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 what is otherwise called 'rudiments',
currently taught as the elements of notation,
of key signatures, of time signatures, of
rhythmic notation, and so on. [...] The second
is the study of writings about music from
ancient times onwards. [...] The third is
an area of current musicological study that
seeks to define processes and general principles
in music — a sphere of research that can
be distinguished from analysis in that it
takes as its starting-point not the individual
work or performance but the fundamental materials
from which it is built.
Music theory is frequently concerned with
describing how musicians and composers make
music, including tuning systems and composition
methods among other topics. Because of the
ever-expanding conception of what constitutes
music (see Definition of music), a more inclusive
definition could be that music theory is the
consideration of any sonic phenomena, including
silence, as they relate to music. This is
not an absolute guideline; for example, the
study of "music" in the Quadrivium liberal
arts university curriculum that was common
in medieval Europe was an abstract system
of proportions that was carefully studied
at a distance from actual musical practice.
However, this medieval discipline became the
basis for tuning systems in later centuries,
and it is generally included in modern scholarship
on the history of music theory.Music theory
as a practical discipline encompasses the
methods and concepts composers and other musicians
use in creating music. The development, preservation,
and transmission of music theory in this sense
may be found in oral and written music-making
traditions, musical instruments, and other
artifacts. For example, ancient instruments
from Mesopotamia, China, and prehistoric sites
around the world reveal details about the
music they produced and potentially something
of the musical theory that might have been
used by their makers (see History of music
and Musical instrument). In ancient and living
cultures around the world, the deep and long
roots of music theory are clearly visible
in instruments, oral traditions, and current
music making. Many cultures, at least as far
back as ancient Mesopotamia and ancient China,
have also considered music theory in more
formal ways such as written treatises and
music notation. Practical and scholarly traditions
overlap, as many practical treatises about
music place themselves within a tradition
of other treatises, which are cited regularly
just as scholarly writing cites earlier research.
In modern academia, music theory is a subfield
of musicology, the wider study of musical
cultures and history. Etymologically, music
theory is an act of contemplation of music,
from the Greek θεωρία, a looking at,
viewing, contemplation, speculation, theory,
also a sight, a spectacle. As such, it is
often concerned with abstract musical aspects
such as tuning and tonal systems, scales,
consonance and dissonance, and rhythmic relationships,
but there is also a body of theory concerning
practical aspects, such as the creation or
the performance of music, orchestration, ornamentation,
improvisation, and electronic sound production.
A person who researches, teaches, or writes
articles about music theory is a music theorist.
University study, typically to the M.A. or
Ph.D level, is required to teach as a tenure-track
music theorist in a US or Canadian university.
Methods of analysis include mathematics, graphic
analysis, and especially analysis enabled
by Western music notation. Comparative, descriptive,
statistical, and other methods are also used.
Music theory textbooks, especially in the
United States of America, often include elements
of musical acoustics, considerations of musical
notation, and techniques of tonal composition
(harmony and counterpoint), among other topics.
== History ==
=== 
Prehistory ===
Preserved prehistoric instruments, artifacts,
and later depictions of performance in artworks
can give clues to the structure of pitch systems
in prehistoric cultures. See for instance
Paleolithic flutes, Gǔdí, and Anasazi flute.
=== Antiquity ===
==== Mesopotamia ====
Several surviving Sumerian and Akkadian clay
tablets include musical information of a theoretical
nature, mainly lists of intervals and tunings.
The scholar Sam Mirelman reports that the
earliest of these texts dates from before
1500 BCE, a millennium earlier than surviving
evidence from any other culture of comparable
musical thought. Further, "All the Mesopotamian
texts [about music] are united by the use
of a terminology for music that, according
to the approximate dating of the texts, was
in use for over 1,000 years."
==== 
China ====
Much of Chinese music history and theory remains
unclear.The earliest texts about Chinese music
theory are inscribed on the stone and bronze
bells excavated in 1978 from the tomb of Marquis
Yi (died 433 BCE) of the Zeng state. They
include more than 2800 words describing theories
and practices of music pitches of the time.
The bells produce two intertwined pentatonic
scales three tones apart with additional pitches
completing the chromatic scale.Chinese theory
starts from numbers, the main musical numbers
being twelve, five and eight. Twelve refers
to the number of pitches on which the scales
can be constructed. The Lüshi chunqiu from
about 239 BCE recalls the legend of Ling Lun.
On order of the Yellow Emperor, Ling Lun collected
twelve bamboo lengths with thick and even
nodes. Blowing on one of these like a pipe,
he found its sound agreeable and named it
huangzhong, the "Yellow Bell." He then heard
phoenixes singing. The male and female phoenix
each sang six tones. Ling Lun cut his bamboo
pipes to match the pitches of the phoenixes,
producing twelve pitch pipes in two sets:
six from the male phoenix and six from the
female: these were called the lülü or later
the shierlü.The lülü formed the ritual
scale to which many instruments were tuned.
The name of the lowest sound, huangzhong also
implied 'musical correctness.' Its pitch formed
a pitch standard, setting the base pitch of
zithers, flutes and singers of imperial court
orchestras. Straight-walled pitch pipes without
finger holes were made of cast metal, their
lengths specified by court regulations. The
resulting chromatic scale provided twelve
fundamental notes for the construction of
the musical scales themselves. The lülü
also has a cosmological value: its notes describe
the energetic frequency of the twelve months
of the year, the daily rhythm of the twelve
bi-hours of the Chinese clock, the twelve
main acupuncture meridians, etc.The two sets
of tones (male and female) dividing the twelve-tone
scale were generated by the "Method of Subtracting
and Adding Thirds," or sanfen sunyi, which
involved alternately rising a fifth and descending
a fourth through the subtraction or addition
of a third of the length of the preceding
pitch pipe. The resulting pitches produced
by adding a third (and descending a fourth)
were referred to by Sima Qian in the Records
of the Grand Historian (91 BCE) as pitches
of "superior generation," that is, the pitches
of Ling Lun’s male phoenix; the pitches
produced by subtracting a third (and ascending
a fifth) were referred to as pitches of "inferior
generation," that is, the pitches of Ling
Lun’s female phoenix."Apart from technical
and structural aspects, ancient Chinese music
theory also discusses topics such as the nature
and functions of music. The Yueji ("Record
of music", c1st and 2nd centuries BCE), for
example, manifests Confucian moral theories
of understanding music in its social context.
