Search Results for cube

...Scott Murphy The metric cube is a kind of graph of meters proposed as a complement to the types of metric spaces that have already been put forth in music-theoretic scholarship, particularly by Richard Cohn. Whereas Cohn's most recent kind of metric space (2001) can compare meters only...

... by three main families of lattices. Two of these are particularly use- ful in analysis: the first consists of a circle of n-dimensional cubes linked by Thanks to Richard Cohn and Gilles Baroin for helpful comments. 1 The chicken-wire torus was introduced in Douthett and Steinbach 1998...

...- tonic collections lie within it.48 The three set classes thus have different “degrees of connectedness,” giving rise to the complex structure shown in Example 11. There are two ways to understand this lattice: as a series of stacked cubes, and as a series of intertwining strands. We will consider...

... in three Euclidean dimensions, they lie at the vertices of a cube whose edges again connect closely related thaats (Example 1a , lower). Repeating this geometric process with four variable notes, we could create a four-dimensional cube, or tesseract. Repeating this for the five variable notes present...

... sprinkle references to these in the following paragraphs. Cohn primarily uses three graphs in his book—Cube Dance, 4-Cube Trio, and an updated version of the Tonnetz. As the second of these graphs contains a significant error, it has been...

..., Scott. 2006 . “Metric Cubes and Metric Transformations in Some Music of Brahms.” Paper presented at the Society for Music Theory Conference , los Angeles. Recordings Cited Ameling, Elly, soprano, and Norman Shetler, piano. 1995 remaster of 1967. Elly Ameling: The Early Recordings , vol...

... chords. With the aspect of key change abbreviated as K, this new scope is the IRK scope. 12 Just as there are 32 (2 5 ) possible equivalence relations within the OPTIC scope, there are 8 (2 3 ) possible equivalence relations within the IRK scope. Example 3 portrays them on a cube, such that two...

... on its compactness: the core of the prism contains the most equally spaced three-note chords (augmented triads), while the chain of cubes surrounding the center of the space contains the next most evenly spaced chords (major and minor triads). The outermost edges of the prism contain the sets with three...

...Example 10. “Cube Dance without Steps.” ...

... blind, and now adult, and taught by his touch to dis- tinguish between a cube, and a Sphere of the same metal, and nighly of the same bigness, so as to tell, when he felt one and t’other, which is the Cube, which the Sphere. Suppose then the Cube and Sphere placed on a Table, and the Blind...

... . ———. 1997 . “ Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations .” Journal of Music Theory 41/1 : 1 – 66 . ———. 1998 . “ Square Dances with Cubes .” Journal of Music Theory 42/2 : 283 – 96 . ———. 2012 . Audacious Euphony: Chromatic Harmony and the Triad’s...

...’ and Music Psychology in Hugo Riemann’s Harmonic Theory .” Ph.D. diss. , Columbia University . Muzzulini Daniel . 1994 . “ Leonhard Eulers Konsonanztheorie .” Musiktheorie 9 : 135 – 46 . Murphy Scott . 2010 . “ Metric Cubes in Some Music of Brahms .” Journal of Music Theory 53...

... Analysis 26 , no. 3 : 323 – 53 . Murphy Scott . 2009 . “ Metric Cubes in Some Music of Brahms ” Journal of Music Theory 53 , no. 1 : 1 – 56 . Murphy Scott . 2016 . “ Cohn’s Platonic Model and the Regular Irregularities of Recent Popular Multimedia ” Music Theory Online 22...

... 42 : 167 –80. ———. 2000 . “Weitzmann's Regions, My Cycles, and Douthett's Dancing Cubes.” Music Theory Spectrum 22 : 89 –103. ———. 2004 . “Uncanny Resemblances: Tonal Signification in the Freudian Age.” Journal of the American Musicological Society 57 : 285 –323. Cook, Robert C...

...-Riemannian Theory: A Survey and Historical Perspective.” Journal of Music Theory 42 : 167 -80. ____. 1998b . “Square Dances with Cubes.” Journal of Music Theory 42 : 283 -96. ____. 2000 . “Weitzmann's Regions, My Cycles, and Douthett's Dancing Cubes.” Music Theory Spectrum 22 : 89 -103...

... This diagram is the two-dimensional analogue to Jack how it is embedded in Figure 3. Douthett and Steinbach’s dis- Douthett and Peter Steinbach’s “cube dance” (1998). How- crete graphs, such as “cube dance,” contain similar twists, ever, I have explicitly shown that the graph is topologically though...