Neo-Riemannian theory is a loose collection of ideas present in the writings of music theorists such as David Lewin, Brian Hyer, Richard Cohn, and Henry...

Riemannian theory, in general, refers to the musical theories of German theorist Hugo Riemann (1849–1919). His theoretical writings cover many topics...

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...

connection on a Riemannian manifold. Albert Einstein used the theory of pseudo-Riemannian manifolds (a generalization of Riemannian manifolds) to develop...

Fokker periodicity block Neo-Riemannian theory Musical set-theory Riemannian theory Transformational theory Tuning theory Traité de l'harmonie réduite...

his contributions are now termed as Riemannian theory, a variety of related ideas on many aspects of music theory. Riemann was born at Grossmehlra,...

any pseudo-Riemannian manifold, or indeed any manifold equipped with an affine connection. It is a central mathematical tool in the theory of general...

concluded that general relativity could be formulated in the context of Riemannian geometry which had been developed in the 1800s. In 1915, he devised the...

Sub-Riemannian manifold Riemannian submanifold Riemannian metric Riemannian circle Riemannian submersion Riemannian Penrose inequality Riemannian holonomy Riemann...

In mathematical physics, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is...

Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian...

partial differential equations. The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a...

approach has implications in Neo-Riemannian theory, and leads to some interesting connections between diatonic and chromatic theory. Emmanuel Amiot has discovered...

studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan...

Edward; Rehding, Alexander, eds. (2011). The Oxford Handbook of Neo-Riemannian Music Theories. Oxford U.P. p. 105. ISBN 9780195321333. Gjerdingen, Robert O...

the 19:16 minor third which many find pleasing.(p298) In the Neo-Riemannian theory, the minor mode is considered the inverse of the major mode, an upside...

(see above). The device drew renewed interest as the Tonnetz in Neo-Riemannian theory (see also Lattice (music)). Euler further used the principle of the...

Einstein's general theory of relativity is expressed. According to the theory, the universe is a smooth manifold equipped with a pseudo-Riemannian metric, which...

the general settings of potential theory. In addition, insight and clarity is obtained by generalizations to Riemannian manifolds and fiber bundles, allowing...

Fill Riffusion Vamp Capuzzo, Guy. Neo-Riemannian Theory and the Analysis of Pop-Rock Music, pp. 186–187, Music Theory Spectrum, Vol. 26, No. 2, pp. 177–199...

developed the basic theory of Lévy families and identified a number of examples, most importantly coming from sequences of Riemannian manifolds in which...

dominant, subdominant chords typically have predominant function. In Riemannian theory, it is considered to balance the dominant around the tonic (being...

quantum gravity. The early attempts at creating a unified field theory began with the Riemannian geometry of general relativity, and attempted to incorporate...

of Riemannian geometry, where in many cases exact solutions can be given. This general setting then extends to quantum field theory and string theory, again...

doublings," as a feature of tonal writing. Neo-Riemannian theory examines another facet of this principle. That theory decomposes movements from one chord to...

Randall, p. 99 Capuzzo, Guy. "Neo-Riemannian Theory and the Analysis of Pop-Rock Music", p.186–87, Music Theory Spectrum, Vol. 26, No. 2, pp. 177–199...

The decomposition and classification of Riemannian holonomy has applications to physics and to string theory. Let E be a rank-k vector bundle over a smooth...

Music Theory. 56 (1): 1–52. doi:10.1215/00222909-1546958 – via dmitri.mycpanel.princeton.edu. Neo-Riemannian theory Pitch space Transformational theory Amico...

as in Morse theory. In his subsequent work Almgren used these ideas to prove that for every k=1,...,n-1 a closed n-dimensional Riemannian manifold contains...

in the music of Alexander Scriabin", Journal of Music Theory 42, no. 2 ("Neo-Riemannian Theory", Autumn): 219–233. Tymoczko, Dmitri. 1997. "The Consecutive-Semitone...