Related papers: Musical Chords by the Numbers
Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…
The statistical precision of a chord method for estimating fractal dimension from a correlation integral is derived. The optimal chord length is determined, and a comparison is made to other estimators. These calculations use the…
In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base…
In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system,…
In this paper, graph theory is used to explore the musical notion of tonal modulation, in theory and application. We define (pivot) modulation graphs based on the common scales used in popular music. Properties and parameters of these…
Following the ideas of von Helmholtz and Plomp-Levelt, an algorithm for calculating the total dissonance of complex sounds, free from logical inconsistencies and useful for comparing different chords, is proposed. The method is tested by…
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…
Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of…
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…
Rhythms and vibrations represent the quintessence of life, they are ubiquitous (systemic) in all living systems. Recognising, unfolding these rhythms is paramount in medicine, for example in the physiology of the heart, lung, hearing,…
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…
Scales, sets of discrete pitches that form the basis of melodies, are thought to be one of the most universal hallmarks of music. But we know relatively little about cross-cultural diversity of scales or how they evolved. To remedy this, we…
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…
A commonly-cited reason for the poor performance of automatic chord estimation (ACE) systems within music information retrieval (MIR) is that non-chord tones (i.e., notes outside the supporting harmony) contribute to error during the…
In this paper we present a mathematical way of defining musical modes and we define the musicality of a mode as a product of three different factors. We conclude by classifying the modes which are most musical according to our definition.
We investigate a dynamically adapting tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the…
Western music is predominantly based on the equal temperament with a constant semitone frequency ratio of $2^{1/12}$. Although this temperament has been in use since the 19th century and in spite of its high degree of symmetry, various…
Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the…
Modeling polyphonic music is a particularly challenging task because of the intricate interplay between melody and harmony. A good model should satisfy three requirements: statistical accuracy (capturing faithfully the statistics of…
The dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the…