Music theory is the study of ideas and rules that help people understand how music is created and performed. The Oxford Companion to Music explains three main ways the term "music theory" is used: First, it includes basic knowledge needed to read music, such as key signatures, time signatures, and rhythm. Second, it involves studying how scholars from ancient times to today have thought about music. Third, it is a part of musicology, which looks for general rules and patterns in music. Musicology focuses on the basic materials of music, not just individual songs or performances.

Music theory often describes how musicians and composers create music, including topics like tuning systems and ways to write music. As ideas about what music is have changed over time, some people now think music theory should include any sounds, even silence. However, this is not always the case. For example, in medieval Europe, a part of the Quadrivium curriculum studied an abstract system of proportions, not directly connected to real music. This system later influenced tuning methods and is still studied today in music history.

As a practical skill, music theory includes the methods and ideas composers and musicians use to create and perform music. These ideas are passed down through oral traditions, written music, instruments, and other objects. For example, ancient instruments found in prehistoric places give clues about the music they made and the theories that might have guided their creation. In many cultures around the world, music theory has deep roots in instruments, oral traditions, and current music. Some cultures have also written formal rules about music, such as treatises and written notation. Practical and scholarly traditions often connect, as many music writings reference earlier works, just like research in other fields.

In modern schools, music theory is a part of musicology, which studies music cultures and history. In the late 1800s, Guido Adler, who helped create musicology, said that the study of music began when people started measuring pitches and comparing them. He believed that any culture with a musical tradition also has a way to study music, meaning music theory exists in all musical traditions worldwide.

Music theory often focuses on abstract ideas like tuning systems, scales, and rhythm. It also covers practical topics, such as writing music, arranging for an orchestra, adding musical details, improvising, and creating electronic sounds. A person who studies or teaches music theory is called a music theorist. In the United States, most music theorists have a master's or doctorate degree. They use methods like math, visual analysis, and written music notation to study music. Other methods, such as comparing different types of music or using statistics, are also used. Music theory books often include topics like how sound works, how to read music, and techniques for writing harmonies and counterpoint.

History

Several ancient clay tablets from Sumer and Akkadia contain information about music theory, such as lists of musical intervals and tunings. A scholar named Sam Mirelman says these texts date back to before 1500 BCE, which is about 1,000 years earlier than similar musical writings from other cultures. These Mesopotamian texts share a common way of describing music using specific terms, and these terms were used for over 1,000 years according to the dates of the texts.

Much about Chinese music history and theory is still unknown. Chinese music theory begins with numbers: twelve, five, and eight. Twelve refers to the number of pitches used to create scales. Five refers to the pentatonic scale, which uses five notes. Eight refers to the eight categories of Chinese musical instruments, grouped by the materials they are made from: metal, stone, silk, bamboo, gourd, clay, leather, and wood. A text called the Lüshi chunqiu, written around 238 BCE, tells a story about a man named Ling Lun. At the order of the Yellow Emperor, Ling Lun collected bamboo tubes with evenly spaced nodes. When he blew on one, he liked the sound and named it huangzhong, the "Yellow Bell." He then heard phoenixes singing, with each phoenix singing six tones. Ling Lun cut his bamboo tubes to match these tones, creating twelve pitch pipes in two groups: six from the male phoenix and six from the female. These were called lülü or later shierlü.

The Samaveda and Yajurveda (around 1200–1000 BCE) are among the earliest records of Indian music, but they do not include music theory. A text called the Natya Shastra, written between 200 BCE and 200 CE, discusses musical intervals, scales, consonance and dissonance, types of melodies, and musical instruments.

Early Greek writings about music theory include two kinds of works:
– Technical manuals that explain the Greek musical system, including notation, scales, rhythm, and types of music.
– Writings that explore how music reflects universal patterns of order and connects to knowledge and understanding.

Before these works, several theorists were known, such as Pythagoras (c. 570–495 BCE), Philolaus (c. 470–385 BCE), and Archytas (428–347 BCE).

Examples of technical manuals include:
– Division of the Canon (4th–3rd century BCE).
– On the Mathematics Useful for Understanding Plato (115–140 CE).
– Manual of Harmonics (100–150 CE).
– Introduction to Harmonics (2nd century CE).
– Harmonic Introduction (3rd or 4th century CE).
– Introduction to the Art of Music (4th century CE or later).
– Introduction to Music (4th–5th century CE).

Examples of philosophical writings include:
– Harmonic Elements (375–360 BCE).
– Rhythmic Elements (before 320 BCE).
– Harmonics (127–148 CE).
– On Ptolemy's Harmonics (c. 232–305 CE).

