In
music theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...
, a scale is any set of musical
notes
Note, notes, or NOTE may refer to:
Music and entertainment
* Musical note, a pitched sound (or a symbol for a sound) in music
* Notes (album), ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian
* ''Notes'', a common (yet unofficial) sho ...
ordered by
fundamental frequency
The fundamental frequency, often referred to simply as the ''fundamental'', is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In ...
or
pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale.
Often, especially in the context of the
common practice period
In European art music, the common-practice period is the era of the tonal system. Most of its features persisted from the mid- Baroque period through the Classical and Romantic periods, roughly from 1650 to 1900. There was much stylistic evoluti ...
, most or all of the
melody
A melody (from Greek language, Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a Linearity#Music, linear succession of musical tones that the listener perceives as a single entity. In its most liter ...
and
harmony
In music, harmony is the process by which individual sounds are joined together or composed into whole units or compositions. Often, the term harmony refers to simultaneously occurring frequencies, pitches ( tones, notes), or chords. However ...
of a
musical work
Musical composition can refer to an original piece or work of music, either vocal or instrumental, the structure of a musical piece or to the process of creating or writing a new piece of music. People who create new compositions are called c ...
is built using the notes of a single scale, which can be conveniently represented on a
staff with a standard
key signature
In Western musical notation, a key signature is a set of sharp (), flat (), or rarely, natural () symbols placed on the staff at the beginning of a section of music. The initial key signature in a piece is placed immediately after the clef at ...
.
Due to the principle of
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
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
Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of tw ...
, 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
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
interval, while a
major scale
The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double i ...
is defined by the interval pattern W–W–H–W–W–W–H, where W stands for
whole step
In Western culture, Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a interval (music), musical interval encompassing two adjacent staff positions ( ...
(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
diatonic
Diatonic and chromatic are terms in music theory that are most often used to characterize Scale (music), scales, and are also applied to musical instruments, Interval (music), intervals, Chord (music), chords, Musical note, notes, musical sty ...
,
chromatic
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, ...
,
major
Major (commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicators ...
,
minor
Minor may refer to:
* Minor (law), a person under the age of certain legal activities.
** A person who has not reached the age of majority
* Academic minor, a secondary field of study in undergraduate education
Music theory
*Minor chord
** Barb ...
, and others.
A specific scale is defined by its characteristic interval pattern and by a special note, known as its first
degree
Degree may refer to:
As a unit of measurement
* Degree (angle), a unit of angle measurement
** Degree of geographical latitude
** Degree of geographical longitude
* Degree symbol (°), a notation used in science, engineering, and mathematics
...
(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
C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
indicates a major scale with a C tonic.
Background
Scales, steps, and intervals
![C chromatic circle](https://upload.wikimedia.org/wikipedia/commons/7/75/C_chromatic_circle.svg)
Scales are typically listed from low to high pitch. Most scales are ''
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
-repeating'', meaning their pattern of notes is the same in every octave (the
Bohlen–Pierce scale
The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal-tempered diatonic scale.
The ...
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–
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–
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
In Schenkerian theory, a scale-step (german: Stufe) is a triad (based on one of the diatonic scale degrees) that is perceived as an organizing force for a passage of music (in accordance with the principle of composing-out). In ''Harmony'', S ...
.
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
Scientific pitch notation (SPN), also known as American standard pitch notation (ASPN) and international pitch notation (IPN), is a method of specifying musical Pitch (music), pitch by combining a musical Note (music), note name (with accidental ...
) 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
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, ...
, or dodecatonic (12 notes per octave)
*
Nonatonic (9 notes per octave): a
chromatic
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, ...
variation of the
heptatonic blues scale
*
Octatonic
An octatonic scale is any eight-Musical note, note musical scale. However, the term most often refers to the symmetric scale composed of alternating major second, whole and semitone, half steps, as shown at right. In classical theory (in contras ...
(8 notes per octave): used in
jazz
Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a major ...
and
modern classical music
Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" also ...
