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

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

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

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

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

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

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...

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...

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

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

as formal transformations, the branch of transformation theory called Neo-Riemannian theory was popularized by Brian Hyer (1995), Michael Kevin Mooney...

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...

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...

and Rehding, Alexander; eds. (2011). The Oxford Handbook of Neo-Riemannian Music Theories, p.105. Oxford. ISBN 9780195321333. The German text, in the 11th...

(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...

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

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...

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

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...

in contrast to the usual diatonic concept of Tonart. In the neo-Riemannian theory of the late 20th century, however, the same chromatic chord relations...

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

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...

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

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...

and radiation are present. A version of non-Euclidean geometry, called Riemannian geometry, enabled Einstein to develop general relativity by providing...

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

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...