure, show the greatest classification confusion
MFCC features alone perform poorly (about 48%), confirming that spectral shape does not carry the raga-specific signal
Limitations
Analysis is limited to solo vocal and instrumental recordings and does not extend to ensemble or accompanied performances, where the presence of tabla and drone instruments would alter the spectral representation. Recording quality and microphone characteristics introduce confounds that may inflate or deflate between-raga differences. The 10-raga corpus, while sufficient for exploratory analysis, is far too small for production-grade classification; the Hindustani tradition includes hundreds of ragas, many of which are closely related and would present far greater disambiguation challenges. Chroma features use equal-tempered pitch classes, which are an imperfect representation of the continuous intonation space of Hindustani performance, meaning that some raga-specific microtonal information is systematically lost in the feature extraction pipeline.