*
Heptatonic
A heptatonic scale is a musical scale that has seven pitches, or tones, per octave. Examples include the major scale or minor scale; e.g., in C major: C D E F G A B C—and in the relative minor, A minor, natural minor: A B C D E F G A; the mel ...
(7 notes per octave): the most common modern Western scale
*
Hexatonic
In music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole-tone scale, C D E F G A C; the augmented scale, C D E G A B C; the Prometheus scale, C D E F A B C; and the blues sc ...
(6 notes per octave): common in Western folk music
*
Pentatonic
A pentatonic scale is a musical scale with five notes per octave, in contrast to the heptatonic scale, which has seven notes per octave (such as the major scale and minor scale).
Pentatonic scales were developed independently by many ancie ...
(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
A tetratonic scale is a musical scale or mode with four notes per octave. This is in contrast to a heptatonic (seven-note) scale such as the major scale and minor scale, or a dodecatonic (chromatic 12-note) scale, both common in modern Western ...
(4 notes),
tritonic
A tritonic scale is a musical scale or mode with three notes per octave. This is in contrast to a heptatonic (seven-note) scale such as the major scale and minor scale, or a dodecatonic (chromatic 12-note) scale, both common in modern Western ...
(3 notes), and
ditonic (2 notes): generally limited to
prehistoric
Prehistory, also known as pre-literary history, is the period of human history between the use of the first stone tools by hominins 3.3 million years ago and the beginning of recorded history with the invention of writing systems. The use of ...
("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
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as the words ''madam'' or ''racecar'', the date and time ''11/11/11 11:11,'' and the sentence: "A man, a plan, a canal – Panam ...
,
chiral
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from ...
, or having rotational symmetry as in Messiaen's
modes of limited transposition Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. These scales may be transposed to all twelve notes of the chromatic scale, but at leas ...
.
Harmonic content
The notes of a scale form intervals with each of the other notes of the chord in
combination
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are th ...
. A 5-note scale has 10 of these
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note scale has 28.
[Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', pp.7ff. New York: Appleton-Century-Crofts. LOC 58-8138.] 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
Key or The Key may refer to:
Common meanings
* Key (cryptography), a piece of information that controls the operation of a cryptography algorithm
* Key (lock), device used to control access to places or facilities restricted by a lock
* Key (map ...
intervals plays a large part in the sound of the scale, the natural movement of melody within the scale, and the selection of
chords
Chord may refer to:
* Chord (music), an aggregate of musical pitches sounded simultaneously
** Guitar chord a chord played on a guitar, which has a particular tuning
* Chord (geometry), a line segment joining two points on a curve
* Chord (as ...
taken naturally from the scale.
A musical scale that contains
tritone
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three a ...
s 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
A performance is an act of staging or presenting a play, concert, or other form of entertainment. It is also defined as the action or process of carrying out or accomplishing an action, task, or function.
Management science
In the work place ...
or
composition
Composition or Compositions may refer to:
Arts and literature
*Composition (dance), practice and teaching of choreography
*Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
. They are also often used
precompositional
In music, precompositional decisions are those decisions which a composer decides upon before or while beginning to create a composition. These limits may be given to the composer, such as the length or style needed, or entirely decided by the comp ...
ly 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
(Achille) Claude Debussy (; 22 August 1862 – 25 March 1918) was a French composer. He is sometimes seen as the first Impressionist composer, although he vigorously rejected the term. He was among the most influential composers of the ...
's ''
L'Isle Joyeuse
L'isle joyeuse, L. 106 (The Joyful Island) is a piece for solo piano by Claude Debussy composed in 1904. According to Jim Samson (1977), the "central relationship in the work is that between material based on the whole-tone scale, the lydian ...
''. 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
Scales in
traditional Western music generally consist of seven notes and repeat at the octave. Notes in the commonly used scales (see just below) are separated by
whole and half step intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets
* A statistical level of measurement
* Interval est ...
of ''tones'' and ''semitones.'' The harmonic minor scale includes a three-semitone step; the anhemitonic pentatonic includes two of those and no semitones.
