In music, harmony is the way different sounds are combined to create new and unique musical ideas. Theories of harmony help explain how different pitches or tones interact when they occur at the same time. These theories study harmonic elements like chords, textures, and tonalities, which are described, defined, and grouped into categories. Harmony includes two aspects: one related to how sounds exist at the same time (called the "vertical" dimension) and one related to how sounds change over time (called the "horizontal" dimension). Harmony often connects with other musical ideas such as melody, timbre, and form.

A strong focus on harmony is a key idea in Western music theory and practice. Studying harmony involves placing individual pitches next to each other to form chords, and then placing chords next to each other to create larger patterns called chord progressions. The rules that guide how these structures connect have been studied for centuries through both written theories and practical musical traditions.

Harmony is influenced by both music theory and the study of how humans hear sounds (called psychoacoustics). The way people perceive harmony often involves recognizing consonance, which refers to how sounds that are pleasant to the ear are created. Consonance is often linked to simple mathematical relationships between the frequencies of sounds. In scientific terms, consonance is measured by how well the brain processes sound information. Culturally, consonant sounds are often described as pleasant, smooth, and beautiful, while dissonant sounds—those that are less pleasant—are described as harsh or rough.

In popular and jazz music, chords are named using their root note and additional terms that describe their qualities. In many types of music, including baroque, romantic, modern, and jazz, chords are often added with "tensions." A tension is an extra note in a chord that creates a dissonant sound when compared to the lowest note in the chord. The study of counterpoint explores how different melodies interact, especially in music with multiple independent melodies played at the same time. This can sometimes be considered a type of harmony, or it may be treated as a separate concept.

During the classical common practice period, a dissonant chord (a chord with tension) usually moves to a consonant chord. Harmony sounds pleasant when there is a balance between consonance and dissonance. This happens when music has a mix of "tense" and "relaxed" moments. Dissonance plays an important role in harmony when it is resolved and helps shape the overall musical composition. A note that is played incorrectly or a sound that disrupts the overall musical piece can be called disharmonious rather than dissonant.

Etymology and definitions

The word "harmony" comes from the Greek word "harmonia," which means "joint, agreement, or concord." This word is connected to the Greek verb "harmozō," meaning "to fit together or join." A Greek writer named Aristoxenus wrote a book called Elements of Harmony, which is believed to be the first European work about harmony. In this book, Aristoxenus described earlier experiments by the Pythagoreans, who studied how small whole-number ratios relate to musical notes. For example, the ratio 1:2 represents an octave, which means a sound’s frequency doubles. Although Aristoxenus was influenced by the Pythagoreans, he argued that numbers alone do not determine harmony. Instead, he believed that how people hear music determines what sounds harmonious.

Modern dictionary definitions of harmony are often brief but highlight its unclear meaning today. This confusion comes from two areas: one is how people judge what sounds pleasing, and the other is how harmony is used in music. For example, "harmonic" refers to sounds that happen at the same time, while "contrapuntal" refers to sounds that follow one after another. According to A. Whittall, many music experts believe that modern harmony in Western music began around 1600. This change is often linked to a shift from Renaissance music, which focused on horizontal (contrapuntal) composition, to music that emphasized vertical harmony. However, some modern scholars disagree with this idea.

Carl Dahlhaus noted that descriptions of harmony often focus on European (or Western) traditions, even though many cultures use vertical harmony. For example, South Asian music, such as Hindustani and Carnatic music, does not emphasize harmony in the same way as Western music. Instead, these traditions often use a "drone," which is a sustained note that remains unchanged throughout a piece. In South Asian music, the simultaneous occurrence of pitches is not a major focus. However, other musical elements, such as the system of ragas (which combine melody and mode), are important.

In Indian classical music, simultaneous pitches are used, but they are not typically studied as step-by-step harmonic or contrapuntal changes like in Western music. This difference is reflected in performance styles: Indian music relies heavily on improvisation, while Western music has rarely used improvisation since the late 1800s. When improvisation does occur in Western music, it usually adds to pre-written music or follows established models, using familiar harmonic patterns.

The focus on precomposed music in European art music and its written theory shows a strong cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) explains that the development of harmony in Western music was helped by the practice of writing music down first. This allowed theorists and composers to study and analyze specific works where pitches (and sometimes rhythms) remained the same, no matter how the music was performed.

Historical rules

Early Western religious music often used parallel intervals that kept the clear sound of plainsong. These pieces were created and performed in cathedrals, where the natural sound patterns helped create harmonies. As polyphony developed, the use of parallel intervals was gradually replaced by the English style of consonance, which used thirds and sixths. The English style was thought to have a softer sound and allowed for more flexibility in writing music for different parts.

