Extension of Neo-Riemannian PLR-group to Seventh Chords
نویسنده
چکیده
This paper extends the concept of the PLR-group from the neo-Riemannian theory, which acts on the set of major and minor triads, to a PS-group, which acts on the set of major and minor seventh chords. Like the PLR-group, the PS-group is isomorphic to D12, the dihedral group of order 24, and only compositions of two operations are needed to generate all group elements. Unlike the actions from PLR-group, there are only two operations that both preserve the closure of the set of major and minor seventh chords, as well as map three out of four notes from a chord to a resulting image.
منابع مشابه
Charting Enharmonicism on the Just Intonation Tonnetz: A Practical Approach to Neo-Riemannian Analysis
In this study, I propose a theory of voice leading for use with the tonal space of the justintonation Tonnetz. The theory is based largely upon established theories of diatonic voice leading and chromatic harmony, and also draws upon the principles of just intonation within the tonal system. The unambiguous expression of intervals as untempered ratios is dependent upon an established seven-step...
متن کاملCommuting Groups and the Topos of Triads
The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair of dual groups is isomorphic to the left and right regular representations of some group (Cayley’s Theorem), 2) given a simply transitive group action, we sh...
متن کاملPermutation Groups and Chord Tesselations
Analytical approaches to musical analysis have generally attempted to provide some kind of justification, and, in the last decades, to develop analytical elements based on tesselations of pitch class sets. When applied to atonal music, analytical approaches frequently fail to find internal coherence. Most of the time, tilings of chords are based on a torus representation, which follows the trad...
متن کاملThe "Harmonic Walk": an Interactive Educational Environment to Discover Musical Chords
Harmony has always been considered a difficult matter to learn, also by experienced musicians. The aim of this paper is to present a system designed to provide unskilled users with an indication about the sound of the different harmonic regions and to help them to build a cognitive map of their relationships, linking musical perception to spatial abilities like orientation and wayfinding. The H...
متن کاملQuantifying the Benefits of Using an Interactive Decision Support Tool for Creating Musical Accompaniment in a Particular Style
We present a human-centered experiment designed to measure the degree of support for creating musical accompaniment provided by an interactive composition decision-support system. We create an interactive system with visual and audio cues to assist users in the choosing of chords to craft an accompaniment in a desired style. We propose general measures for objectively evaluating the effectivene...
متن کامل