Western music in the
Medieval
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the Post-classical, post-classical period of World history (field), global history. It began with t ...
and
Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas ...
periods (1100–1600) tends to use the white-note
diatonic scale
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, ...
C–D–E–F–G–A–B.
Accidentals
In music, an accidental is a note of a pitch (or pitch class) that is not a member of the scale or mode indicated by the most recently applied key signature. In musical notation, the sharp (), flat (), and natural () symbols, among others, ma ...
are rare, and somewhat unsystematically used, often to avoid the
tritone
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three a ...
.
Music of the common practice periods (1600–1900) uses three types of scale:
* The
diatonic scale
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, ...
(seven notes)—this includes the major scale and the natural minor
* The melodic and harmonic
minor scale
In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which also ...
s (seven notes)
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
chromatic scale
The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...
(twelve notes)
* The
whole-tone scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' sc ...
(six notes)
* The
pentatonic scale
A pentatonic scale is a musical scale with five notes per octave, in contrast to the heptatonic scale, which has seven notes per octave (such as the major scale and minor scale).
Pentatonic scales were developed independently by many ancien ...
(five notes)
* The octatonic or
diminished scale
An octatonic scale is any eight- note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetric ...
s (eight notes)
A large variety of other scales exists, some of the more common being:
* The
Phrygian dominant scale
In music, the Phrygian dominant scale is the fifth musical mode, mode of the minor scale#Harmonic and melodic minor, harmonic minor scale, the fifth being the dominant (music), dominant.Dave Hunter (2005). ''Play Acoustic'', San Francisco: Backbe ...
(a mode of the harmonic minor scale)
* The
Arabic scales
* The
Hungarian minor scale
The Hungarian minor scale,Christiansen, Mike (2000). ''Guitar Scale Dictionary'', p. 14. .Stetina, Troy (2007). ''Fretboard Mastery'', p. 126. .Kent Cleland, Mary Dobrea-Grindahl (2010). ''Developing Musicianship Through Aural Skills'', p. 495. Ca ...
* The
Byzantine music
Byzantine music (Greek: Βυζαντινή μουσική) is the music of the Byzantine Empire. Originally it consisted of songs and hymns composed to Greek texts used for courtly ceremonials, during festivals, or as paraliturgical and liturgical ...
scales (called echoi)
* The
Persian scale
The Persian scale is a musical scale occasionally found in guitar scale books, along with other scales inspired by Middle Eastern music. It is characterized by the liberal use of half steps (4), augmented seconds (2), and frequent use of chromatic ...
Scales such as the pentatonic scale may be considered ''gapped'' relative to the diatonic scale. An ''auxiliary scale'' is a scale other than the primary or original scale. See:
modulation (music)
In music, modulation is the change from one tonality ( tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature (a key change). Modulations articulate or create the structure or form of many pieces, as ...
and
Auxiliary diminished scale.
Note names
In many musical circumstances, a specific note of the scale is chosen as the
tonic—the central and most stable note of the scale. In Western tonal music, simple songs or pieces typically start and end on the tonic note. Relative to a choice of a certain tonic, the notes of a scale are often labeled with numbers recording how many scale steps above the tonic they are. For example, the notes of the C
major scale
The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double i ...
(C, D, E, F, G, A, B) can be labeled , reflecting the choice of C as tonic. The expression
scale degree
In music theory, the scale degree is the position of a particular note on a scale relative to the tonic, the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals and ...
refers to these numerical labels. Such labeling requires the choice of a "first" note; hence scale-degree labels are not intrinsic to the scale itself, but rather to its modes. For example, if we choose A as tonic, then we can label the notes of the C major scale using A = 1, B = 2, C = 3, and so on. When we do so, we create a new scale called the A
minor scale
In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which also ...
. See the
musical note
In music, a note is the representation of a musical sound.
