The Interval Angle: A Similarity Measure for Pitch-Class Sets

Scott, Damon; Isaacson, Eric J.

doi:10.2307/833526

Cited by 18 publications

(14 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It has been shown that all pc-sets can be grouped into six different categories [13,7]. This can be done by applying a cluster analysis [13] to several similarity measures [8,11,14,15,17] for pc-sets.…”

Section: Interval Categoriesmentioning

confidence: 99%

Clustering and Classification of Music by Interval Categories

Honingh

Bod

2011

Mathematics and Computation in Music

View full text Add to dashboard Cite

Abstract. 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.

show abstract

Section: Interval Categoriesmentioning

confidence: 99%

Clustering and Classification of Music by Interval Categories

Honingh

Bod

2011

Mathematics and Computation in Music

View full text Add to dashboard Cite

show abstract

“…Algunos de ellos son: el índice de similitud (Teitelbaum, 1965), la similitud sobre el vector de clases interválicas IcVSIM (E. J. Isaacson, 1990), el ángulo entre vectores interválicos ANGLE (Scott e Isaacson, 1998), la distancia euclidiana y ángulo en el espacio de Fourier hexadimensional (Callender, 2007). 8 A continuación se describen algunos conceptos y operaciones que fueron fundamentales para el desarrollo del sistema armónico del proyecto.…”

Section: Universos Armónicosunclassified

“…Es perfectamente apropiado que su valor máximo sea 90 (es decir π/2 ), representando perpendicularidad, en lugar de 180, representando una dirección negativa. (Scott e Isaacson, 1998). La distancia angular está definida por la siguiente ecuación:…”

Section: Distancia Angularunclassified

Simbiosis: Composición para bandola andina colombiana y entidades sónicas

Gooding¹,

Borbón

2018

estud. artist.

View full text Add to dashboard Cite

La relación entre el ser humano y la máquina, desde una perspectiva simbiótica, posibilita un nuevo paradigma para comprender, concebir y percibir el sonido, lo cual nos permite experimentar situaciones creativas sustancialmente innovadoras, siendo fundamental el caos, el indeterminismo y la aleatoriedad. Simbiosis, es una composición en donde se pretende aplicar algunos conceptos y técnicas de la inteligencia artificial, la computación evolutiva y estrategias bio-inspiradas; es decir, mecanismos de programación basados o inspirados en procesos de evolución y selección biológica. Em este artículo, resultado de un proyecto de investigación-creación, se pretende extrapolar el concepto simbiosis en una composición musical, pretende explorar las relaciones que pueden surgir entre un intérprete humano y la máquina, en este caso una población de entidades sónicas autónomas, esta relación simbiótica es determinada, controlada y/o direccionada por un director/interprete (mentor) en tiempo real.

show abstract

“…Equations (15) (16) into subspaces, each of which can be simplified (this process is fully explained in in Appendix C in the online supplementary to this article). The computational complexity can be further reduced by exploiting the sparsity of the tensors to calculate only non-zero values; furthermore, due to their construction, the tensors are invariant with respect to any transposition of their indices, so only non-duplicated elements need to be calculated.…”

Section: R-ad Expectation Tensorsmentioning

confidence: 99%

“…The cosine distance between two vectors is equivalent to their uncentred correlation, and the use of such metrics is an established procedure in music theory and cognition [15][16][17]. For expectation tensors, the meaning of the cosine distance is easier to discern (and is a more obvious choice) than that of the L p -metrics: It gives a normalised value for the expected number of ways in which each different r-ad in one pitch collection can be matched to a corresponding r-ad in another pitch collection.…”

Section: Metricsmentioning

confidence: 99%

Modelling the similarity of pitch collections with expectation tensors

Milne

Sethares

Laney

et al. 2011

Journal of Mathematics and Music

View full text Add to dashboard Cite

Models of the perceived distance between pairs of pitch collections are a core component of broader models of music cognition. Numerous distance measures have been proposed, including voice-leading [1], psychoacoustic [2][3][4], and pitch and interval class distances [5]; but, so far, there has been no attempt to bind these different measures into a single mathematical or conceptual framework, nor to incorporate the uncertain or probabilistic nature of pitch perception. This paper embeds pitch collections in expectation tensors and shows how metrics between such tensors can model their perceived dissimilarity. Expectation tensors indicate the expected number of tones, ordered pairs of tones, ordered triples of tones, etc., that are heard as having any given pitch, dyad of pitches, triad of pitches, etc.. The pitches can be either absolute or relative (in which case the tensors are invariant with respect to transposition). Examples are given to show how the metrics accord with musical intuition.

show abstract

The Interval Angle: A Similarity Measure for Pitch-Class Sets

Cited by 18 publications

References 5 publications

Clustering and Classification of Music by Interval Categories

Clustering and Classification of Music by Interval Categories

Simbiosis: Composición para bandola andina colombiana y entidades sónicas

Modelling the similarity of pitch collections with expectation tensors

Contact Info

Product

Resources

About