Studied and implemented by Confucian scholar-officials
[...], these theories helped form a musical
Confucianism that overshadowed but did not
erase rival approaches. These include the
assertion of Mozi (c468–c376 BCE) that music
wasted human and material resources, and Laozi’s
claim that the greatest music had no sounds.
[...] Even the music of the qin zither, a
genre closely affiliated with Confucian scholar-officials,
includes many works with Daoist references,
such as Tianfeng huanpei ("Heavenly Breeze
and Sounds of Jade Pendants")."
==== India ====
The Samaveda and Yajurveda (c. 1200 – 1000
BCE) are among the earliest testimonies of
Indian music, but they contain no theory properly
speaking. The Natya Shastra, written between
200 BCE to 200 CE, discusses intervals (Śrutis),
scales (Grāmas), consonances and dissonances,
classes of melodic structure (Mūrchanās,
modes?), melodic types (Jātis), instruments,
etc.
==== Greece ====
Early preserved Greek writings on music theory
include two types of works:
technical manuals describing the Greek musical
system including notation, scales, consonance
and dissonance, rhythm, and types of musical
compositions
treatises on the way in which music reveals
universal patterns of order leading to the
highest levels of knowledge and understanding.Several
names of theorists are known before these
works, including Pythagoras (c. 570 – c.
495 BCE), Philolaus (c. 470 – c. 385 BCE),
Archytas (428–347 BCE), and others.
Works of the first type (technical manuals)
include
Anonymous (erroneously attributed to Euclid)
Division of the Canon, Κατατομή κανόνος,
4th–3rd century BCE.
Theon of Smyrna, On Mathematics Useful for
the Understanding of Plato, Τωv κατά
τό μαθηματικόν χρησίμων
είς τήν Πλάτωνος άνάγνωσις,
115–140 CE.
Nicomachus of Gerasa, Manual of Harmonics,
Άρμονικόν έγχειρίδιον,
100–150 CE
Cleonides, Introduction to Harmonics, Είσαγωγή
άρμονική, 2nd century CE.
Gaudentius, Harmonic Introduction, Άρμονική
είσαγωγή, 3d or 4th century CE.
Bacchius Geron, Introduction to the Art of
Music, Είσαγωγή τέχνης μουσικής,
4th century CE or later.
Alypius, Introduction to Music, Είσαγωγή
μουσική, 4th–5th century CE.More
philosophical treatises of the second type
include
Aristoxenus, Harmonic Elements, Άρμονικά
στοιχεία, 375/360 – after 320 BCE.
Aristoxenus, Rhythmic Elements, Ρυθμικά
στοιχεία.
Claudius Ptolemy, Harmonics, Άρμονικά,
127–148 CE.
Porphyrius, On Ptolemy's Harmonics, Είς
τά άρμονικά Πτολεμαίον
ύπόμνημα, 232/3-c. 305 CE.
=== Middle Ages ===
==== 
China ====
Some imported early Chinese instruments became
important components of the entertainment
music of the Sui (581–618) and Tang (618–907)
courts: the bent-neck pipa (quxiang pipa),
the bili, the konghou and the jiegu. They
generated not only new repertories and performing
practices but also new music theories. The
pipa, for example, carried with it a theory
of musical modes that subsequently led to
the Sui and Tang theory of 84 musical modes.
==== Arabic countries / Persian countries
====
Medieval Arabic music theorists include:
Abū Yūsuf Ya'qūb al-Kindi († Bagdad,
873 CE), who uses the first twelve letters
of the alphabet to describe the twelve frets
on five strings of the oud, producing a chromatic
scale of 25 degrees.
[Yaḥyā ibn] al-Munajjin (Baghdad, 856–912),
author of Risāla fī al-mūsīqī ("Treatise
on music", MS GB-Lbl Oriental 2361) which
describes a Pythagorean tuning of the oud
and a system of eight modes perhaps inspired
by Ishaq al-Mawsili (767–850).
Abū n-Nașr Muḥammad al-Fārābi (Persia,
872? – Damas, 950 or 951 CE), author of
Kitab al-Musiqa al-Kabir ("The Great Book
of Music").
`Ali ibn al-Husayn ul-Isfahānī (897–967),
known as Abu al-Faraj al-Isfahani, author
of Kitāb al-Aghānī ("The Book of Songs").
Abū 'Alī al-Ḥusayn ibn ʿAbd-Allāh ibn
Sīnā, known as Avicenna (c. 980 – 1037),
whose contribution to music theory consists
mainly in Chapter 12 of the section on mathematics
of his Kitab Al-Shifa ("The Book of Healing").
al-Ḥasan ibn Aḥmad ibn 'Ali al-Kātib,
author of Kamāl adab al Ghinā' ("The Perfection
of Musical Knowledge"), copied in 1225 (Istanbul,
Topkapi Museum, Ms 1727).
Safi al-Din al-Urmawi (1216–1294 CE), author
of the Kitabu al-Adwār ("Treatise of musical
cycles") and ar-Risālah aš-Šarafiyyah ("Epistle
to Šaraf").
Mubārak Šāh, commentator of Safi al-Din's
Kitāb al-Adwār (British Museum, Ms 823).
Anon. LXI, Anonymous commentary on Safi al-Din's
Kitāb al-Adwār.
Shams al-dῑn al-Saydᾱwῑ Al-Dhahabῑ
(14th Century CE (?)), music theorist. Author
of Urjῡza fi'l-mῡsῑqᾱ ("A Didatic
Poem on Music").
==== Europe ====
The Latin treatise De institutione musica
by the Roman philosopher Boethius (written
c. 500) was a touchstone for other writings
on music in medieval Europe. Boethius represented
Classical authority on music during the Middle
Ages, as the Greek writings on which he based
his work were not read or translated by later
Europeans until the 15th century. This treatise
carefully maintains distance from the actual
practice of music, focusing mostly on the
mathematical proportions involved in tuning
systems and on the moral character of particular
modes. Several centuries later, treatises
began to appear which dealt with the actual
composition of pieces of music in the plainchant
tradition. At the end of the ninth century,
Hucbald worked towards more precise pitch
notation for the neumes used to record plainchant.
