In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency. The word scale originates from the Latin scala, which literally means "ladder". Therefore, any scale is distinguishable by its "step-pattern", or how its intervals interact with each other. Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature. Due to the principle of octave equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or interval) between two successive notes of the scale. However, there is no need for scale steps to be equal within any scale and, particularly as demonstrated by microtonal music, there is no limit to how many notes can be injected within any given musical interval. A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern W–W–H–W–W–W–H, where W stands for whole step (an interval spanning two semitones, e.g. from C to D), and H stands for half-step (e.g. from C to D♭). Based on their interval patterns, scales are put into categories including pentatonic, diatonic, chromatic, major, minor, and others. A specific scale is defined by its characteristic interval pattern and by a special note, known as its first degree (or tonic). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern. For example, C major indicates a major scale with a C tonic.
Background
Scales, steps, and intervals
Scales are typically listed from low to high pitch. Most scales are octave-repeating, meaning their pattern of notes is the same in every octave (the Bohlen–Pierce scale is one exception). An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B–[C], with the bracket indicating that the last note is an octave higher than the first note, and the decreasing C major scale is C–B–A–G–F–E–D–[C], with the bracket indicating an octave lower than the first note in the scale. The distance between two successive notes in a scale is called a scale step. The notes of a scale are numbered by their steps from the first degree of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to each other: C and E create an interval of a third (in this case a major third); D and F also create a third (in this case a minor third).
Pitch A single scale can be manifested at many different pitch levels. For example, a C major scale can be started at C4 (middle C; see scientific pitch notation) and ascending an octave to C5; or it could be started at C6, ascending an octave to C7.
Types of scale Scales may be described according to the number of different pitch classes they contain: Chromatic, or dodecatonic (12 notes per octave) Nonatonic (9 notes per octave): a chromatic variation of the heptatonic blues scale Octatonic (8 notes per octave): used in jazz and modern classical music Heptatonic (7 notes per octave): the most common modern Western scale Hexatonic (6 notes per octave): common in Western folk music Pentatonic (5 notes per octave): the anhemitonic form (lacking semitones) is common in folk music, especially in Asian music; also known as the "black note" scale Tetratonic (4 notes), tritonic (3 notes), and ditonic (2 notes): generally limited to prehistoric ("primitive") music Scales may also be described by their constituent intervals, such as being hemitonic, cohemitonic, or having imperfections. Many music theorists concur that the constituent intervals of a scale have a large role in the cognitive perception of its sonority, or tonal character. "The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality." "The pitch distances or intervals among the notes of a scale tell us more about the sound of the music than does the mere number of tones." Scales may also be described by their symmetry, such as being palindromic, chiral, or having rotational symmetry as in Messiaen's modes of limited transposition.
Harmonic content The notes of a scale form intervals with each of the other notes of the chord in combination. A 5-note scale has 10 of these harmonic intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note scale has 28, a scale with n notes has n(n-1)/2. Though the scale is not a chord, and might never be heard more than one note at a time, still the absence, presence, and placement of certain key intervals plays a large part in the sound of the scale, the natural movement of melody within the scale, and the selection of chords taken naturally from the scale. A musical scale that contains tritones is called tritonic (though the expression is also used for any scale with just three notes per octave, whether or not it includes a tritone), and one without tritones is atritonic. A scale or chord that contains semitones is called hemitonic, and without semitones is anhemitonic.
Scales in composition Scales can be abstracted from performance or composition. They are also often used precompositionally to guide or limit a composition. Explicit instruction in scales has been part of compositional training for many centuries. One or more scales may be used in a composition, such as in Claude Debussy's L'Isle Joyeuse. To the right, the first scale is a whole-tone scale, while the second and third scales are diatonic scales. All three are used in the opening pages of Debussy's piece.
Western music
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