Notes can represent the Pitch (music), pitch and Duration (music), duration of a sound in musical notation. A note can also represent a pitch class.
Notes are the building blocks of much ...
article for how the notes are customarily named in different countries.
The scale degrees of a heptatonic (7-note) scale can also be named using the terms
tonic,
supertonic
In music, the supertonic is the second degree () of a diatonic scale, one whole step above the tonic. In the movable do solfège system, the supertonic note is sung as ''re''.
The triad built on the supertonic note is called the supertonic chor ...
,
mediant In music, the mediant (''Latin'': to be in the middle) is the third scale degree () of a diatonic scale, being the note halfway between the tonic and the dominant.Benward & Saker (2003), p.32. In the movable do solfège system, the mediant note i ...
,
subdominant
In music, the subdominant is the fourth tonal degree () of the diatonic scale. It is so called because it is the same distance ''below'' the tonic as the dominant is ''above'' the tonicin other words, the tonic is the dominant of the subdomina ...
,
dominant,
submediant
In music, the submediant is the sixth degree () of a diatonic scale. The submediant ("lower mediant") is named thus because it is halfway between tonic and subdominant ("lower dominant") or because its position below the tonic is symmetrical to t ...
,
subtonic
In music, the subtonic is the degree of a musical scale which is a whole step below the tonic note. In a major key, it is a lowered, or flattened, seventh scale degree (). It appears as the seventh scale degree in the natural minor and descendin ...
. If the subtonic is a semitone away from the tonic, then it is usually called the
leading-tone
In music theory, a leading-tone (also called a subsemitone, and a leading-note in the UK) is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, ''the ...
(or leading-note); otherwise the leading-tone refers to the raised subtonic. Also commonly used is the (movable do)
solfège
In music, solfège (, ) or solfeggio (; ), also called sol-fa, solfa, solfeo, among many names, is a music education method used to teach aural skills, Pitch (music), pitch and sight-reading of Western classical music, Western music. Solfège is ...
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 chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...
. It is assumed that the scale is tuned using
12-tone equal temperament
Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resultin ...
(so that, for instance, C is the same as D), and that the tonic is in the leftmost position. For example, the
binary number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one).
The base-2 numeral system is a positional notatio ...
101011010101, equivalent to the
decimal number
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
2773, would represent any major scale (such as C–D–E–F–G–A–B). This system includes scales from 100000000000 (2048) to 111111111111 (4095), providing a total of 2048 possible
species
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
, but only 351 unique scales containing from 1 to 12 notes.
Scales may also be shown as
semitones
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
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
The bass guitar, electric bass or simply bass (), is the lowest-pitched member of the string family. It is a plucked string instrument similar in appearance and construction to an electric or an acoustic guitar, but with a longer neck and ...
, scales can be notated in
tabulature
Tablature (or tabulature, or tab for short) is a form of musical notation indicating instrument fingering rather than musical pitches.
Tablature is common for fretted stringed instruments such as the guitar, lute or vihuela, as well as many ...
, an approach which indicates the fret number and string upon which each scale degree is played.
Transposition and modulation
Composers transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the
C major
C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
scale, the pattern C–D–E might be shifted up, or
transposed
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal;
that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other notations).
The tr ...
, a single scale step to become D–E–F. This process is called "scalar transposition" or "shifting to a new key" and can often be found in
musical sequences and patterns. (It is D-E-F in Chromatic transposition). Since the steps of a scale can have various sizes, this process introduces subtle melodic and harmonic variation into the music. In Western tonal music, the simplest and most common type of modulation (or changing keys) is to shift from one major key to another key built on the first key's fifth (or dominant) scale degree. In the key of C major, this would involve moving to the key of G major (which uses an F). Composers also often modulate to other related keys. In some
Romantic music era
Romantic music is a stylistic movement in Western Classical music associated with the period of the 19th century commonly referred to as the Romantic era (or Romantic period). It is closely related to the broader concept of Romanticism—the ...
pieces and contemporary music, composers modulate to "remote keys" that are not related to or close to the tonic. An example of a remote modulation would be taking a song that begins in C major and modulating (changing keys) to F major.
