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Its parallel major, C-sharp major, is usually written instead as the enharmonic key of D-flat major, since C-sharp major’s key signature with seven sharps is not normally used. Its enharmonic equivalent, D-flat minor , having eight flats including the B , has a similar problem.
Flat and sharp are mutually inverse isomorphisms of smooth vector bundles, hence, for each p in M, there are mutually inverse vector space isomorphisms between T p M and T ∗ p M. The flat and sharp maps can be applied to vector fields and covector fields by applying them to each point. Hence, if X is a vector field and ω is a covector field,
In Hungarian Rhapsody No. 6, Franz Liszt takes the unusual step of changing the key from D-flat major to C-sharp major near the start of the piece, and then back again to B-flat minor. Maurice Ravel selected C-sharp major as the tonic key of "Ondine" from his piano suite Gaspard de la nuit. Erich Wolfgang Korngold composed his Piano Concerto ...
However, in common guitar tabs notation, a minor key is designated with a lowercase "m". For example, A-minor is "Am" and D-sharp minor is "D ♯ m"). The small interval between equivalent notes, such as F-sharp and G-flat, is the Pythagorean comma .
A piece in a major key might modulate up a fifth to the dominant (a common occurrence in Western music), resulting in a new key signature with an additional sharp. If the original key was C-sharp, such a modulation would lead to the theoretical key of G-sharp major (with eight sharps) requiring an F in place of the F ♯. This section could be ...
When a musical key or key signature is referred to in a language other than English, that language may use the usual notation used in English (namely the letters A to G, along with translations of the words sharp, flat, major and minor in that language): languages which use the English system include Irish, Welsh, Hindi, Japanese (based on katakana in iroha order), Korean (based on hangul in ...
The Yamabe problem refers to a conjecture in the mathematical field of differential geometry, which was resolved in the 1980s. It is a statement about the scalar curvature of Riemannian manifolds: Let (M,g) be a closed smooth Riemannian manifold.
In mathematics, the signature (v, p, r) [clarification needed] of a metric tensor g (or equivalently, a real quadratic form thought of as a real symmetric bilinear form on a finite-dimensional vector space) is the number (counted with multiplicity) of positive, negative and zero eigenvalues of the real symmetric matrix g ab of the metric tensor with respect to a basis.