A solution to the mystery of the sub-harmonic series via a linear model of the cochlea
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917268680605696 |
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| author | Boscain, Ugo Ma, Xiangyu Prandi, Dario Turco, Giuseppina |
| author_facet | Boscain, Ugo Ma, Xiangyu Prandi, Dario Turco, Giuseppina |
| contents | In this paper, we study a simple linear model of the cochlea as a set of vibrating strings. We make hypothesis that the information sent to the auditory cortex is the energy stored in the strings and consider all oscillation modes of the strings. We show the emergence of the sub-harmonic series whose existence was hypothesized in the XVI century to explain the consonance of the minor chord. We additionally show how the nonlinearity of the energy can be used to study the emergence of the combination tone (Tartini's third sound) shedding new light on this long debated subject. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_26395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A solution to the mystery of the sub-harmonic series via a linear model of the cochlea Boscain, Ugo Ma, Xiangyu Prandi, Dario Turco, Giuseppina Signal Processing Analysis of PDEs Biological Physics Classical Physics Medical Physics In this paper, we study a simple linear model of the cochlea as a set of vibrating strings. We make hypothesis that the information sent to the auditory cortex is the energy stored in the strings and consider all oscillation modes of the strings. We show the emergence of the sub-harmonic series whose existence was hypothesized in the XVI century to explain the consonance of the minor chord. We additionally show how the nonlinearity of the energy can be used to study the emergence of the combination tone (Tartini's third sound) shedding new light on this long debated subject. |
| title | A solution to the mystery of the sub-harmonic series via a linear model of the cochlea |
| topic | Signal Processing Analysis of PDEs Biological Physics Classical Physics Medical Physics |
| url | https://arxiv.org/abs/2509.26395 |