Tonal harmony

Tonal harmony is the system of chord relationships that organizes much Western music around a central chord, the tonic. It is commonly associated with the common-practice period, from the mid-17th century to the second half of the 19th.^[1:1] Theorists describe it using harmonic function, the categories of tonic, predominant and dominant chords, and through conventional progressions and cadences that mark the ends of phrases.^[2:1][2:2] Many of the same chords are used in popular music, but corpus studies of rock find that they are combined differently. Rock lacks the strong preference for particular directions of root motion that characterizes common-practice music.^[3:1]

The related term "tonality" is broader and contested. It can name a historical repertoire, the perception of keys and tonics, or a set of features shared by many musical styles.^[4:1][5:1]

History of the concept

Alexandre-Étienne Choron and François-Joseph Fétis introduced the term tonalité in the early 19th century; it first appears in print in a work by Choron and Fayelle published in 1810. They used it to sort ancient and modern music within an evolutionary narrative, and most music theorists regard Fétis as the originator of the concept. In his Histoire générale de la musique (1869), Fétis explicitly linked his concept of tonality to biological racism and white-supremacist thought.^[4:2]

Jason Yust argues that the term has two senses that do not fit together. In one, tonality is a practical, historical category that separates "tonal" from "post-tonal" repertoire, courses and analytical tools. In the other, it is a musical property concerned with the perception of keys and tonics. Yust contends that the combination perpetuates the term's racist origins and that music theory could drop the term without loss.^[4:1]

Theories of harmonic function

"Harmonic function" has never had a single agreed meaning. David Kopp lists several senses it has carried:

• the identity of a chord by its scale degree;
• a chord's tendency to move to another chord;
• a grouping of chords that behave alike;
• the primacy of the tonic, dominant and subdominant;
• a chord's role within a phrase.^[6:1]

Kopp contrasts three theorists commonly associated with the idea:

• Rameau (18th century) defined his tonique, dominante and sous-dominante by how chords move to the next chord, and explained those tendencies by dissonances added to the chord.
• Gottfried Weber (1820s) labelled chords with Roman numerals according to their position in a key. He had no concept of secondary dominants, so he analysed chromatic passages as rapid successions of modulations.
• Hugo Riemann, who popularized the term "function", treated tonic, dominant and subdominant as the three primary chords of a key. He related every diatonic and chromatic chord to one of them, so that chromatic music could be understood within a single key. Riemann's functions describe what chords mean rather than determining which chord comes next.^[6:2]

Harmonic function and the phrase model

Theory textbooks such as Open Music Theory group the chords of a key into three functions:

• Tonic: I (or i in minor), which sounds stable.
• Predominant: chords such as IV and ii, which lead away from the tonic toward the dominant.
• Dominant: V and vii°, which create a sense of urgency to resolve to the tonic.

The "phrase model" describes the usual order of these functions. A phrase needs at least tonic and dominant harmonies to have a sense of direction, often includes a predominant before the dominant, and almost always moves from tonic toward dominant rather than in reverse.^[2:1]

Trevor de Clercq and David Temperley stress that these principles are general norms that hold most of the time, not exceptionless laws. Research has nonetheless found that common-practice composers largely follow them.^[3:2] Yust describes harmonic function as specific to certain styles: the common practice (roughly 18th- and 19th-century European concert music) and later music that draws on it. In his account it developed in 18th-century Europe to make long-form dramatic instrumental music possible.^[4:3]

Cadences

Cadences are melodic and harmonic patterns that mark the end of a phrase and help establish a key. An authentic cadence ends with the progression V–I. It is "perfect" when both chords are in root position with the tonic note in the top voice, and "imperfect" otherwise. A half cadence ends on V and sounds inconclusive. Perfect authentic cadences are the strongest kind and half cadences the weakest.^[2:2]

Chord progressions and directedness

Moss and colleagues characterize tonal harmony along four dimensions:

