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cardinality

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Journal Article
Journal of Music Theory (2022) 66 (1): 93–128.
Published: 01 April 2022
... similarities between pairs of contours with different lengths, and fewer still can measure shared characteristics among an entire family of contours. This article introduces a new method for evaluating familial similarities between related contours, even if the contours have different cardinalities. The model...
FIGURES | View All (25)
Image
Published: 01 April 2022
Example 3. Cardinality variants of melody M 4a from Example 2 . More
Journal Article
Journal of Music Theory (2016) 60 (1): 23–50.
Published: 01 April 2016
... − 1, where n equals cardinality. This notation identifies pitches solely by their relative height, thereby eschewing any reference to specific interval size and effectively transforming pitches in pitch space into contour pitches in contour space. The variable end-point mechanism this procedure...
Image
Published: 01 April 2022
Figure 1b. Conceptual model representing Quinn's motivic categorization for his “family M,” showing the hidden category of cardinality. More
Journal Article
Journal of Music Theory (2023) 67 (1): 1–70.
Published: 01 April 2023
... approximate chord categories much of their significance. The approach is most useful for chords with five or fewer notes and works tolerably for hexachords, but it breaks down with larger collections. This is not a failure of the model but a reflection of the fact that quality space contracts as cardinality...
FIGURES | View All (53)
Journal Article
Journal of Music Theory (2008) 52 (2): 219–249.
Published: 01 October 2008
... of a particular cardinality appears at the vertex of the cone modeling voice leadings connecting sets of that cardinality. The promi- nence of perfectly even sets in voice-leading spaces has also been important in forging links between voice-leading and Fourier spaces because, as we shall soon see, even...
Journal Article
Journal of Music Theory (2002) 46 (1-2): 1–56.
Published: 01 October 2002
...- rence, ordinarily the octave. A scale sometimes serves as a kind of tone bank, or pitch repository, providing pitch-class material for scales of smaller cardinalities. The Arabic maqam system of 17 notes to the octave comes to mind in this context as well as the 22 srutis in Indian music...
Journal Article
Journal of Music Theory (2001) 45 (2): 263–343.
Published: 01 October 2001
... of interval- or subset- classes and, through their mechanisms, attempted to form cardinality- neutral comparisons. My aim here is not to evaluate these indices, but to suggest that one way to facilitate such cardinality-neutral comparisons is through a contextualization of the vector data itself before...
Journal Article
Journal of Music Theory (2019) 63 (2): 231–260.
Published: 01 October 2019
... (2009, 2010, 2011) theory of the metric matrix, developed in response to the music of the Ewe ethnic group of West Africa. 12 Moonhyuk Chung (2008) takes a similar approach. His generalized interval system of semimeters represents pulses by their beat cardinality visvis a fixed, common time span, what...
Journal Article
Journal of Music Theory (2001) 45 (1): 1–29.
Published: 01 April 2001
.... 1.2 QUESTION 1: What are necessary and sufficient conditions on a pair <X,Y> of pcsets, that they should be a constant-IFUNC pair? Because <X,Y <X*,Y>, and <X*,Y*> are such pairs if and only if <X,Y> is, we may restrict our attention to X and Y of cardinality less than or equal to 6. We can...
Journal Article
Journal of Music Theory (2005) 49 (1): 45–108.
Published: 01 April 2005
... and between tiers. The tiers consist of rows and columns and are them- selves gathered into stacks, which combine to form complexes of stacks. In this way, a five-dimensional space that contains set-classes of cardinal- ity 1 through 6 can be grasped with relative ease. Essentially, I will be offering...
Journal Article
Journal of Music Theory (1999) 43 (1): 21–82.
Published: 01 April 1999
... principal concern here—we will nonetheless define one useful measure that quantifies, from one perspec- tive, the relative amount of “chunking” that “accurate” perception of the partition requires. 1.2. Definition. For any partition p, the cardinality of p, written CARD(p), is the sum of the numbers (k2...
Journal Article
Journal of Music Theory (2019) 63 (2): 167–207.
Published: 01 October 2019
... (pitchn or gpitchn) with no equivalence relations applied. 10 Although most spaces in Straus 2005 depict relation- ships between chords of a fixed cardinality, a few of the spaces relate sets with different cardinalities. For instance, Straus s figure 6 shows voice-leading relationships between two...
Journal Article
Journal of Music Theory (2015) 59 (1): 121–181.
Published: 01 April 2015
..., and Dmitri Tymoczko (2008) also take chords as objects (see also Tymoczko 2011). But because the range of chords is much wider—all chords of a given cardinality, including multisets and not restricted to equal temperament— the mathematical structure of voice-leading...
Journal Article
Journal of Music Theory (2007) 51 (2): 277–332.
Published: 01 October 2007
... with respect a member to the of a-cycle. set, and that the magnitude of a set Figure 9.  Magnitude of P = {0, 5, 15} {with respect} to the `-cycle ∞ with respect to the -cycle will be equal to the cardinality of the set. There are other (lesser) peaks∞ in the graph of P at x 3, x...
Journal Article
Journal of Music Theory (2014) 58 (1): 79–101.
Published: 01 April 2014
... with “optimal voice-leading structure” within their cardinality exclusively exhibit. But the distribution of the individual notes of a set within pitch-class space does not perfectly correlate with voice-leading mobility, as shown in Table 1. The dif...
Journal Article
Journal of Music Theory (2008) 52 (2): 251–272.
Published: 01 October 2008
... to the nearest doubled subset of the n-note set-class, we can plot these two numbers for every (twelve-tone equal-tempered) multiset-class of a given cardinality. Figure 5 shows, for trichordal multiset-classes, both the FC3 magnitude and the size of the minimal voice leading to the nearest doubled...
Includes: Supplementary data
Journal Article
Journal of Music Theory (1999) 43 (2): 193–230.
Published: 01 October 1999
.... Figure 2 enumerates the Odd inventory. The top part of the figure lists the set-classes in shorthand: numbers in boldface designate the cardinal- ities and Arabic numbers indicate the Forte set-class names.6 “2–: 1 1 3 3 5 5,” for example, represents the Odd dyads 2–1[01], 2–1, 2–3[03], 2–3, 2–5[05...
Journal Article
Journal of Music Theory (2005) 49 (1): 109–140.
Published: 01 April 2005
... shows the four possibilities.22 The definition of m has to do with augmented triads only because we imagined it acting on them. In principle, what m does has to do only with equal divisions of the octave, not with any properties, cardinality or oth- erwise, of equal divisions themselves. We...
Journal Article
Journal of Music Theory (2016) 60 (2): 213–262.
Published: 01 October 2016
... the number of set types under theoretical consideration by applying criteria that distin- guish a small number of scale-like collections (typically cardinality plus some kind of evenness conditions). An interesting formulation of scale theory roughly...