Related papers: Revising the Musical Equal Temperament
The impossibility of a transposable 12 semitone tuning of the octave arises from the mathematical fact that $2 \times 2^{7/12} \neq 3$ i.e., the second harmonic of the fifth can not exactly match the third harmonic of the fundamental. This…
Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains…
Music is a complex socio-cultural construct, which fascinates researchers in diverse fields, as well as the general public. Understanding the historical development of music may help us understand perceptual and cognition, while also…
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 mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
Much of Western classical music relies on instruments based on acoustic resonance, which produce harmonic or quasi-harmonic sounds. In contrast, since the mid-twentieth century, popular music has increasingly been produced in recording…
This paper deals with the algebraic structure of the sequence of harmonics when combined with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The sequence of physical harmonics is an increasingly enumerable…
The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this…
Mathematical steps are developed to obtain optimised well tempered model "temperaments", based on a musical Well Temperament definition by H. Kelletat, that is derived from A. Werckmeister. This supports objective mathematical ranking of…
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…
The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just…
We analyze the concept of virtuosity as a collective attribute in music and its relationship with the entropy based on an experiment that compares two sets of digital signals played by composer-performer electric guitarists. Based on an…
The standard theory of musical scales since antiquity has been based on harmony, rather than melody. While recent analyses provide mixed support for a role of melody as well as harmony, we lack a comparative analysis based on cross-cultural…
After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…
How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…
Every art form ultimately aims to invoke an emotional response over the audience, and music is no different. While the precise perception of music is a highly subjective topic, there is an agreement in the "feeling" of a piece of music in…
Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…
The relationship between sensory consonance and Western harmony is an important topic in music theory and psychology. We introduce new methods for analysing this relationship, and apply them to large corpora representing three prominent…
The Pythagorean school attributed consonance in music to simplicity of frequency ratios between musical tones. In the last two centuries, the consonance curves developed by Helmholtz, Plompt and Levelt shifted focus to psycho-acoustic…
We measure the complexity of songs in the Million Song Dataset (MSD) in terms of pitch, timbre, loudness, and rhythm to investigate their evolution from 1960 to 2010. By comparing the Billboard Hot 100 with random samples, we find that the…