This is a fascinating, research-driven approach to tuning that blends physics, information theory, and psychoacoustics. Instead of relying purely on human ears or traditional electronic tuners, it uses entropy minimization as the guiding principle.
Core Idea
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The human ear perceives sounds as “in tune” when their harmonic spectra are correlated—that is, when the overtones line up in a way that creates order in the auditory system.
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Entropy (in the Shannon sense) measures disorder or unpredictability.
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By minimizing the entropy of the combined Fourier spectra of notes, one can mathematically approximate the same “order” that the human ear perceives as consonance.
How It Works
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Record the sound of the instrument (e.g., piano notes).
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Fourier transform the signal to analyze its harmonic content.
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Preprocess the spectra to highlight relevant harmonics.
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Calculate Shannon entropy of the combined spectra.
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Adjust tuning to minimize entropy across intervals.
This process naturally produces:
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The stretch curve (slight widening of octaves) that piano tuners use aurally.
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Small pitch fluctuations similar to those found in high-quality human tuning.
Why It Matters
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Traditional electronic tuners often fail to capture the subtle stretch and compromises that human tuners introduce.
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Entropy-based tuning provides a scientifically grounded, automated method that mimics human aural tuning more closely than simple frequency-matching devices.
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It bridges objective measurement with subjective perception of harmony.
Reference:
Original paper: Entropy-based Tuning of Musical Instruments by Haye Hinrichsen (2012) – https://arxiv.org/abs/1203.5101
Details
Haye Hinrichsen
Universitat Wurzburg
Fakultat fur Physik und Astronomie
D-97074 Wurzburg, Germany
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