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In music theory, a scale is "any consecutive series of Musical note 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.Benward, Bruce and Saker, Marilyn Nadine (2003). Music: In Theory and Practice, seventh edition: vol. 1, p. 25. Boston: McGraw-Hill. .
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.Hewitt, Michael (2013). Musical Scales of the World, pp. 2–3. The Note Tree. . 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 scale, diatonic scale, chromatic scale, major scale, minor scale, 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.
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).
"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."Nzewi, Meki, and Odyke Nzewi (2007), A Contemporary Study of Musical Arts. Pretoria: Centre for Indigenous Instrumental African Music and Dance. Volume 1 p. 34 . "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."Nettl, Bruno, and Helen Myers (1976). Folk Music in the United States, p.39. .
Scales may also be described by their symmetry, such as being palindrome, Chirality, or having rotational symmetry as in Messiaen's modes of limited transposition.
A musical scale that contains 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.
Western music in the Medieval music and Renaissance periods (1100–1600) tends to use the white-note diatonic scale C–D–E–F–G–A–B. Accidentals are rare, and somewhat unsystematically used, often to avoid the tritone.
Music of the common practice periods (1600–1900) uses three types of scale:
These scales are used in all of their transpositions. The music of this period introduces modulation, which involves systematic changes from one scale to another. Modulation occurs in relatively conventionalized ways. For example, major-mode pieces typically begin in a "tonic" diatonic scale and modulate to the "dominant" scale a fifth above. In the 19th century (to a certain extent), but more in the 20th century, additional types of scales were explored:
The scale degrees of a heptatonic (7-note) scale can also be named using the terms tonic, supertonic, mediant, subdominant, dominant, submediant, subtonic. If the subtonic is a semitone away from the tonic, then it is usually called the leading-tone (or leading-note); otherwise the leading-tone refers to the raised subtonic. Also commonly used is the (movable do) solfège naming convention in which each scale degree is denoted by a syllable. In the major scale, the solfège syllables are: do, re, mi, fa, so (or sol), la, ti (or si), do (or ut).
In naming the notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A major scale is written A–B–C–D–E–F–G rather than A–B–D–D–E–E–G. However, it is impossible to do this in scales that contain more than seven notes, at least in the English-language nomenclature system.
Scales may also be identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale. The most common binary numbering scheme defines lower pitches to have lower numeric value (as opposed to low pitches having a high numeric value). Thus a single pitch class n in the pitch class set is represented by 2^n. This maps the entire power set of all pitch class sets in 12-TET to the numbers 0 to 4095. The binary digits read as ascending pitches from right to left, which some find discombobulating because they are used to low to high reading left to right, as on a piano keyboard. In this scheme, the major scale is 101010110101 = 2741. This binary representation permits easy calculation of interval vectors and common tones, using logical binary operators. It also provides a perfect index for every possible combination of tones, as every scale has its own number.Daniel Starr. ‘Sets, Invariance, and Partitions’. In: Journal of Music Theory 22.1 (1978), pp. 1–42Alexander Brinkman. Pascal Programming for Music Research. University of Chicago Press, 1990.
Scales may also be shown as semitones from the tonic. For instance, 0 2 4 5 7 9 11 denotes any major scale such as C–D–E–F–G–A–B, in which the first degree is, obviously, 0 semitones from the tonic (and therefore coincides with it), the second is 2 semitones from the tonic, the third is 4 semitones from the tonic, and so on. Again, this implies that the notes are drawn from a chromatic scale tuned with 12-tone equal temperament. For some fretted string instruments, such as the guitar and the bass guitar, scales can be notated in tabulature, an approach which indicates the fret number and string upon which each scale degree is played.
In blues, a pentatonic scale is often used. In jazz, many different musical mode and scales are used, often within the same piece of music. Chromatic scales are common, especially in modern jazz.
Some scales span part of an octave; several such short scales are typically combined to form a scale spanning a full octave or more, and usually called with a third name of its own. The Turkish and Middle Eastern music has around a dozen such basic short scales that are combined to form hundreds of full-octave spanning scales. Among these scales Hejaz scale has one scale step spanning 14 intervals (of the middle eastern type found 53 in an octave) roughly similar to 3 semitones (of the western type found 12 in an octave), while Saba scale, another of these middle eastern scales, has 3 consecutive scale steps within 14 commas, i.e. separated by roughly one western semitone either side of the middle tone.
Gamelan music uses a small variety of scales including Pélog and Sléndro, none including equally tempered nor harmonic intervals. Indian classical music uses a moveable swara. Indian Rāgas often use intervals smaller than a semitone.Burns, Edwaard M. 1998. "Intervals, Scales, and Tuning.", p. 247. In The Psychology of Music, second edition, edited by Diana Deutsch, 215–264. New York: Academic Press. . Turkish music and Arabic music Arabic maqam may use quarter tone intervals. In both rāgas and maqamat, the distance between a note and an inflection (e.g., śruti) of that same note may be less than a semitone.
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