Types

Carl Dahlhaus (1990) explains the difference between coordinate and subordinate harmony. Subordinate harmony refers to the organized musical structure, or tonal harmony, that is widely used today. Coordinate harmony describes the older style of music from the Medieval and Renaissance periods, called "tonalité ancienne." This term means that sounds are connected in a sequence without creating the sense of moving toward a specific goal. For example, one chord forms a "progression" with the next chord, and the next chord forms a progression with the one after it. However, each progression is separate and does not depend on the others. Coordinate harmony uses direct, neighboring relationships between sounds, unlike subordinate harmony, which uses indirect relationships. Interval cycles create balanced and repeated harmonies. These have been used by composers such as Alban Berg, George Perle, Arnold Schoenberg, Béla Bartók, and Edgard Varèse in his work Density 21.5.

Close harmony and open harmony use close position and open position chords, respectively. For more information, see: Voicing (music) and Close and open harmony.

Other types of harmony are based on the intervals used in the chords. Most chords in Western music are built using "tertian" harmony, which means they are made with intervals of thirds. For example, in the chord C Major7, the interval between C and E is a major third, between E and G is a minor third, and between G and B is a major third. Other types of harmony include quartal harmony, which uses intervals of fourths, and quintal harmony, which uses intervals of fifths.

A unison is a harmonic interval, like a third or a fifth, but it is unique because it involves two identical notes played together. In orchestration, unison is important. In pop music, singing the same notes at the same time is often called "doubling," a technique used by The Beatles in their early recordings. When musicians play the same notes simultaneously, using different instruments, it is called "monophonic harmonization."

Intervals

An interval is the relationship between two different musical pitches. For example, in the melody "Twinkle Twinkle Little Star," the interval between the first two notes (the first "twinkle") and the second two notes (the second "twinkle") is called a fifth. This means that if the first two notes were the pitch C, the second two notes would be the pitch G—four steps up the scale or seven steps on the chromatic scale (a perfect fifth) above it.

Common intervals include:

When tuning notes using equal temperament, such as the 12-tone equal temperament used in Western music, each interval is created using equal steps. This makes the intervals slightly less accurate than the pure ratios used by ancient Greeks. Equal temperament was developed as a compromise from older systems, like just intonation and well temperament, where intervals were based on a chosen root frequency. In those systems, a major third starting from C did not match a minor third starting from D♭. Many instruments, such as keyboards and fretted instruments, were designed to play notes like G♯ and A♭ without needing to be retuned. These notes (even those like E and F♭) were not the same note in any way.

Using the diatonic scale, major and minor keys can be built with each of the 12 notes as the tonic by using only flats or sharps, never both. This is often shown as moving around the circle of fifths, where each step changes only one note's accidental. This allows additional accidentals to provide more detailed information about the music. Even outside of diatonic contexts, it is standard to use each letter of the alphabet only once when describing a scale.

A note spelled as F♭ has different harmonic meaning compared to a note spelled as E. In some tuning systems, notes that are spelled differently but sound the same are called enharmonic. Even though they may sound the same alone, different spellings help musicians understand the music better. For example, E is a major third above C, while F♭ is a diminished fourth above C. In a C major key, E is the third note of the scale, while F♭ might be part of a D♭ minor chord, a borrowed chord from outside the key.

The combination of notes with specific intervals forms a chord, which creates harmony. For example, a C chord has three notes: C, E, and G. The note C is the root. The notes E and G create harmony. In a G7 (G dominant 7th) chord, the root G and the notes B, D, and F create harmony.

In a musical scale, there are twelve pitches. Each pitch is called a "degree" of the scale. The names A, B, C, D, E, F, and G are not important. The intervals are. For example:

As shown, no note is always the same scale degree. The tonic, or first-degree note, can be any of the 12 notes in the chromatic scale. All other notes adjust accordingly. For example, when C is the tonic, the fourth degree (subdominant) is F. When D is the tonic, the fourth degree is G. While the note names stay the same, they can refer to different scale degrees, meaning different intervals in relation to the tonic. This allows any piece of music to be played in any key, as long as the intervals remain the same. When intervals go beyond the perfect octave (12 semitones), they are called compound intervals. These include the 9th, 11th, and 13th, which are widely used in jazz and blues music.

Compound intervals are formed and named as follows:
• 2nd + Octave = 9th
• 3rd + Octave = 10th
• 4th + Octave = 11th
• 5th + Octave = 12th
• 6th + Octave = 13th
• 7th + Octave = 14th

These numbers do not "add" because intervals are numbered starting from the root note (e.g., one step up is a 2nd). Adding them counts the root twice. Intervals can also be divided into consonant and dissonant. Consonant intervals create a feeling of relaxation, while dissonant intervals create tension. In tonal music, consonant intervals also mean they bring a sense of resolution, while dissonant intervals require resolution.

