WebSep 4, 2016 · The Tonnetz is a lattice diagram representing tonal space. It can be used to visualize harmonic relationships in music. Each node in the diagram corresponds to one … WebThe most famous example is given by the Tonnetz, a graph whose basic idea was introduced by Euler in 1739, and developed by several musicologists of the XIXth century, …

The Generalized Tonnetz - Dmitri Tymoczko

WebNeo-Riemannian transformations can be modeled with several interrelated geometric structures. The Riemannian Tonnetz ("tonal grid," shown on the right) is a planar array of … The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae. Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is … See more In musical tuning and harmony, the Tonnetz (German for 'tone network') is a conceptual lattice diagram representing tonal space first described by Leonhard Euler in 1739. Various visual representations of the Tonnetz can be … See more The harmonic table note layout is a recently developed musical interface that uses a note layout topologically equivalent to the Tonnetz. A Tonnetz of the syntonic temperament can be derived from a given isomorphic keyboard by … See more • Johnston, Ben (2006). "Rational Structure in Music", "Maximum Clarity" and Other Writings on Music, edited by Bob Gilmore. Urbana: University of Illinois Press. ISBN 0-252-03098-2 See more Recent research by Neo-Riemannian music theorists David Lewin, Brian Hyer, and others, have revived the Tonnetz to further explore properties of pitch structures. Modern music theorists generally construct the Tonnetz using equal temperament, … See more • Neo-Riemannian theory • Musical set-theory • Riemannian theory See more • Music harmony and donuts by Paul Dysart • Charting Enharmonicism on the Just-Intonation Tonnetz by Robert T. Kelley • Midi-Instrument based on Tonnetz (Melodic Table) by The Shape of Music See more butler\u0027s corkscrew

A Tonnetz in Practice — STEPHANIE E. LEOTSAKOS

Weba–c) Cohn’s convertible Tonnetz. d–e) Two representations of hexatonic pole on the Tonnetz. Example 2 The hexatonic pole on a Tonnetz. contains E, which is ^7 in F major, and it contains Cƒ, which when respelled as Dß is ß^6. The progression therefore has a high potential for tonal ambiguity. WebThe zones are assigned numbers, whose differences modulo 12 are equivalent to the number of semitonal work required for their constituent triads. Progressions through the … WebJun 12, 2012 · The tonnetz is a visual method for representing chords and voice leading relationships in the plane. Modern examples of the tonnetz include threedimensional … butler\u0027s crossing inwood wv