Jazz and blues
Through the introduction of
blue note
In jazz and blues, a blue note is a note that—for expressive purposes—is sung or played at a slightly different pitch from standard. Typically the alteration is between a quartertone and a semitone, but this varies depending on the musical co ...
s, jazz and
blues
Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spirituals, work songs, field hollers, shouts, chants, and rhymed simple narrative ballads from the Afr ...
employ scale intervals smaller than a semitone. The blue note is an
interval that is technically neither
major nor minor but "in the middle", giving it a characteristic flavour. A regular
piano
The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...
cannot play blue notes, but with
electric guitar
An electric guitar is a guitar that requires external amplification in order to be heard at typical performance volumes, unlike a standard acoustic guitar (however combinations of the two - a semi-acoustic guitar and an electric acoustic gui ...
,
saxophone
The saxophone (often referred to colloquially as the sax) is a type of single-reed woodwind instrument with a conical body, usually made of brass. As with all single-reed instruments, sound is produced when a reed on a mouthpiece vibrates to pr ...
,
trombone
The trombone (german: Posaune, Italian, French: ''trombone'') is a musical instrument in the Brass instrument, brass family. As with all brass instruments, sound is produced when the player's vibrating lips cause the Standing wave, air column ...
and
trumpet
The trumpet is a brass instrument commonly used in classical and jazz ensembles. The trumpet group ranges from the piccolo trumpet—with the highest register in the brass family—to the bass trumpet, pitched one octave below the standard ...
, performers can "bend" notes a fraction of a tone sharp or flat to create blue notes. For instance, in the key of E, the blue note would be either a note between G and G or a note moving between both.
In blues, a
pentatonic scale
A pentatonic scale is a musical scale with five notes per octave, in contrast to the heptatonic scale, which has seven notes per octave (such as the major scale and minor scale).
Pentatonic scales were developed independently by many ancien ...
is often used. In jazz, many different
modes
Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to:
Arts and entertainment
* '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine
* ''Mode'' magazine, a fictional fashion magazine which is ...
and scales are used, often within the same piece of music. Chromatic scales are common, especially in modern jazz.
Non-Western scales
Equal temperament
In Western music, scale notes are often separated by
equally tempered
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, w ...
tones or semitones, creating 12 intervals per octave. Each interval separates two tones; the higher tone has an oscillation frequency of a fixed ratio (by a factor equal to the
twelfth root of two
The twelfth root of two or \sqrt 2/math> (or equivalently 2^) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio ( musical interval) of a se ...
, or approximately 1.059463) higher than the frequency of the lower one. A scale uses a subset consisting typically of 7 of these 12 as scale steps.
Other
Many other musical traditions use scales that include other intervals. These scales originate within the derivation of the
harmonic series.
Musical intervals are complementary values of the
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
overtone
An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...
s series. Many musical scales in the world are based on this system, except most of the musical scales from
Indonesia
Indonesia, officially the Republic of Indonesia, is a country in Southeast Asia and Oceania between the Indian and Pacific oceans. It consists of over 17,000 islands, including Sumatra, Java, Sulawesi, and parts of Borneo and New Guine ...
and the
Indochina
Mainland Southeast Asia, also known as the Indochinese Peninsula or Indochina, is the continental portion of Southeast Asia. It lies east of the Indian subcontinent and south of Mainland China and is bordered by the Indian Ocean to the west an ...
Peninsulae, which are based on inharmonic resonance of the dominant metalophone and xylophone instruments.
Intra-scale intervals
Some scales use a different number of pitches. A common scale in Eastern music is the pentatonic scale, which consists of five notes that span an octave. For example, in the Chinese culture, the pentatonic scale is usually used for folk music and consists of C, D, E, G and A, commonly known as gong, shang, jue, chi and yu.
