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...

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

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

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

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

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

mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described...

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

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

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...

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

of C major, the key of D major (or D minor) is the supertonic. In Riemannian theory, the supertonic is considered the subdominant parallel: Sp/T in major...

Fokker periodicity block Neo-Riemannian theory Musical set-theory Riemannian theory Transformational theory Tuning theory Treatise on Harmony Euler, Leonhard...

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

(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...

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...

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

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...

. In Riemannian geometry and pseudo-Riemannian geometry: Let ( M , g ) {\displaystyle (M,g)} and ( N , h ) {\displaystyle (N,h)} be Riemannian manifolds...

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

spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph. In a Riemannian manifold or submanifold, geodesics...

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...

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. The following...

The fundamental theorem of Riemannian geometry states that on any Riemannian manifold (or pseudo-Riemannian manifold) there is a unique affine connection...

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...

Lick 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...

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...

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...