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That is, when the first goes up, the second goes down the same number of diatonic steps (with some chromatic alteration); and when the first goes down, the second goes up the same number of steps. In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of ...
Retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." [1] Retrograde reverses the order of the motif's pitches: what was the first pitch becomes the last, and vice versa. [2] This is a technique used in music, specifically in twelve-tone technique, where ...
In music, a permutation ( order) of a set is any ordering of the elements of that set. [3] A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion ...
Complement (music) Traditional interval complementation: P4 + P5 = P8. In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism. In interval complementation a complement is the interval which, when added to the original interval, spans an octave in total.
Thematic transformation (also known as thematic metamorphosis or thematic development) is a musical technique in which a leitmotif, or theme, is developed by changing the theme by using permutation (transposition or modulation, inversion, and retrograde), augmentation, diminution, and fragmentation. It was primarily developed by Franz Liszt and ...
The inverse of a given fragment of melody is the fragment turned upside down—so if the original fragment has a rising major third (see interval), the inverted fragment has a falling major (or perhaps minor) third, etc. (Compare, in twelve-tone technique, the inversion of the tone row, which is the so-called prime series turned upside down ...
In music, a transformation consists of any operation or process that may apply to a musical variable (usually a set or tone row in twelve tone music, or a melody or chord progression in tonal music), or rhythm in composition, performance, or analysis. Transformations include multiplication, rotation, permutation (i.e. transposition, inversion ...
Music and mathematics. A spectrogram of a violin waveform, with linear frequency on the vertical axis and time on the horizontal axis. The bright lines show how the spectral components change over time. The intensity colouring is logarithmic (black is −120 dBFS). Music theory analyzes the pitch, timing, and structure of music.