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The simplest pitch space model is the real line. A fundamental frequency f is mapped to a real number p according to the equation = + (/) This creates a linear space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60, as it is in MIDI. 440 Hz is the standard frequency of 'concert A', which ...
For example, C4, C5, and C6, though different pitches, are represented by the same point in pitch class space. Since pitch-class space is a circle, we return to our starting point by taking a series of steps in the same direction: beginning with C, we can move "upward" in pitch-class space, through the pitch classes C♯, D, D♯, E, F, F♯, G ...
A false sequence is a literal repetition of the beginning of a figure and stating the rest in sequence: [1] J.S. Bach Prelude from Cello Suite in G J.S. Bach Prelude from Cello Suite in G, BWV 1007. A modulating sequence is a sequence that leads from one tonal center to the next, with each segment technically being in a different key in some ...
An equivalence class of such metrics is known as a conformal metric or conformal class. Thus, a conformal metric may be regarded as a metric that is only defined "up to scale". Often conformal metrics are treated by selecting a metric in the conformal class, and applying only "conformally invariant" constructions to the chosen metric.
"Mirror forms", P, R, I, and RI, of a tone row (from Arnold Schoenberg's Variations for Orchestra Op. 31, "Called mirror forms because...they are identical". [1]In music, a tone row or note row (German: Reihe or Tonreihe), also series or set, [2] is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both ...
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is
The primary criticisms of Forte's nomenclature are: (1) Forte's labels are arbitrary and difficult to memorize, and it is in practice often easier simply to list an element of the set class; (2) Forte's system assumes equal temperament and cannot easily be extended to include diatonic sets, pitch sets (as opposed to pitch-class sets), multisets ...
The concept of "mode" in Western music theory has three successive stages: in Gregorian chant theory, in Renaissance polyphonic theory, and in tonal harmonic music of the common practice period. In all three contexts, "mode" incorporates the idea of the diatonic scale , but differs from it by also involving an element of melody type .
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