Guido d'Arezzo' wrote in 1028 a letter to
Michael of Pomposa, entitled Epistola de ignoto
cantu, in which he introduced the practice
of using syllables to describe notes and intervals.
This was the source of the hexachordal solmization
that was to be used until the end of the Middle
Ages. Guido also wrote about emotional qualities
of the modes, the phrase structure of plainchant,
the temporal meaning of the neumes, etc.;
his chapters on polyphony "come closer to
describing and illustrating real music than
any previous account" in the Western tradition.During
the thirteenth century, a new rhythm system
called mensural notation grew out of an earlier,
more limited method of notating rhythms in
terms of fixed repetitive patterns, the so-called
rhythmic modes, which were developed in France
around 1200. An early form of mensural notation
was first described and codified in the treatise
Ars cantus mensurabilis ("The art of measured
chant") by Franco of Cologne (c. 1280). Mensural
notation used different note shapes to specify
different durations, allowing scribes to capture
rhythms which varied instead of repeating
the same fixed pattern; it is a proportional
notation, in the sense that each note value
is equal to two or three times the shorter
value, or half or a third of the longer value.
This same notation, transformed through various
extensions and improvements during the Renaissance,
forms the basis for rhythmic notation in European
classical music today.
=== Modern ===
==== 
China ====
==== Arabic countries ====
Bᾱqiyᾱ Nᾱyinῑ (Uzbekistan, 17th Century
CE), Uzbek author and music theorist. Author
of Zamzama e wahdat-i-mῡsῑqῑ ("The Chanting
of Unity in Music").
Baron Francois Rodolphe d'Erlanger (Tunis,
Tunisia, 1910–1932 CE), Arabic musicologist.
Author of La musique arabe and Ta'rῑkh al-mῡsῑqᾱ
al-arabiyya wa-usῡluha wa-tatawwurᾱtuha
("A History of Arabian Music, its principles
and its Development")D'Erlanger divulges that
the Arabic music scale is derived from the
Greek music scale, and that Arabic music is
connected to certain features of Arabic culture,
such as astrology.
==== Europe ====
===== Renaissance =====
===== 
Baroque =====
===== 1750–1900 =====
As Western musical influence spread throughout
the world in the 1800s, musicians adopted
Western theory as an international standard—but
other theoretical traditions in both textual
and oral traditions remain in use. For example,
the long and rich musical traditions unique
to ancient and current cultures of Africa
are primarily oral, but describe specific
forms, genres, performance practices, tunings,
and other aspects of music theory.Sacred Harp
music uses a different kind of scale and theory
in practice. The music focuses around the
solfege "fa, sol, la" on the music scale.
Sacred Harp also employs a different notation
involving "shape notes", or notes that are
shaped to correspond to a certain solfege
syllable on the music scale. Sacred Harp music
and its music theory originated with Reverend
Thomas Symmes in 1720, where he developed
a system for "singing by note" in order to
help his church members with note accuracy.
=== Contemporary ===
== 
Fundamentals of music ==
Music is composed of aural phenomena; "music
theory" considers how those phenomena apply
in music. Music theory considers melody, rhythm,
counterpoint, harmony, form, tonal systems,
scales, tuning, intervals, consonance, dissonance,
durational proportions, the acoustics of pitch
systems, composition, performance, orchestration,
ornamentation, improvisation, electronic sound
production, etc.
=== Pitch ===
Pitch is the lowness or highness of a tone,
for example the difference between middle
C and a higher C. The frequency of the sound
waves producing a pitch can be measured precisely,
but the perception of pitch is more complex
because single notes from natural sources
are usually a complex mix of many frequencies.
Accordingly, theorists often describe pitch
as a subjective sensation.Specific frequencies
are often assigned letter names. Today most
orchestras assign Concert A (the A above middle
C on the piano) to the frequency of 440 Hz.
This assignment is somewhat arbitrary; for
example, in 1859 France, the same A was tuned
to 435 Hz. Such differences can have a noticeable
effect on the timbre of instruments and other
phenomena. Thus, in historically informed
performance of older music, tuning is often
set to match the tuning used in the period
when it was written. Additionally, many cultures
do not attempt to standardize pitch, often
considering that it should be allowed to vary
depending on genre, style, mood, etc.
The difference in pitch between two notes
is called an interval. The most basic interval
is the unison, which is simply two notes of
the same pitch. The octave interval is two
pitches that are either double or half the
frequency of one another. The unique characteristics
of octaves gave rise to the concept of pitch
class: pitches of the same letter name that
occur in different octaves may be grouped
into a single "class" by ignoring the difference
in octave. For example, a high C and a low
C are members of the same pitch class—the
class that contains all C's. Musical tuning
systems, or temperaments, determine the precise
size of intervals. Tuning systems vary widely
within and between world cultures. In Western
culture, there have long been several competing
tuning systems, all with different qualities.
Internationally, the system known as equal
temperament is most commonly used today because
it is considered the most satisfactory compromise
that allows instruments of fixed tuning (e.g.
the piano) to sound acceptably in tune in
all keys.
=== Scales and modes ===
Notes can be arranged in a variety of scales
and modes. Western music theory generally
divides the octave into a series of twelve
tones, called a chromatic scale, within which
the interval between adjacent tones is called
a half step or semitone. Selecting tones from
this set of 12 and arranging them in patterns
of semitones and whole tones creates other
scales.The most commonly encountered scales
are the seven-toned major, the harmonic minor,
the melodic minor, and the natural minor.
