Tone colour in music and bifurcation control

Gazor, Majid; Shoghi, Ahmad

doi:10.1016/j.jde.2022.04.011

Cited by 8 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It verifies that the right superior temporal gyrus and the left inferior frontal gyrus significantly influence the pitch coding expression through a sampling test method. Literature [14] attempted to interpret the qualitative changes of musical timbre from a bifurcation perspective, and in different bifurcation situations, the corresponding temporal amplitude bifurcation of the sound was obtained. Literature [15] designed a research methodology using EEG technology as a core logic to explore and investigate how the brain interacts with harmonic and non-harmonic sounds, learned that harmonic sounds have greater amplitudes than non-harmonic sounds, and noted that the harmonic effect is significantly affected by the characteristics of the sound.…”

Section: Introductionmentioning

confidence: 99%

Computer Simulation of Piano Tones and Design of Virtual Piano System

Zhang,

Guo,

Pan

et al. 2024

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

With the advancement of contemporary technology, there is an increasing demand for sophisticated tone libraries in intelligent and digital pianos. This paper introduces a virtual piano system based on timbre simulation. Drawing upon the articulation principles of the piano, a mathematical model is formulated to derive the equation governing string vibrations. This equation facilitates a comprehensive analysis of the components constituting piano timbre and establishes a model for synthesizing these timbres using a frequency envelope algorithm. The short-time Fourier transform (STFT) is utilized to extract features from the synthesized timbre and to accomplish its digital simulation. Subsequently, the integration of the piano’s timbre features with computer programming facilitates the comprehensive design of the virtual piano system. Performance testing and evaluation of the system reveal promising results: the detection rate for each musical piece exceeds 90%, with an average detection rate of 94.81% across ten pieces and an average deviation (Mean-D) of 3.35 in the scoring of 100 music samples. This research contributes to the flexibility in timbre editing, enhances the expressiveness of intelligent and digital pianos, and aims to elevate the music industry to new heights.

show abstract

Section: Introductionmentioning

confidence: 99%

Computer Simulation of Piano Tones and Design of Virtual Piano System

Zhang,

Guo,

Pan

et al. 2024

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

show abstract

“…Also, [9,10] propose a natural geometrical scheme for investigating and generating varieties of pitch simultaneity and sound intensity using Eulerian flows with n-tuple Hopf singularity for a sufficiently large n.…”

Section: Introductionmentioning

confidence: 99%

Music through Curve Insights

Gul

2023

Mathematics

View full text Add to dashboard Cite

This manuscript endeavors to establish a framework for the mapping of music onto a three-dimensional structure. Our objective is to transform the guitar choruses of Beatles songs into curves, with each chorus corresponding to its respective curve. We aim to investigate and characterize the intricacy of each song by employing mathematical techniques derived from differential geometry, specifically focusing on the total curvature of the chorus curve. Given that a single song may possess varying chord progressions in different verses, the performer can determine the geometric representation they aim to convey through the number of loops and the direction of the curve. The overarching objective of our study is to enable viewers to identify specific songs or motives by visually examining an object and exploring its geometric properties. Furthermore, we posit that these ideas can provide composers with a fresh perspective on their own musical compositions while also granting non-professional audiences a glimpse into the intricacies involved in the process of composing.

show abstract

“…Music was viewed as a dynamical system in order to study tonal relationships [19] or musical performances [20]. On the level of audio signals, [21,22] use Hopf bifurcation control to study sound changes in music. In [23,24], music theory for classical and jazz music is formalized by providing a mathematical model for tonality, voice leading and chord progressions, which is very different from the geometric and psychoacoustic approach presented in this paper but could help in further developing it.…”

Section: Introductionmentioning

confidence: 99%

Geometry of Music Perception

Himpel

2022

Mathematics

View full text Add to dashboard Cite

Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown to be a Whitney stratified space. Each stratum is a Riemannian manifold which naturally yields a geodesic distance across strata. The resulting metric is compatible with voice-leading satisfying the triangle inequality. The geometric model allows for rigorous studies of psychoacoustic quantities such as roughness and harmonicity as height functions. In order to show how to use the geometric framework in psychoacoustic studies, concepts for the perception of chord resolutions are introduced and analyzed.

show abstract

Tone colour in music and bifurcation control

Cited by 8 publications

References 29 publications

Computer Simulation of Piano Tones and Design of Virtual Piano System

Computer Simulation of Piano Tones and Design of Virtual Piano System

Music through Curve Insights

Geometry of Music Perception

Contact Info

Product

Resources

About