The pipa instrument carried a theory of musical modes that later influenced the Sui and Tang theories of 84 musical modes.

Medieval Arabic music theorists include:
– Abū Yūsuf Ya'qūb al-Kindi (873 CE), who used the first twelve letters of the alphabet to describe the twelve frets on five strings of the oud, creating a chromatic scale of 25 degrees.
– [Yaḥyā ibn] al-Munajjim (856–912), who wrote a treatise describing a Pythagorean tuning of the oud and a system of eight modes.
– Abū n-Nașr Muḥammad al-Fārābi (872?–950 or 951 CE), who wrote The Great Book of Music.
– 'Ali ibn al-Husayn ul-Isfahānī (897–967), who wrote The Book of Songs.
– Avicenna (c. 980–1037), who wrote about music in The Book of Healing.
– al-Ḥasan ibn Aḥmad ibn 'Ali al-Kātib, who wrote The Perfection of Musical Knowledge.
– Safi al-Din al-Urmawi (1216–1294 CE), who wrote Treatise of musical cycles and Epistle to Šaraf.
– Mubārak Šāh, who commented on Safi al-Din’s work.
– An anonymous commentary on Safi al-Din’s Treatise of musical cycles.
– Shams al-dῑn al-Sayyid (17th century), who wrote about music in Uzbekistan.

A medieval European text called Ars cantus mensurabilis (c. 1280) described a new rhythm system called mensural notation. This system used different note shapes to show different note lengths, allowing scribes to write music with varying rhythms instead of repeating fixed patterns. This system, improved over time, became the basis for rhythmic notation in European classical music.

Guido d'Arezzo wrote a letter in 1028 called Epistola de ignoto cantu, where he introduced using syllables to describe notes and intervals. This led to the hexachordal solmization system used in Western music until the end of the Middle Ages. Guido also wrote about the emotional qualities of musical modes, the structure of plainchant, and the meaning of symbols used to write music. His descriptions of polyphony were the first to closely describe real music in Western tradition.

Fundamentals of music

Music is made up of sounds you hear. Music theory studies how these sounds are used in music. It includes topics like melody, rhythm, how melodies work together, harmony, structure, sound systems, scales, tuning, pitch differences, how sounds are balanced or clash, how long notes last, how sound works in different spaces, writing music, playing music, arranging instruments, adding special sounds, making up music on the spot, and creating electronic sounds.

Pitch is how high or low a sound is. For example, middle C and a higher C have different pitches. The exact number of vibrations that create a pitch can be measured, but how people hear pitch is more complicated. Natural sounds often mix many vibrations, so theorists describe pitch as a feeling people have, not just a measurement.

Certain vibrations are given letter names. Most orchestras today use the note A above middle C as 440 Hz. This choice is not fixed; in 1859, France used 435 Hz for the same note. These differences can change how instruments sound. When performing older music, musicians often use the tuning that was common when the music was written. Many cultures do not set a standard pitch, letting it change based on the music's style or mood.

The difference in pitch between two notes is called an interval. The simplest interval is a unison, where two notes have the same pitch. An octave is an interval where one note has double or half the frequency of the other. Because octaves sound similar, theorists group all notes with the same letter name (like high C and low C) into a "pitch class."

Tuning systems decide how big or small intervals are. Different cultures use many types of tuning. In Western music, several systems have been used, but today, equal temperament is most common. This system allows instruments with fixed tuning, like pianos, to sound good in all musical keys.

Notes can be arranged into scales and modes. Western music divides the octave into 12 notes, called a chromatic scale. The space between each note is a semitone, or half step. Choosing and arranging these notes creates different scales.

Common scales include the major scale, harmonic minor, melodic minor, and natural minor. Other scales, like the octatonic and pentatonic (used in folk and blues music), also exist. Some cultures, like those in Ottoman, Persian, Indian, and Arabic music, use scales with smaller intervals, such as quarter tones.

In Western music, the scale used in a piece is shown by a key signature at the start. As music plays, the scale may change. Transposing a piece moves all its notes up or down in pitch but keeps the same relationships between notes. For example, moving from C major to D major raises all notes by a whole step. This change might not be noticed by listeners but can affect how the music sounds.

The circle of fifths shows how different keys in Western music are related. Some compositions use unique key signatures. During the Baroque period, certain keys were linked to emotions, but this idea faded with equal temperament. In Indian classical music, keys are still connected to emotions and other ideas, and equal temperament is not used.