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
Gamelan () ( jv, ꦒꦩꦼꦭꦤ꧀, su, ᮌᮙᮨᮜᮔ᮪, ban, ᬕᬫᭂᬮᬦ᭄) is the traditional ensemble music of the Javanese, Sundanese, and Balinese peoples of Indonesia, made up predominantly of percussive instruments. T ...
music uses a small variety of scales including
Pélog
Pelog ( su, ᮕᮦᮜᮧᮌ᮪, translit=Pélog /pelog/, jv, ꦥꦺꦭꦺꦴꦒ꧀, ban, ᬧᬾᬮᭀᬕ᭄, translit=Pélog /pelok/) is one of the essential tuning systems used in gamelan instruments that has heptatonic scale. The other, ...
and
Sléndro
Slendro ( jv, ꦱ꧀ꦭꦺꦤ꧀ꦢꦿꦺꦴ, ban, slendro, translit=Sléndro) ( su, salendro, translit=Saléndro) is one of the essential tuning systems used in gamelan instruments that have pentatonic scale. Based on Javanese mythology, ...
, none including equally tempered nor harmonic intervals.
Indian classical music
Indian classical music is the classical music of the Indian subcontinent. It has two major traditions: the North Indian classical music known as '' Hindustani'' and the South Indian expression known as '' Carnatic''. These traditions were not ...
uses a moveable
seven-note scale. Indian
Rāga
A ''raga'' or ''raag'' (; also ''raaga'' or ''ragam''; ) is a melodic framework for improvisation in Indian classical music akin to a melodic mode. The ''rāga'' is a unique and central feature of the classical Indian music tradition, and as ...
s often use intervals smaller than a semitone.
Turkish music
The music of Turkey includes mainly Turkic and Byzantine elements as well as partial influences ranging from Ottoman music, Middle Eastern music and Music of Southeastern Europe, as well as references to more modern European and American popular ...
Turkish makam
The Turkish makam ( Turkish: ''makam'' pl. ''makamlar''; from the Arabic word ) is a system of melody types used in Turkish classical music and Turkish folk music. It provides a complex set of rules for composing and performance. Each makam speci ...
s and
Arabic music
Arabic music or Arab music ( ar, الموسيقى العربية, al-mūsīqā al-ʿArabīyyah) is the music of the Arab world with all its diverse music styles and genres. Arabic countries have many rich and varied styles of music and also man ...
maqamat may use
quarter tone
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...
intervals.
[Zonis ahler Ella. 1973. ''Classical Persian Music: An Introduction''. Cambridge, Massachusetts: Harvard University Press.] In both rāgas and maqamat, the distance between a note and an inflection (e.g.,
śruti
''Shruti'' ( sa, श्रुति, , ) in Sanskrit means "that which is heard" and refers to the body of most authoritative, ancient religious texts comprising the central canon of Hinduism. Manusmriti states: ''Śrutistu vedo vijñeyaḥ'' ( ...
) of that same note may be less than a semitone.
See also
*
List of musical scales and modes
The following is a list of musical scales and modes. Degrees are relative to the major scale.
See also
* Bebop scale
* Chord-scale system
*Heptatonic scale
* Jazz scale
*List of chord progressions
* List of chords
* List of musical interva ...
*
Melodic pattern
In music and jazz improvisation, a melodic pattern (or motive) is a cell or germ serving as the basis for repetitive pattern. It is a figure that can be used with any scale. It is used primarily for solos because, when practiced enough, it ca ...
*
Pitch circularity
Pitch circularity is a fixed series of tones that are perceived to ascend or descend endlessly in pitch. It's an example of an auditory illusion. Explanation
Pitch is often defined as extending along a one-dimensional continuum from high to low ...
*
Shepard tone
A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the bass pitch of the tone moving upward or downward, it is referred to as the ''Shepard scale''. This cre ...
References
Further reading
*
*
External links
Octave Frequency Sweep, Consonance & DissonanceVisual representation of scales from WolframTones
{{DEFAULTSORT:Musical Scale
Musical tuning
Music theory