Other examples of scales are the octatonic
scale and the pentatonic or five-tone scale,
which is common in folk music and blues. Non-Western
cultures often use scales that do not correspond
with an equally divided twelve-tone division
of the octave. For example, classical Ottoman,
Persian, Indian and Arabic musical systems
often make use of multiples of quarter tones
(half the size of a semitone, as the name
indicates), for instance in 'neutral' seconds
(three quarter tones) or 'neutral' thirds
(seven quarter tones)—they do not normally
use the quarter tone itself as a direct interval.In
traditional Western notation, the scale used
for a composition is usually indicated by
a key signature at the beginning to designate
the pitches that make up that scale. As the
music progresses, the pitches used may change
and introduce a different scale. Music can
be transposed from one scale to another for
various purposes, often to accommodate the
range of a vocalist. Such transposition raises
or lowers the overall pitch range, but preserves
the intervallic relationships of the original
scale. For example, transposition from the
key of C major to D major raises all pitches
of the scale of C major equally by a whole
tone. Since the interval relationships remain
unchanged, transposition may be unnoticed
by a listener, however other qualities may
change noticeably because transposition changes
the relationship of the overall pitch range
compared to the range of the instruments or
voices that perform the music. This often
affects the music's overall sound, as well
as having technical implications for the performers.The
interrelationship of the keys most commonly
used in Western tonal music is conveniently
shown by the circle of fifths. Unique key
signatures are also sometimes devised for
a particular composition. During the Baroque
period, emotional associations with specific
keys, known as the doctrine of the affections,
were an important topic in music theory, but
the unique tonal colorings of keys that gave
rise to that doctrine were largely erased
with the adoption of equal temperament. However,
many musicians continue to feel that certain
keys are more appropriate to certain emotions
than others. Indian classical music theory
continues to strongly associate keys with
emotional states, times of day, and other
extra-musical concepts and notably, does not
employ equal temperament.
=== Consonance and dissonance ===
Consonance and dissonance are subjective qualities
of the sonority of intervals that vary widely
in different cultures and over the ages.
Consonance (or concord) is the quality of
an interval or chord that seems stable and
complete in itself. Dissonance (or discord)
is the opposite in that it feels incomplete
and "wants to" resolve to a consonant interval.
Dissonant intervals seem to clash. Consonant
intervals seem to sound comfortable together.
Commonly, perfect fourths, fifths, and octaves
and all major and minor thirds and sixths
are considered consonant. All others are dissonant
to greater or lesser degree.Context and many
other aspects can affect apparent dissonance
and consonance. For example, in a Debussy
prelude, a major second may sound stable and
consonant, while the same interval may sound
dissonant in a Bach fugue. In the Common Practice
era, the perfect fourth is considered dissonant
when not supported by a lower third or fifth.
Since the early 20th century, Arnold Schoenberg’s
concept of "emancipated" dissonance, in which
traditionally dissonant intervals can be treated
as "higher," more remote consonances, has
become more widely accepted.
=== Rhythm ===
Rhythm is produced by the sequential arrangement
of sounds and silences in time. Meter measures
music in regular pulse groupings, called measures
or bars. The time signature or meter signature
specifies how many beats are in a measure,
and which value of written note is counted
or felt as a single beat.
Through increased stress, or variations in
duration or articulation, particular tones
may be accented. There are conventions in
most musical traditions for regular and hierarchical
accentuation of beats to reinforce a given
meter. Syncopated rhythms contradict those
conventions by accenting unexpected parts
of the beat. Playing simultaneous rhythms
in more than one time signature is called
polyrhythm.In recent years, rhythm and meter
have become an important area of research
among music scholars. The most highly cited
of these recent scholars are Maury Yeston,
Fred Lerdahl and Ray Jackendoff, Jonathan
Kramer, and Justin London.
=== Melody ===
A melody is a series of tones sounding in
succession that typically move toward a climax
of tension then resolve to a state of rest.
Because melody is such a prominent aspect
in so much music, its construction and other
qualities are a primary interest of music
theory.
The basic elements of melody are pitch, duration,
rhythm, and tempo. The tones of a melody are
usually drawn from pitch systems such as scales
or modes. Melody may consist, to increasing
degree, of the figure, motive, semi-phrase,
antecedent and consequent phrase, and period
or sentence. The period may be considered
the complete melody, however some examples
combine two periods, or use other combinations
of constituents to create larger form melodies.
=== Chord ===
A chord, in music, is any harmonic set of
three or more notes that is heard as if sounding
simultaneously. These need not actually be
played together: arpeggios and broken chords
may, for many practical and theoretical purposes,
constitute chords. Chords and sequences of
chords are frequently used in modern Western,
West African, and Oceanian music, whereas
they are absent from the music of many other
parts of the world.The most frequently encountered
chords are triads, so called because they
consist of three distinct notes: further notes
may be added to give seventh chords, extended
chords, or added tone chords. The most common
chords are the major and minor triads and
then the augmented and diminished triads.
The descriptions major, minor, augmented,
and diminished are sometimes referred to collectively
as chordal quality. Chords are also commonly
classed by their root note—so, for instance,
the chord C major may be described as a triad
of major quality built on the note C. Chords
may also be classified by inversion, the order
in which the notes are stacked.
A series of chords is called a chord progression.
Although any chord may in principle be followed
by any other chord, certain patterns of chords
have been accepted as establishing key in
common-practice harmony. To describe this,
chords are numbered, using Roman numerals
(upward from the key-note), per their diatonic
function. Common ways of notating or representing
chords in western music other than conventional
staff notation include Roman numerals, figured
bass (much used in the Baroque era), macro
symbols (sometimes used in modern musicology),
and various systems of chord charts typically
found in the lead sheets used in popular music
to lay out the sequence of chords so that
the musician may play accompaniment chords
or improvise a solo.
=== Harmony ===
In music, harmony is the use of simultaneous
pitches (tones, notes), or chords. The study
of harmony involves chords and their construction
and chord progressions and the principles
of connection that govern them. Harmony is
often said to refer to the "vertical" aspect
of music, as distinguished from melodic line,
or the "horizontal" aspect. Counterpoint,
which refers to the interweaving of melodic
lines, and polyphony, which refers to the
relationship of separate independent voices,
are thus sometimes distinguished from harmony.In
popular and jazz harmony, chords are named
by their root plus various terms and characters
indicating their qualities. For example, a
lead sheet may indicate chords such as C major,
D minor, and G dominant seventh. In many types
of music, notably Baroque, Romantic, modern,
and jazz, chords are often augmented with
"tensions". A tension is an additional chord
member that creates a relatively dissonant
interval in relation to the bass. Typically,
in the classical common practice period a
dissonant chord (chord with tension) "resolves"
to a consonant chord. Harmonization usually
sounds pleasant to the ear when there is a
balance between the consonant and dissonant
sounds. In simple words, that occurs when
there is a balance between "tense" and "relaxed"
moments.