Consonance and dissonance describe how intervals or chords sound. Consonance feels stable and harmonious, while dissonance feels unstable or clashing. In Western music, intervals like perfect fourths, fifths, and octaves, and major and minor thirds and sixths are considered consonant. Other intervals are dissonant.

How consonance and dissonance are heard can change based on context. For example, a major second might sound stable in a Debussy piece but dissonant in a Bach fugue. In the Common Practice era, a perfect fourth was dissonant unless supported by other notes. Since the early 20th century, some composers treat dissonant intervals as stable, a concept called "emancipated dissonance."

Rhythm is created by arranging sounds and silences over time. Meter divides music into regular groups of beats, called measures. The time signature shows how many beats are in each measure and which note value equals one beat.

Some notes are played louder than others, creating accents. Most traditions have rules for how beats are emphasized to support the meter. Syncopation breaks these rules by emphasizing unexpected parts of the beat. Playing different rhythms at the same time is called polyrhythm.

In recent years, scholars like Maury Yeston, Fred Lerdahl, Ray Jackendoff, Jonathan Kramer, and Justin London have studied rhythm and meter in detail.

A melody is a sequence of sounds that form a tune. It is often a key part of music, so how it is built is a major focus of music theory.

The basic parts of a melody are pitch, duration, rhythm, and tempo. Notes in a melody usually come from scales or modes. A melody can include patterns like motives, phrases, and periods.

As academic discipline

In the 20th century, experts studying music theory divided their work into different areas, each focusing on unique questions and methods to understand music. Musical analysis is the process of explaining how a piece of music works. Analysts use different methods depending on their goals and the type of music being studied. According to Ian Bent, the practice of analyzing music became a formal method in the late 19th century, though it was used informally by scholars as early as the Middle Ages. Adolf Bernhard Marx helped shape ideas about how music is composed and understood in the second half of the 19th century. Some composers, like Edgard Varèse, criticized analysis, arguing that breaking down music can harm its original meaning.

Schenkerian analysis is a method used to study tonal music, based on the ideas of Heinrich Schenker. This approach aims to uncover the hidden structure of a musical piece and explain how the notes in the score relate to that structure. Schenker’s theory describes how the spaces between notes in a chord create layers of musical relationships. He used a special type of notation to show how these layers build up to the final version of the music. A key idea in Schenker’s theory is "tonal space," which refers to the way notes in a chord are connected through passing and neighboring notes to form new chords and structures. While Schenker often explained his ideas by starting with the basic structure of a piece and building up to the full score, most modern Schenkerian analyses begin with the score and work backward to reveal the underlying structure. This method is subjective, as it relies on the analyst’s musical intuition rather than a fixed process.

Transformational theory, developed by David Lewin in the 1980s, is a way to study how music changes from one idea to another. Lewin introduced this theory in his 1987 book, Generalized Musical Intervals and Transformations. This approach focuses on the relationships between musical elements, such as chords, rather than the chords themselves. For example, instead of saying a C major chord is followed by a G major chord, a transformational theorist might describe the change as a "Dominant operation" that transforms the first chord into the second. Unlike traditional music theory, which studies the makeup of musical objects, transformational theory examines how music moves from one state to another, asking what steps are needed to get from one musical idea to another.

Music psychology is a field that studies how people experience and create music. It is part of both psychology and musicology and seeks to understand how music is heard, made, and used in daily life. Modern music psychology relies on experiments and observations to gather information about human behavior related to music. This field has practical uses in areas like music performance, teaching, and therapy. It also helps explain how people perceive musical structures such as melody, harmony, and rhythm. Music psychology can provide insights into how music is created and how people respond to it, even in areas not directly related to psychology, such as music history and theory.

A music genre is a way to group music into categories based on shared traditions or styles. It is different from musical form and style, though these terms are sometimes used interchangeably. Music can be divided into genres in many ways, but these categories are often subjective and may overlap. Some scholars, like Douglass M. Green, distinguish between genre and form, using examples like Renaissance-era madrigals and motets. Others, such as Peter van der Merwe, consider genre and style the same, while Allan F. Moore argues they are separate. Genres can also be defined by techniques, cultural context, and themes. Geographical origins are sometimes used to identify genres, though a single region may include many subgenres. Timothy Laurie notes that since the 1980s, genre has become a common framework for studying music.

Musical technique refers to a musician’s ability to control their instrument or voice to produce precise musical effects. Improving technique often involves practicing exercises that build muscle control and speed. Musicians commonly practice basic note patterns, such as major and minor scales, triads, and arpeggios, to develop accuracy and fluency. These exercises help musicians play chords and scales with precision and efficiency.