ChromagramDistance

Introduction

Chromagram Distance is a metric designed to compare the chromagram representations of two audio signals. The chromagram is a time-frequency representation that captures the energy distribution of a signal in terms of its pitch classes. It is widely used in music-related tasks due to its alignment with musical concepts like harmony and melody.

Sense of the Distance

Chromagram Distance measures the dissimilarity between two signals by comparing their chromagram representations. It is particularly useful in musical signal analysis, where the perception of pitch and harmony plays a crucial role in identifying the similarity between two signals.

Formal Representation

The Chromagram Distance between two signals ( x(t) ) and ( y(t) ) can be mathematically expressed as: [ Chroma_{dist}(x, y) = | Chromagram(x) - Chromagram(y) |_p ] where ( Chromagram(x) ) and ( Chromagram(y) ) represent the chromagram transformations of the signals ( x(t) ) and ( y(t) ), respectively, and ( | cdot |_p ) is a suitable distance measure (e.g., L2 norm) applied to the chromagram matrices.

# Example usage:

signal1: List[float] = [0.1 * math.sin(2 * math.pi * 440 * t / 16000) for t in range(16000)]
signal2: List[float] = [0.1 * math.sin(2 * math.pi * 445 * t / 16000) for t in range(16000)]  # Slightly different frequency

chromagram_calculator = ChromagramDistance(num_bins=12)

distance_value: float = chromagram_calculator.compute(signal1, signal2)

print("Chromagram Distance:", distance_value)

Academic Reference

Takuya[1]:

[1]

Fujishima Takuya. Realtime chord recognition of musical sound: asystem using common lisp music. In Proceedings of the International Computer Music Conference 1999, Beijing. 1999.

Conclusion

The ChromagramDistance class offers a valuable tool for measuring similarity between two audio signals, particularly in the context of musical applications where pitch and harmonic structures are essential.