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The three-dimensional orientation of a line can be described with just a plunge and trend. The rake is a useful description of a line because often (in geology) features (lines) follow along a planar surface. In these cases the rake can be used to describe the line's orientation in three dimensions relative to that planar surface.
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 ...
A horizontal line would have a plunge of 0°, and a vertical line would have a plunge of 90°. [3] [7] A linear feature which lies within a plane can also be measured by its rake (or pitch). Unlike plunge, which is the feature's azimuth, the rake is the angle measured within the plane from the strike line. [3]
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. [2] Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, [3] drawing on the twelve-tone theory of Milton Babbitt.
The "transformations" of transformational theory are typically modeled as functions that act over some musical space S, meaning that they are entirely defined by their inputs and outputs: for instance, the "ascending major third" might be modeled as a function that takes a particular pitch class as input and outputs the pitch class a major third above it.
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Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...
In music theory, pitch-class space is the circular space representing all the notes (pitch classes) in a musical octave. In this space, there is no distinction between tones separated by an integral number of octaves. For example, C4, C5, and C6, though different pitches, are represented by the same point in pitch class space.