Voicing Transformations and a Linear Representation of Uniform Triadic Transformations (Preprint name)

Motivated by analytical methods in mathematical music theory, we determine the structure of the subgroup $\mathcal{J}$ of $GL(3,\mathbb{Z}_{12})$ generated by the three voicing reflections. We determine the centralizer of $\mathcal{J}$ in both $GL(3,\mathbb{Z}_{12})$ and the monoid ${Aff}(3,\mathbb{Z}_{12})$ of affine transformations, and recover a Lewinian duality for trichords containing a generator of $\mathbb{Z}_{12}$. We present a variety of musical examples, including Wagner's hexatonic Grail motive and the diatonic falling fifths as cyclic orbits, an elaboration of our earlier work with Satyendra on Schoenberg, String Quartet in $D$ minor, op. 7, and an affine musical map of Joseph Schillinger. Finally, we observe, perhaps unexpectedly, that the retrograde inversion enchaining operation RICH (for arbitrary 3-tuples) belongs to the setwise stabilizer $\mathcal{H}$ in $\Sigma_3 \ltimes \mathcal{J}$ of root position triads. This allows a more economical description of a passage in Webern, Concerto for Nine Instruments, op. 24 in terms of a morphism of group actions. Some of the proofs are located in the Supplementary Material file, so that this main article can focus on the applications

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Essential Neo-Riemannian Theory for Today\u27s Musician

This thesis will build upon the foundation set by Engebretsen and Broman in Transformational Theory in the Undergraduate Curriculum: A Case for Teaching the Neo-Riemannian Approach (Journal of Music Theory Pedagogy 21) and Roig-Francoli’s Harmony in Context (McGraw-Hill) by justifying the inclusion of neo-Riemannian Theory (NRT) in the undergraduate music theory curricula. This thesis also serves as a text for use by undergraduates to supplement a typical theory curriculum. While Engebretsen and Broman introduce the notion of NRT inclusion, and Roig-Francolí dedicates several pages in Harmony to its discussion, NRT remains uncommon in an undergraduate curriculum. NRT, an emerging and relevant analytical system, lends itself to bridging the transition from the chromatic harmony of the nineteenth century to the varied techniques of the twentieth century. NRT’s flexibility assists comprehension of passages from various genres of music, old and new. In an effort to communicate the concepts of NRT to as many undergraduate perspectives as possible, examples and assignments feature musical works of the Common Practice Period, such as those of Beethoven and Liszt, as well as those drawn from the Rock-Pop Era from artists such as Ozzy Osbourne and The Beatles. This thesis addresses the application of NRT through various written, aural, and keyboard assignments that can be easily utilized in most undergraduate curricula. Through the use of written assignments, including examples for analysis as well as composition-exercises, students will achieve an understanding of NRT at the Analytical and Synthesis levels of Bloom’s Taxonomy

Wreaths for Rahn, and valuable exchanges

Accepted manuscrip