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Max Bruch's Concerto for Two Pianos in A-flat minor has its last movement in A-flat major, which is the parallel major; this concerto plays with the contrast between the two keys. Scott Joplin's Maple Leaf Rag is also written in A-flat major (the trio part of the composition is written in D-flat major). Other compositions in A-flat major include:
A map of rings is called flat if it is a homomorphism that makes B a flat A-module. A morphism of schemes is called faithfully flat if it is both surjective and flat. [2] Two basic intuitions regarding flat morphisms are: flatness is a generic property; and; the failure of flatness occurs on the jumping set of the morphism.
A ring homomorphism is flat if S is a flat R-module for the module structure induced by the homomorphism. For example, the polynomial ring R [ t ] is flat over R , for any ring R . For any multiplicative subset S {\displaystyle S} of a commutative ring R {\displaystyle R} , the localization S − 1 R {\displaystyle S^{-1}R} is a flat R ...
The ongoing debate about progressive vs. flat taxes isn’t likely to end, as what some view as a pro for a certain system is seen as a con by those on the other side of the argument.
E-flat major was the second-flattest key Mozart used in his music. For him, E-flat major was associated with Freemasonry; "E-flat evoked stateliness and an almost religious character." [4] Edward Elgar wrote his Variation IX "Nimrod" from the Enigma Variations in E-flat major. Its strong, yet vulnerable character has led the piece to become a ...
The above definition assumes that, if M has a boundary, x is not a boundary point of M.If x is a point on the boundary of M then the definition is modified as follows. We say that N is locally flat at a boundary point x of M if there is a neighborhood of x such that the topological pair (,) is homeomorphic to the pair (+,), where + is a standard half-space and is included as a standard ...
A flat can be described by a system of linear equations.For example, a line in two-dimensional space can be described by a single linear equation involving x and y: + = In three-dimensional space, a single linear equation involving x, y, and z defines a plane, while a pair of linear equations can be used to describe a line.
C-flat major is the home key of the harp, with all its pedals in the top position, and it is considered the most resonant key for the instrument.Thus, in Richard Strauss's Ein Heldenleben, the first cue for the harps is written in C-flat major even though the rest of the orchestra, having previously played in E-flat major, retains a 3-flat key signature and is now playing in B major, marked ...