=== Timbre ===
Timbre, sometimes called "color", or "tone
color," is the principal phenomenon that allows
us to distinguish one instrument from another
when both play at the same pitch and volume,
a quality of a voice or instrument often described
in terms like bright, dull, shrill, etc. It
is of considerable interest in music theory,
especially because it is one component of
music that has as yet, no standardized nomenclature.
It has been called "...the psychoacoustician's
multidimensional waste-basket category for
everything that cannot be labeled pitch or
loudness," but can be accurately described
and analyzed by Fourier analysis and other
methods because it results from the combination
of all sound frequencies, attack and release
envelopes, and other qualities that a tone
comprises.
Timbre is principally determined by two things:
(1) the relative balance of overtones produced
by a given instrument due its construction
(e.g. shape, material), and (2) the envelope
of the sound (including changes in the overtone
structure over time). Timbre varies widely
between different instruments, voices, and
to lesser degree, between instruments of the
same type due to variations in their construction,
and significantly, the performer's technique.
The timbre of most instruments can be changed
by employing different techniques while playing.
For example, the timbre of a trumpet changes
when a mute is inserted into the bell, the
player changes their embouchure, or volume.A
voice can change its timbre by the way the
performer manipulates their vocal apparatus,
(e.g. the shape of the vocal cavity or mouth).
Musical notation frequently specifies alteration
in timbre by changes in sounding technique,
volume, accent, and other means. These are
indicated variously by symbolic and verbal
instruction. For example, the word dolce (sweetly)
indicates a non-specific, but commonly understood
soft and "sweet" timbre. Sul tasto instructs
a string player to bow near or over the fingerboard
to produce a less brilliant sound. Cuivre
instructs a brass player to produce a forced
and stridently brassy sound. Accent symbols
like marcato (^) and dynamic indications (pp)
can also indicate changes in timbre.
==== Dynamics ====
In music, "dynamics" normally refers to variations
of intensity or volume, as may be measured
by physicists and audio engineers in decibels
or phons. In music notation, however, dynamics
are not treated as absolute values, but as
relative ones. Because they are usually measured
subjectively, there are factors besides amplitude
that affect the performance or perception
of intensity, such as timbre, vibrato, and
articulation.
The conventional indications of dynamics are
abbreviations for Italian words like forte
(f) for loud and piano (p) for soft. These
two basic notations are modified by indications
including mezzo piano (mp) for moderately
soft (literally "half soft") and mezzo forte
(mf) for moderately loud, sforzando or sforzato
(sfz) for a surging or "pushed" attack, or
fortepiano (fp) for a loud attack with a sudden
decrease to a soft level. The full span of
these markings usually range from a nearly
inaudible pianissississimo (pppp) to a loud-as-possible
fortissississimo (ffff).
Greater extremes of pppppp and fffff and nuances
such as p+ or più piano are sometimes found.
Other systems of indicating volume are also
used in both notation and analysis: dB (decibels),
numerical scales, colored or different sized
notes, words in languages other than Italian,
and symbols such as those for progressively
increasing volume (crescendo) or decreasing
volume (decrescendo), often called "hairpins"
when indicated with diverging or converging
lines as shown in the graphic above.
==== Articulation ====
Articulation is the way the performer sounds
notes. For example, staccato is the shortening
of duration compared to the written note value,
legato performs the notes in a smoothly joined
sequence with no separation. Articulation
is often described rather than quantified,
therefore there is room to interpret how to
execute precisely each articulation.
For example, staccato is often referred to
as "separated" or "detached" rather than having
a defined or numbered amount by which to reduce
the notated duration. Violin players use a
variety of techniques to perform different
qualities of staccato. The manner in which
a performer decides to execute a given articulation
is usually based on the context of the piece
or phrase, but many articulation symbols and
verbal instructions depend on the instrument
and musical period (e.g. viol, wind; classical,
baroque; etc.).
There are a set of articulations that most
instruments and voices perform in common.
They are—from long to short: legato (smooth,
connected); tenuto (pressed or played to full
notated duration); marcato (accented and detached);
staccato ("separated", "detached"); martelé
(heavily accented or "hammered"). Many of
these can be combined to create certain "in-between"
articulations. For example, portato is the
combination of tenuto and staccato. Some instruments
have unique methods by which to produce sounds,
such as spicatto for bowed strings, where
the bow bounces off the string.
=== Texture ===
In music, texture is how the melodic, rhythmic,
and harmonic materials are combined in a composition,
thus determining the overall quality of the
sound in a piece. Texture is often described
in regard to the density, or thickness, and
range, or width, between lowest and highest
pitches, in relative terms as well as more
specifically distinguished according to the
number of voices, or parts, and the relationship
between these voices. For example, a thick
texture contains many "layers" of instruments.
One of these layers could be a string section,
or another brass.
The thickness also is affected by the amount
and the richness of the instruments playing
the piece. The thickness varies from light
to thick. A lightly textured piece will have
light, sparse scoring. A thickly or heavily
textured piece will be scored for many instruments.
A piece's texture may be affected by the number
and character of parts playing at once, the
timbre of the instruments or voices playing
these parts and the harmony, tempo, and rhythms
used. The types categorized by number and
relationship of parts are analyzed and determined
through the labeling of primary textural elements:
primary melody, secondary melody, parallel
supporting melody, static support, harmonic
support, rhythmic support, and harmonic and
rhythmic support.Common types included monophonic
texture (a single melodic voice, such as a
piece for solo soprano or solo flute), biphonic
texture (two melodic voices, such as a duo
for bassoon and flute in which the bassoon
plays a drone note and the flute plays the
melody), polyphonic texture and homophonic
texture (chords accompanying a melody).
=== Form or structure ===
The term musical form (or musical architecture)
refers to the overall structure or plan of
a piece of music, and it describes the layout
of a composition as divided into sections.
