Related papers: A Non-Pythagorean Musical Scale Based on Logarithm…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see…

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from…

Equal temperament, in which semitones are tuned in the irrational ratio of $2^{1/12} : 1$, is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intonation, in which intervals are given by products of powers of…

A new definition of musical pitch is proposed. A Finite-Difference Time Domain (FDTM) model of the cochlea is used to calculate spike trains caused by tone complexes and by a recorded classical guitar tone. All harmonic tone complexes,…

Quantification of stylistic differences between musical artists is of academic interest to the music community, and is also useful for other applications such as music information retrieval and recommendation systems. Information about…

Count or non-negative data are often log transformed to improve heteroscedasticity and scaling. To avoid undefined values where the data are zeros, a small pseudocount (e.g. 1) is added across the dataset prior to applying the…

Chord estimation metrics treat chord labels as independent of one another. This fails to represent the pitch relationships between the chords in a meaningful way, resulting in evaluations that must make compromises with complex chord…

We study the differential structure of the set of real logarithms of a non-singular real matrix, under the assumption that the matrix is either semi-simple or orthogonal.

Large Language Models (LLMs) are becoming very popular and are used for many different purposes, including creative tasks in the arts. However, these models sometimes have trouble with specific reasoning tasks, especially those that involve…

Musical scales are used throughout the world, but the question of how they evolved remains open. Some suggest that scales based on the harmonic series are inherently pleasant, while others propose that scales are chosen that are easy to…

Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and…

The paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with introduction of new concepts like the smoothing operator and semi-harmonic…

The relationship between perceptual loudness and physical attributes of sound is an important subject in both computer music and psychoacoustics. Early studies of "equal-loudness contour" can trace back to the 1920s and the measured…

This paper presents a generative AI model for automated music composition with LSTM networks that takes a novel approach at encoding musical information which is based on movement in music rather than absolute pitch. Melodies are encoded as…

We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…

We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing…

The concept of complexity as considered in terms of its algorithmic definition proposed by G.J. Chaitin and A.N. Kolmogorov is revisited for the dynamical complexity of music. When music pieces are cast in the form of time series of pitch…

To date, calculating the frequencies of musical notes requires one to know the frequency of some reference note. In this study, first-order ordinary differential equations are used to arrive at a mathematical model to determine tonal…

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…