Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude re... more Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude relatie (denk bijvoorbeeld aan Pythagoras, Euler, Kepler en Descartes), maar toch blijken er steeds meer elementen binnen de muziektheorie te profiteren van een wiskundige aanpak. In dit artikel beschrijven we een aantal voorbeelden van muziekgerelateerd onderzoek waarbij een heel scala wiskundige technieken is gebruikt. Verder zullen we
Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude re... more Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude relatie (denk bijvoorbeeld aan Pythagoras, Kepler, Descartes en Euler), en ook nu blijken er steeds meer elementen binnen de huidige muziektheorie te profiteren van een wiskundige aanpak. In dit artikel beschrijven we een aantal voorbeelden van theoretisch, cognitief en computationeel onderzoek rond muziek waarbij een heel scala
We present a novel approach to clustering and classification of music, based on the concept of in... more We present a novel approach to clustering and classification of music, based on the concept of interval categories. Six interval categories exist, each with its own musical character. A piece of music can be represented by six numbers, reflecting the percentages of occurrences of each interval category. A piece of music can, in this way, be visualized as a point
In this paper, we present a novel approach to clustering and classification of music. The approac... more In this paper, we present a novel approach to clustering and classification of music. The approach is based on the concept of interval categories, which is a theoretical, but perceptually motivated construct that groups sets of pitch events into six different categories each of which has its own musical character. A piece of music can be represented by six percentages that express the occurrences of each category in the piece. This piece of music can, in this way, be represented as one point in a six dimensional space. We choose the three most significant dimensions to visualize music from different composers and genres. We will see that, using this approach, automatic classification between tonal and atonal music is possible. Furthermore, we will present a successful visual clustering of 1) the three periods of Beethoven, 2) the genres Rock and Jazz, and 3) several composers through various musical time periods.
It is well known that subsets of the two-dimensional space ℤ can represent prominent musical and ... more It is well known that subsets of the two-dimensional space ℤ can represent prominent musical and music-theoretical objects such as scales, chords and chord vocabularies. It has been noted that the major and minor diatonic scale form convex subsets in this space. This triggers the question whether convexity is a more widespread concept in music. This article systematically investigates the
It has been observed that tonal spaces can be mapped onto a two-dimensional lattice Z 2 (1). It h... more It has been observed that tonal spaces can be mapped onto a two-dimensional lattice Z 2 (1). It has also been shown that various musical items, such as the major and minor diatonic scales, form convex1 subsets in this space (1, 4 ). This triggers the question whether convexity is a more widespread concept in music. The current paper systematically
This Special Issue is dedicated to explicate and discuss methodological issues in the interdiscip... more This Special Issue is dedicated to explicate and discuss methodological issues in the interdisciplinary research field of mathematical and computational approaches to music. It arose from a lively panel discussion at the third International Conference on Mathematics and Computation in Music 2011 in Paris. We have organized this panel in order to initiate the much needed interdisciplinary dialogue on the
Musical scales have both general and culture-specific properties. While most common
scales use o... more Musical scales have both general and culture-specific properties. While most common
scales use octave equivalence and discrete pitch relationships, there seem to be no other
universal properties. This paper presents an additional property across the world’s musical
scales that may qualify for universality. When the intervals of 998 (just intonation) scales
from the Scala Archive are represented on an Euler lattice, 96.7% of them form star-convex
structures. For the subset of traditional scales this percentage is even 100%. We present
an attempted explanation for the star-convexity feature, suggesting that the mathematical
search for universal musical properties has not yet reached its limits.
Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude re... more Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude relatie (denk bijvoorbeeld aan Pythagoras, Euler, Kepler en Descartes), maar toch blijken er steeds meer elementen binnen de muziektheorie te profiteren van een wiskundige aanpak. In dit artikel beschrijven we een aantal voorbeelden van muziekgerelateerd onderzoek waarbij een heel scala wiskundige technieken is gebruikt. Verder zullen we
Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude re... more Mathematische muziektheorie is een vakgebied in opkomst. Muziek en wiskunde hebben een oeroude relatie (denk bijvoorbeeld aan Pythagoras, Kepler, Descartes en Euler), en ook nu blijken er steeds meer elementen binnen de huidige muziektheorie te profiteren van een wiskundige aanpak. In dit artikel beschrijven we een aantal voorbeelden van theoretisch, cognitief en computationeel onderzoek rond muziek waarbij een heel scala
We present a novel approach to clustering and classification of music, based on the concept of in... more We present a novel approach to clustering and classification of music, based on the concept of interval categories. Six interval categories exist, each with its own musical character. A piece of music can be represented by six numbers, reflecting the percentages of occurrences of each interval category. A piece of music can, in this way, be visualized as a point
In this paper, we present a novel approach to clustering and classification of music. The approac... more In this paper, we present a novel approach to clustering and classification of music. The approach is based on the concept of interval categories, which is a theoretical, but perceptually motivated construct that groups sets of pitch events into six different categories each of which has its own musical character. A piece of music can be represented by six percentages that express the occurrences of each category in the piece. This piece of music can, in this way, be represented as one point in a six dimensional space. We choose the three most significant dimensions to visualize music from different composers and genres. We will see that, using this approach, automatic classification between tonal and atonal music is possible. Furthermore, we will present a successful visual clustering of 1) the three periods of Beethoven, 2) the genres Rock and Jazz, and 3) several composers through various musical time periods.
It is well known that subsets of the two-dimensional space ℤ can represent prominent musical and ... more It is well known that subsets of the two-dimensional space ℤ can represent prominent musical and music-theoretical objects such as scales, chords and chord vocabularies. It has been noted that the major and minor diatonic scale form convex subsets in this space. This triggers the question whether convexity is a more widespread concept in music. This article systematically investigates the
It has been observed that tonal spaces can be mapped onto a two-dimensional lattice Z 2 (1). It h... more It has been observed that tonal spaces can be mapped onto a two-dimensional lattice Z 2 (1). It has also been shown that various musical items, such as the major and minor diatonic scales, form convex1 subsets in this space (1, 4 ). This triggers the question whether convexity is a more widespread concept in music. The current paper systematically
This Special Issue is dedicated to explicate and discuss methodological issues in the interdiscip... more This Special Issue is dedicated to explicate and discuss methodological issues in the interdisciplinary research field of mathematical and computational approaches to music. It arose from a lively panel discussion at the third International Conference on Mathematics and Computation in Music 2011 in Paris. We have organized this panel in order to initiate the much needed interdisciplinary dialogue on the
Musical scales have both general and culture-specific properties. While most common
scales use o... more Musical scales have both general and culture-specific properties. While most common
scales use octave equivalence and discrete pitch relationships, there seem to be no other
universal properties. This paper presents an additional property across the world’s musical
scales that may qualify for universality. When the intervals of 998 (just intonation) scales
from the Scala Archive are represented on an Euler lattice, 96.7% of them form star-convex
structures. For the subset of traditional scales this percentage is even 100%. We present
an attempted explanation for the star-convexity feature, suggesting that the mathematical
search for universal musical properties has not yet reached its limits.
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Papers by Aline Honingh
scales use octave equivalence and discrete pitch relationships, there seem to be no other
universal properties. This paper presents an additional property across the world’s musical
scales that may qualify for universality. When the intervals of 998 (just intonation) scales
from the Scala Archive are represented on an Euler lattice, 96.7% of them form star-convex
structures. For the subset of traditional scales this percentage is even 100%. We present
an attempted explanation for the star-convexity feature, suggesting that the mathematical
search for universal musical properties has not yet reached its limits.
scales use octave equivalence and discrete pitch relationships, there seem to be no other
universal properties. This paper presents an additional property across the world’s musical
scales that may qualify for universality. When the intervals of 998 (just intonation) scales
from the Scala Archive are represented on an Euler lattice, 96.7% of them form star-convex
structures. For the subset of traditional scales this percentage is even 100%. We present
an attempted explanation for the star-convexity feature, suggesting that the mathematical
search for universal musical properties has not yet reached its limits.