In the tenth edition of The Oxford Companion
to Music, Percy Scholes defines musical form
as "a series of strategies designed to find
a successful mean between the opposite extremes
of unrelieved repetition and unrelieved alteration."
According to Richard Middleton, musical form
is "the shape or structure of the work." He
describes it through difference: the distance
moved from a repeat; the latter being the
smallest difference. Difference is quantitative
and qualitative: how far, and of what type,
different. In many cases, form depends on
statement and restatement, unity and variety,
and contrast and connection.
=== Expression ===
Musical expression is the art of playing or
singing music with emotional communication.
The elements of music that comprise expression
include dynamic indications, such as forte
or piano, phrasing, differing qualities of
timbre and articulation, color, intensity,
energy and excitement. All of these devices
can be incorporated by the performer. A performer
aims to elicit responses of sympathetic feeling
in the audience, and to excite, calm or otherwise
sway the audience's physical and emotional
responses. Musical expression is sometimes
thought to be produced by a combination of
other parameters, and sometimes described
as a transcendent quality that is more than
the sum of measurable quantities such as pitch
or duration.
Expression on instruments can be closely related
to the role of the breath in singing, and
the voice's natural ability to express feelings,
sentiment and deep emotions. Whether these
can somehow be categorized is perhaps the
realm of academics, who view expression as
an element of musical performance that embodies
a consistently recognizable emotion, ideally
causing a sympathetic emotional response in
its listeners. The emotional content of musical
expression is distinct from the emotional
content of specific sounds (e.g., a startlingly-loud
'bang') and of learned associations (e.g.,
a national anthem), but can rarely be completely
separated from its context.The components
of musical expression continue to be the subject
of extensive and unresolved dispute.
=== Notation ===
Musical notation is the written or symbolized
representation of music. This is most often
achieved by the use of commonly understood
graphic symbols and written verbal instructions
and their abbreviations. There are many systems
of music notation from different cultures
and different ages. Traditional Western notation
evolved during the Middle Ages and remains
an area of experimentation and innovation.In
the 2000s, computer file formats have become
important as well. Spoken language and hand
signs are also used to symbolically represent
music, primarily in teaching.
In standard Western music notation, tones
are represented graphically by symbols (notes)
placed on a staff or staves, the vertical
axis corresponding to pitch and the horizontal
axis corresponding to time. Note head shapes,
stems, flags, ties and dots are used to indicate
duration. Additional symbols indicate keys,
dynamics, accents, rests, etc. Verbal instructions
from the conductor are often used to indicate
tempo, technique, and other aspects.
In Western music, a range of different music
notation systems are used. In Western Classical
music, conductors use printed scores that
show all of the instruments' parts and orchestra
members read parts with their musical lines
written out. In popular styles of music, much
less of the music may be notated. A rock band
may go into a recording session with just
a handwritten chord chart indicating the song's
chord progression using chord names (e.g.,
C major, D minor, G7, etc.). All of the chord
voicings, rhythms and accompaniment figures
are improvised by the band members.
== Music theory as academic discipline ==
The scholarly study of music theory in the
twentieth century has a number of different
subfields, each of which takes a different
perspective on what are the primary phenomenon
of interest and the most useful methods for
investigation.
=== Analysis ===
Musical analysis is the attempt to answer
the question how does this music work? The
method employed to answer this question, and
indeed exactly what is meant by the question,
differs from analyst to analyst, and according
to the purpose of the analysis. According
to Ian Bent, "analysis, as a pursuit in its
own right, came to be established only in
the late 19th century; its emergence as an
approach and method can be traced back to
the 1750s. However, it existed as a scholarly
tool, albeit an auxiliary one, from the Middle
Ages onwards." Adolf Bernhard Marx was influential
in formalising concepts about composition
and music understanding towards the second
half of the 19th century. The principle of
analysis has been variously criticized, especially
by composers, such as Edgard Varèse's claim
that, "to explain by means of [analysis] is
to decompose, to mutilate the spirit of a
work".Schenkerian analysis is a method of
musical analysis of tonal music based on the
theories of Heinrich Schenker (1868–1935).
The goal of a Schenkerian analysis is to interpret
the underlying structure of a tonal work and
to help reading the score according to that
structure. The theory's basic tenets can be
viewed as a way of defining tonality in music.
A Schenkerian analysis of a passage of music
shows hierarchical relationships among its
pitches, and draws conclusions about the structure
of the passage from this hierarchy. The analysis
makes use of a specialized symbolic form of
musical notation that Schenker devised to
demonstrate various techniques of elaboration.
The most fundamental concept of Schenker's
theory of tonality may be that of tonal space.
The intervals between the notes of the tonic
triad form a tonal space that is filled with
passing and neighbour notes, producing new
triads and new tonal spaces, open for further
elaborations until the surface of the work
(the score) is reached.
Although Schenker himself usually presents
his analyses in the generative direction,
starting from the fundamental structure (Ursatz)
to reach the score, the practice of Schenkerian
analysis more often is reductive, starting
from the score and showing how it can be reduced
to its fundamental structure. The graph of
the Ursatz is arrhythmic, as is a strict-counterpoint
cantus firmus exercise. Even at intermediate
levels of the reduction, rhythmic notation
(open and closed noteheads, beams and flags)
shows not rhythm but the hierarchical relationships
between the pitch-events. Schenkerian analysis
is subjective. There is no mechanical procedure
involved and the analysis reflects the musical
intuitions of the analyst. The analysis represents
a way of hearing (and reading) a piece of
music.
Transformational theory is a branch of music
theory developed by David Lewin in the 1980s,
and formally introduced in his 1987 work,
Generalized Musical Intervals and Transformations.
The theory, which models musical transformations
as elements of a mathematical group, can be
used to analyze both tonal and atonal music.
The goal of transformational theory is to
change the focus from musical objects—such
as the "C major chord" or "G major chord"—to
relations between objects. Thus, instead of
saying that a C major chord is followed by
G major, a transformational theorist might
say that the first chord has been "transformed"
into the second by the "Dominant operation."
