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Music is often experienced as a progression of concurrent streams of notes, or voices. The degree to which this happens depends on the position along a voice-leading continuum, ranging from monophonic, to homophonic, to polyphonic, which…
Piano tones vary according to how pianist touches the keys. Many possible factors contribute to the relations between piano touch and tone. Focusing on the stiffness of string, we establish a model for vibration of a real piano string and…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
Multi-pitch perception is investigated in a listening test using 30 recordings of musical sounds with two tones played simultaneously, except for two gong sounds with inharmonic overtone spectrum, judging roughness and separateness as the…
We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…
Different questions lead to the same class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying $f(a)-f(b)\equiv0 \pmod {(a-b)}$ for all $a>b$. We characterize this class of functions…
Music tone quality evaluation is generally performed by experts. It could be subjective and short of consistency and fairness as well as time-consuming. In this paper we present a new method for identifying the clarinet reed quality by…
Music source separation is the task of separating a mixture of instruments into constituent tracks. Music source separation models are typically trained using only audio data, although additional information can be used to improve the…
The divergence of the harmonic series is proved by direct comparison with a series whose nth partial sum telescopes to the natural logarithm of n. The key idea is to apply the classical inequality x>=log(1+x) (valid for x>-1) with x=1/k and…
We explore the logarithmic terms in the soft theorem in four dimensions by analyzing classical scattering with generic incoming and outgoing states and one loop quantum scattering amplitudes. The classical and quantum results are consistent…
We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated…
Human categorization of sound seems predominantly based on sound source properties. To estimate these source properties we propose a novel sound analysis method, which separates sound into different sonic textures: tones, pulses, and…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
This study argues that electronic tones routinely used in contemporary popular music - including 808-style bass and power chords - are structurally and perceptually equivalent to multiphonics in contemporary classical music. Using listening…
Expressive variations of tempo and dynamics are an important aspect of music performances, involving a variety of underlying factors. Previous work has showed a relation between such expressive variations (in particular expressive tempo)…
Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts…
Automatic music transcription converts audio recordings into symbolic representations, facilitating music analysis, retrieval, and generation. A musical note is characterized by pitch, onset, and offset in an audio domain, whereas it is…
We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An…
The framework of a new scale invariant analysis on a Cantor set $C\subset $ $% I=[0,1] $, presented originally in {\it S. Raut and D. P. Datta, Fractals, 17, 45-52, (2009)}, is clarified and extended further. For an arbitrarily small…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…