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Journal Article
Journal of Music Theory (2002) 46 (1-2): 57–126.
Published: 01 October 2002
... distinctions in general. Most of the problematic issues just raised are addressed, directly or indirectly, by the simple algebraic framework proposed on the following pages for the study of triadic transformations. A uniform triadic trans- formation, or UTT, is described in componentwise fashion, through...
Journal Article
Journal of Music Theory (2005) 49 (1): 109–140.
Published: 01 April 2005
... Hook calls uniform triadic transformations, or UTTs (Hook 2002). A UTT is named by an ordered triple t +, t where + indicates mode preservation, − indicates mode reversal, t+ indicates the root-interval transposition when acting on a major triad, and t – indicates the root...
Journal Article
Journal of Music Theory (2010) 54 (2): 143–177.
Published: 01 October 2010
..., then the operations X, Y, . . . of COMM are exactly the interval-preserving operations for the GIS.” Julian Hook (2002a, 2002b) has done related work with commuting groups. His uniform triadic transformations (UTTs) constitute the commut- ing...
Journal Article
Journal of Music Theory (2011) 55 (1): 1–41.
Published: 01 April 2011
... demonstrates the relative advantages of another analytical model: a space constructed of three distinctive gestures drawn from a special family, K(1, 11), of uniform triadic transformations (UTTs; see Hook 2002). At the basis of the entire progression is a three-chord succession resulting...
Journal Article
Journal of Music Theory (2006) 50 (1): 111–127.
Published: 01 April 2006
...- automorphism on IVLSNeoR. Cf. GMIT, 5.1.6(C) and 6.7.2(C). tem of Uniform Triadic Transformations (UTTs). A more gen- If IVLS were commutative, then the resulting set after con- eral result is also easily proved: given any intervallic schritt jugation would always have the same internal intervallic...