(Symbolically, one might write "Dominant(C
major) = G major.") While traditional musical
set theory focuses on the makeup of musical
objects, transformational theory focuses on
the intervals or types of musical motion that
can occur. According to Lewin's description
of this change in emphasis, "[The transformational]
attitude does not ask for some observed measure
of extension between reified 'points'; rather
it asks: 'If I am at s and wish to get to
t, what characteristic gesture should I perform
in order to arrive there?'"
=== Music perception and cognition ===
Music psychology or the psychology of music
may be regarded as a branch of both psychology
and musicology. It aims to explain and understand
musical behavior and experience, including
the processes through which music is perceived,
created, responded to, and incorporated into
everyday life. Modern music psychology is
primarily empirical; its knowledge tends to
advance on the basis of interpretations of
data collected by systematic observation of
and interaction with human participants. Music
psychology is a field of research with practical
relevance for many areas, including music
performance, composition, education, criticism,
and therapy, as well as investigations of
human aptitude, skill, intelligence, creativity,
and social behavior.
Music psychology can shed light on non-psychological
aspects of musicology and musical practice.
For example, it contributes to music theory
through investigations of the perception and
computational modelling of musical structures
such as melody, harmony, tonality, rhythm,
meter, and form. Research in music history
can benefit from systematic study of the history
of musical syntax, or from psychological analyses
of composers and compositions in relation
to perceptual, affective, and social responses
to their music. Ethnomusicology can benefit
from psychological approaches to the study
of music cognition in different cultures.
=== Genre and technique ===
A music genre is a conventional category that
identifies some pieces of music as belonging
to a shared tradition or set of conventions.
It is to be distinguished from musical form
and musical style, although in practice these
terms are sometimes used interchangeably.Music
can be divided into different genres in many
different ways. The artistic nature of music
means that these classifications are often
subjective and controversial, and some genres
may overlap. There are even varying academic
definitions of the term genre itself. In his
book Form in Tonal Music, Douglass M. Green
distinguishes between genre and form. He lists
madrigal, motet, canzona, ricercar, and dance
as examples of genres from the Renaissance
period. To further clarify the meaning of
genre, Green writes, "Beethoven's Op. 61 and
Mendelssohn's Op. 64 are identical in genre—both
are violin concertos—but different in form.
However, Mozart's Rondo for Piano, K. 511,
and the Agnus Dei from his Mass, K. 317 are
quite different in genre but happen to be
similar in form." Some, like Peter van der
Merwe, treat the terms genre and style as
the same, saying that genre should be defined
as pieces of music that came from the same
style or "basic musical language."Others,
such as Allan F. Moore, state that genre and
style are two separate terms, and that secondary
characteristics such as subject matter can
also differentiate between genres. A music
genre or subgenre may also be defined by the
musical techniques, the style, the cultural
context, and the content and spirit of the
themes. Geographical origin is sometimes used
to identify a music genre, though a single
geographical category will often include a
wide variety of subgenres. Timothy Laurie
argues that "since the early 1980s, genre
has graduated from being a subset of popular
music studies to being an almost ubiquitous
framework for constituting and evaluating
musical research objects".Musical technique
is the ability of instrumental and vocal musicians
to exert optimal control of their instruments
or vocal cords to produce precise musical
effects. Improving technique generally entails
practicing exercises that improve muscular
sensitivity and agility. To improve technique,
musicians often practice fundamental patterns
of notes such as the natural, minor, major,
and chromatic scales, minor and major triads,
dominant and diminished sevenths, formula
patterns and arpeggios. For example, triads
and sevenths teach how to play chords with
accuracy and speed. Scales teach how to move
quickly and gracefully from one note to another
(usually by step). Arpeggios teach how to
play broken chords over larger intervals.
Many of these components of music are found
in compositions, for example, a scale is a
very common element of classical and romantic
era compositions.Heinrich Schenker argued
that musical technique's "most striking and
distinctive characteristic" is repetition.
Works known as études (meaning "study") are
also frequently used for the improvement of
technique.
=== Mathematics ===
Music theorists sometimes use mathematics
to understand music, and although music has
no axiomatic foundation in modern mathematics,
mathematics is "the basis of sound" and sound
itself "in its musical aspects... exhibits
a remarkable array of number properties",
simply because nature itself "is amazingly
mathematical". The attempt to structure and
communicate new ways of composing and hearing
music has led to musical applications of set
theory, abstract algebra and number theory.
Some composers have incorporated the golden
ratio and Fibonacci numbers into their work.
There is a long history of examining the relationships
between music and mathematics. Though ancient
Chinese, Egyptians and Mesopotamians are known
to have studied the mathematical principles
of sound, the Pythagoreans (in particular
Philolaus and Archytas) of ancient Greece
were the first researchers known to have investigated
the expression of musical scales in terms
of numerical ratios.
In the modern era, musical set theory uses
the language of mathematical set theory in
an elementary way to organize musical objects
and describe their relationships. To analyze
the structure of a piece of (typically atonal)
music using musical set theory, one usually
starts with a set of tones, which could form
motives or chords. By applying simple operations
such as transposition and inversion, one can
discover deep structures in the music. Operations
such as transposition and inversion are called
isometries because they preserve the intervals
between tones in a set. Expanding on the methods
of musical set theory, some theorists have
used abstract algebra to analyze music. For
example, the pitch classes in an equally tempered
octave form an abelian group with 12 elements.
It is possible to describe just intonation
in terms of a free abelian group.
=== Serial composition and set theory ===
In music theory, serialism is a method or
technique of composition that uses a series
of values to manipulate different musical
elements. Serialism began primarily with Arnold
Schoenberg's twelve-tone technique, though
his contemporaries were also working to establish
serialism as one example of post-tonal thinking.
Twelve-tone technique orders the twelve notes
of the chromatic scale, forming a row or series
and providing a unifying basis for a composition's
melody, harmony, structural progressions,
and variations. Other types of serialism also
work with sets, collections of objects, but
not necessarily with fixed-order series, and
extend the technique to other musical dimensions
(often called "parameters"), such as duration,
dynamics, and timbre. The idea of serialism
is also applied in various ways in the visual
arts, design, and architecture"Integral serialism"
or "total serialism" is the use of series
for aspects such as duration, dynamics, and
register as well as pitch. Other terms, used
especially in Europe to distinguish post–World
War II serial music from twelve-tone music
and its American extensions, are "general
serialism" and "multiple serialism".Musical
set theory provides concepts for categorizing
musical objects and describing their relationships.