Consonant intervals include the perfect unison, octave, fifth, fourth, and major and minor thirds and sixths, along with their compound forms. An interval is called "perfect" when the harmonic relationship appears naturally in the overtone series (e.g., unison 1:1, octave 2:1, fifth 3:2, fourth 4:3). Other intervals, like seconds, thirds, sixths, and sevenths, are called "imperfect" because their harmonic relationships are not exact in the overtone series. In classical music, a perfect fourth above the bass may be considered dissonant in certain contexts. Intervals like seconds and sevenths (and their compound forms) are generally dissonant and require resolution.

The effect of dissonance depends on the musical context. For example, a major seventh interval (C to B) may sound dissonant alone but can sound more consonant when part of a major seventh chord. A tritone (F to B) sounds very dissonant alone but less so when part of a dominant seventh chord (G7 or D♭7).

Chords and tension

In Western music after the 1700s, harmony is created using chords, which are groups of notes. In tertian harmony, chords are built by stacking intervals of a third. This process starts with the "root" note, then adds a note a third above the root (called the "third"), and a note a third above the third (called the "fifth"). This pattern continues, and each note in the chord is named based on its distance from the root. Dyads, the simplest type of chord, include only two notes (such as power chords).

A chord with three notes is called a triad because it has three members, not because it is built in thirds. Depending on the size of the intervals used, different types of chords are formed. In popular and jazz music, chords are named using their root note plus terms that describe their qualities. For example, the notes C, E, and G form a C Major triad, which is often called simply a "C" chord. In an A♭ chord, the notes are A♭, C, and E♭.

In many styles of music, such as baroque, romantic, modern, and jazz, chords are often expanded with "tensions." A tension is an extra note that creates a dissonant sound when compared to the lowest note (the bass). Using the tertian method of stacking thirds, the first tension is added by placing a note a third above the fifth of a triad. This creates a note a seventh above the root, forming a four-note chord called a "seventh chord."

The size of the intervals used to build the chord determines the type of seventh chord. For example, the chord "C7" includes the notes C, E, G, and B♭. Other types of seventh chords are named more specifically, such as "C Major 7" (C, E, G, B) or "C augmented 7" (C, E, G♯, B♭).

Adding more thirds to a seventh chord creates "extensions," which are called "upper tensions" or "extended tensions." These include notes such as the ninth, eleventh, and thirteenth. These notes are more than an octave above the root when stacked in thirds. A ninth chord, for example, has five notes (root, third, fifth, seventh, ninth). Extensions beyond the thirteenth usually repeat notes already in the chord and are typically not included in the name. Extended chords are common in jazz, late-romantic music, and film scores.

In classical music, dissonant chords (chords with tension) often resolve to consonant chords (chords that sound smooth). This balance between dissonance and consonance creates a pleasing sound. Tension is usually introduced gradually through a series of consonant chords before a dissonant chord appears. After reaching a musical climax, a consonant chord is played to release the tension, providing a moment of relaxation for the listener. This resolution often sounds pleasant, though it may not always be the case in certain works, such as Richard Wagner’s Tristan und Isolde.

Perception

A number of features influence how people hear the harmony of a chord.

Tonal fusion helps people hear chords as more harmonious. It describes how well multiple pitches are heard as one unified tone. Chords with more matching partials (frequency parts) are heard as more harmonious. For example, octaves and perfect fifths are more harmonious because their sound waves look similar to a single tone. According to this idea, major triads blend better than minor triads, and major-minor seventh chords blend better than major-major or minor-minor seventh chords. These differences may not be obvious in certain musical systems, but they explain why major triads and major-minor sevenths are more common in traditional music than other types, even though some intervals, like the tritone, sound dissonant.

In organ registers, pressing one key can produce multiple harmonic intervals and chords at once. The sounds combine into one tone with a new sound quality. This blending effect is also used in synthesizers and orchestral music. For example, in Ravel’s Bolero, the flute, horn, and celesta parts sound like an electric organ.

When nearby harmonics in complex tones interfere, they create a sound called "beating" or "roughness." These effects are closely linked to how dissonant chords sound. For interference to occur, the partials must be within a critical bandwidth, which measures how well the ear can separate different pitches. Critical bandwidth is between 2 and 3 semitones at high pitches and increases at lower pitches. The most dissonant interval in the chromatic scale is the minor second and its opposite, the major seventh. For typical sound patterns in the middle range, the next most dissonant intervals are the major second and minor seventh, followed by the tritone, minor third (major sixth), major third (minor sixth), and perfect fourth (fifth).

Familiarity also affects how harmonious an interval sounds. Chords people hear often in music tend to sound more harmonious. This idea explains the gradual increase in harmonic complexity in Western music over time. For example, around 1600, seventh chords became more familiar and were gradually heard as more harmonious.

Age and musical experience also influence how people perceive harmony.

The inferior colliculus is a brain structure that first combines sounds from both ears. Brain responses called frequency following responses (FFRs) show peaks that match the frequencies of a sound. How well FFRs represent the harmonic parts of a chord is called neural salience, and this is linked to how pleasant people find chords.

The brain also responds more strongly to chords that are more harmonious.