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Breaking a polygon into monotone polygons. A simple polygon may be easily cut into monotone polygons in O(n log n) time. However, since a triangle is a monotone polygon, polygon triangulation is in fact cutting a polygon into monotone ones, and it may be performed for simple polygons in O(n) time with a complex algorithm. [6]
A monotonic scale is a musical scale consisting of only one note in the octave. Having a deliberate fixed note, the monotonic is still a musical form rather than a total absence of melody. The monotonic stands in contrast to more common musical scales, such as the pentatonic (five notes) and modern, common Western heptatonic and chromatic scales.
Monotone preferences, a property of a consumer's preference ordering. Monotonicity (mechanism design), a property of a social choice function. Monotonicity criterion, a property of a voting system. Resource monotonicity, a property of resource allocation rules and bargaining systems.
In instrumental music, a style of playing that imitates the way the human voice might express the music, with a measured tempo and flexible legato. cantilena a vocal melody or instrumental passage in a smooth, lyrical style canto Chorus; choral; chant cantus mensuratus or cantus figuratus (Lat.) Meaning respectively "measured song" or "figured ...
Some definitions refer to music as a score, or a composition: [18] [7] [19] music can be read as well as heard, and a piece of music written but never played is a piece of music notwithstanding. According to Edward E. Gordon the process of reading music , at least for trained musicians, involves a process, called "inner hearing" or "audiation ...
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 ...
The notions of completely and absolutely monotone function/sequence play an important role in several areas of mathematics. For example, in classical analysis they occur in the proof of the positivity of integrals involving Bessel functions or the positivity of Cesàro means of certain Jacobi series. [ 6 ]
An intuitively understandable example for a polyphonic instrument is a (classical) piano, on which the player plays different melody lines with the left and the right hand - depending on music style and composition, these may be musically tightly interrelated or may even be totally unrelated to each other, like in parts of Jazz music.