Many of the notions were first elaborated
by Howard Hanson (1960) in connection with
tonal music, and then mostly developed in
connection with atonal music by theorists
such as Allen Forte (1973), drawing on the
work in twelve-tone theory of Milton Babbitt.
The concepts of set theory are very general
and can be applied to tonal and atonal styles
in any equally tempered tuning system, and
to some extent more generally than that.One
branch of musical set theory deals with collections
(sets and permutations) of pitches and pitch
classes (pitch-class set theory), which may
be ordered or unordered, and can be related
by musical operations such as transposition,
inversion, and complementation. The methods
of musical set theory are sometimes applied
to the analysis of rhythm as well.
=== Musical semiotics ===
Music semiology (semiotics) is the study of
signs as they pertain to music on a variety
of levels. Following Roman Jakobson, Kofi
Agawu adopts the idea of musical semiosis
being introversive or extroversive—that
is, musical signs within a text and without.
"Topics," or various musical conventions (such
as horn calls, dance forms, and styles), have
been treated suggestively by Agawu, among
others. The notion of gesture is beginning
to play a large role in musico-semiotic enquiry.
"There are strong arguments that music inhabits
a semiological realm which, on both ontogenetic
and phylogenetic levels, has developmental
priority over verbal language."Writers on
music semiology include Kofi Agawu (on topical
theory, Heinrich Schenker, Robert Hatten (on
topic, gesture), Raymond Monelle (on topic,
musical meaning), Jean-Jacques Nattiez (on
introversive taxonomic analysis and ethnomusicological
applications), Anthony Newcomb (on narrativity),
and Eero Tarasti (generally considered the
founder of musical semiotics).
Roland Barthes, himself a semiotician and
skilled amateur pianist, wrote about music
in Image-Music-Text, The Responsibilities
of Form, and Eiffel Tower, though he did not
consider music to be a semiotic system.
Signs, meanings in music, happen essentially
through the connotations of sounds, and through
the social construction, appropriation and
amplification of certain meanings associated
with these connotations. The work of Philip
Tagg (Ten Little Tunes, Fernando the Flute,
Music’s Meanings) provides one of the most
complete and systematic analysis of the relation
between musical structures and connotations
in western and especially popular, television
and film music. The work of Leonard Meyer
in Style and Music theorizes the relationship
between ideologies and musical structures
and the phenomena of style change, and focuses
on romanticism as a case study.
=== Education and careers ===
Music theory in the practical sense has been
a part of education at conservatories and
music schools for centuries, but the status
music theory currently has within academic
institutions is relatively recent. In the
1970s, few universities had dedicated music
theory programs, many music theorists had
been trained as composers or historians, and
there was a belief among theorists that the
teaching of music theory was inadequate and
that the subject was not properly recognised
as a scholarly discipline in its own right.
A growing number of scholars began promoting
the idea that music theory should be taught
by theorists, rather than composers, performers
or music historians. This led to the founding
of the Society for Music Theory in the United
States in 1977. In Europe, the French Société
d'Analyse musicale was founded in 1985. It
called the First European Conference of Music
Analysis for 1989, which resulted in the foundation
of the Société belge d'Analyse musicale
in Belgium and the Gruppo analisi e teoria
musicale in Italy the same year, the Society
for Music Analysis in the UK in 1991, the
Vereniging voor Muziektheorie in the Netherlands
in 1999 and the Gesellschaft für Musiktheorie
in Germany in 2000. They were later followed
by the Russian Society for Music Theory in
2013 and the Polish Society for Music Analysis
in 2015, and others are in construction. These
societies coordinate the publication of music
theory scholarship and support the professional
development of music theory researchers.
As part of their initial training, music theorists
will typically complete a B.Mus or a B.A.
in music (or a related field) and in many
cases an M.A. in music theory. Some individuals
apply directly from a bachelor's degree to
a Ph.D, and in these cases, they may not receive
an M.A. In the 2010s, given the increasingly
interdisciplinary nature of university graduate
programs, some applicants for music theory
Ph.D programs may have academic training both
in music and outside of music (e.g., a student
may apply with a B.Mus and a Masters in Music
Composition or Philosophy of Music).
Most music theorists work as instructors,
lecturers or professors in colleges, universities
or conservatories. The job market for tenure-track
professor positions is very competitive. Applicants
must hold a completed Ph.D or the equivalent
degree (or expect to receive one within a
year of being hired—called an "ABD", for
"All But Dissertation" stage) and (for more
senior positions) have a strong record of
publishing in peer-reviewed journals. Some
Ph.D-holding music theorists are only able
to find insecure positions as sessional lecturers.
The job tasks of a music theorist are the
same as those of a professor in any other
humanities discipline: teaching undergraduate
and/or graduate classes in this area of specialization
and, in many cases some general courses (such
as Music Appreciation or Introduction to Music
Theory), conducting research in this area
of expertise, publishing research articles
in peer-reviewed journals, authoring book
chapters, books or textbooks, traveling to
conferences to present papers and learn about
research in the field, and, if the program
includes a graduate school, supervising M.A.
and Ph.D students and giving them guidance
on the preparation of their theses and dissertations.
Some music theory professors may take on senior
administrative positions in their institution,
such as Dean or Chair of the School of Music.
== See also ==
AP Music Theory
Theory of painting
Musicology
List of music theorists
Music psychology
== 
Notes ==
== 
Sources ==
== 
Further reading ==
== External links ==
Dillen, Oscar van, Outline of basic music
theory (2011)
Why A Little Bit of Theory Matters
"Music Theory Online: Guides, Lessons & Exercises".
musictheoryhelp.co.uk. Retrieved 17 December
2017.
"Music basics | Arts and humanities". Khan
Academy. Retrieved 17 December 2017.
"Music Theory is". musictheoryis.com. Retrieved
17 December 2017.
