Search results
Results from the WOW.Com Content Network
Function (music) In music, function (also referred to as harmonic function[1]) is a term used to denote the relationship of a chord [2] or a scale degree [3] to a tonal centre. Two main theories of tonal functions exist today: The German theory created by Hugo Riemann in his Vereinfachte Harmonielehre of 1893, which soon became an international ...
Riemannian theory, in general, refers to the musical theories of German theorist Hugo Riemann (1849–1919). His theoretical writings cover many topics, including musical logic, [1] notation, [2] harmony, [3] melody, [4] phraseology, [5] the history of music theory, [6] etc. More particularly, the term Riemannian theory often refers to his ...
A function that is not monotonic. In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ][ 2 ][ 3 ] This concept first arose in calculus, and was later generalized to the more abstract setting of order theory.
Thus, when one upper adjoint of a Galois connection is given, the other upper adjoint can be defined via this same property. On the other hand, some monotone function f is a lower adjoint if and only if each set of the form { x ∈ A | f (x) ≤ b }, for b in B, contains a greatest element. Again, this can be dualized for the upper adjoint.
Musical form is the plan by which a short piece of music is extended. The term "plan" is also used in architecture, to which musical form is often compared. Like the architect, the composer must take into account the function for which the work is intended and the means available, practicing economy and making use of repetition and order. [10]
Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to communicate information about many musical elements, including pitch, duration, dynamics, or articulation of musical notes; tempo, metre, form (e.g., whether sections are repeated), and details about specific playing techniques (e.g., which ...
In psychoacoustics, a pure tone is a sound with a sinusoidal waveform; that is, a sine wave of constant frequency, phase-shift, and amplitude. [1] By extension, in signal processing a single-frequency tone or pure tone is a purely sinusoidal signal (e.g., a voltage). A pure tone has the property – unique among real-valued wave shapes – that ...
In the mathematical field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the good convergence behaviour of monotonic sequences, i.e. sequences that are non- increasing, or non- decreasing. In its simplest form, it says that a non-decreasing bounded -above sequence of real numbers converges to ...