• Centricity: a few central chords dominate.
• Referentiality: chords are oriented toward reference points such as the tonic.
• Directedness: some progressions are preferred over their reverse.
• Hierarchy: chords are nested within local keys, which in turn are nested within the key of the whole piece.^[1:1]

A progression from one chord to another is asymmetric if it occurs more often than its reverse. Such statistical regularities are thought to shape listeners' expectations through implicit learning. Root motion by a descending fifth, especially from V to I, is generally regarded as central to tonal harmony. Dissonant chords such as seventh chords and suspensions create specific expectations about which chord comes next.^[1:2]

Tonal harmony is closely tied to voice leading. Dmitri Tymoczko describes Western music as lying at the intersection of harmony, which determines which chords and chord sequences are acceptable, and counterpoint, which connects the notes of successive chords into simultaneous melodies.^[7:1] He argues that the consonant chords of tonal music divide the octave nearly evenly, which lets composers connect them by efficient, independent voice leading.^[7:2]

Corpus and computational study

Researchers have built machine-readable corpora of harmonic analyses to test claims about tonal harmony at scale. The Annotated Beethoven Corpus encodes expert Roman numeral analyses of all of Beethoven's string quartets. Its authors argue that raw audio or notation is not enough to study abstract structures such as harmony, and that musicology lacked large datasets pairing scores with harmonic analyses.^[8:1] The "When in Rome" meta-corpus brings together more than 2,000 such analyses of 1,500 works, mostly from the common-practice repertoire. Its compilers reject treating any analysis as "ground truth", because harmonic analysis is subjective and analysts legitimately disagree.^[9:1]

Analysing the Beethoven corpus, Moss and colleagues found that chord frequencies follow a power-law-like distribution, in which a few chords make up much of the data. Tonic and dominant chords alone account for more than 60% of chords in major-key passages and more than 50% in minor-key passages. They also found that progressions are directed in time, and that tonal harmony behaves differently at the level of chords than at the level of keys.^[1:3]

Corpus counts also show that textbook rules work as tendencies. Bach is known for carefully avoiding parallel fifths and octaves. Even so, a set of 382 Bach chorales used to train a machine-learning harmonizer contained 132 parallel fifths, about 0.023 per measure, and 51 parallel octaves. Many of these occur in circumstances that textbooks excuse, such as phrase boundaries or non-chord tones.^[10:1]

Much research in music cognition treats the distribution of pitch classes in a passage as the defining feature of a key. Yust identifies work by Krumhansl, Temperley, Aarden and Sapp as influential examples of this approach. Such pitch-class profiles are a standard tool for automatic key detection. They are often described as "tonal hierarchies" that rank pitch classes into notes outside the scale, scale notes outside the tonic triad, and notes of the tonic triad.^[4:4]

Popular and vernacular harmony

Rock and pop

De Clercq and Temperley analysed 100 highly ranked rock songs from the 1950s to the 1990s. They found that IV is the most common chord after I and is especially common just before the tonic.^[3:3] Unlike common-practice music, rock shows no strong preference for one direction of root motion over the other. Motion by a fourth is the most common in either direction. After IV and V, the next most common chords are VI and ♭VII. Songs from the 1950s use almost only I, IV and V, while later decades draw on a wider range of chords.^[3:1] The McGill Billboard dataset was created partly to support this kind of research at larger scale. It contains chord transcriptions of more than a thousand songs drawn at random from the US Billboard Hot 100 between 1958 and 1991.^[11:1]

Philip Tagg argues that conventional theory textbooks deal only with European classical music, and that their concepts of tonality fit many other musics poorly. He gives the example of the chord loop of "La Bamba", also heard in "Guantanamera", "Wild Thing" and "Twist and Shout". Tagg finds it unproductive to explain this loop in terms of tonic, subdominant and dominant.^[12:1] He describes ♭VI–♭VII–i as a widely used "aeolian cadence", the natural-minor counterpart of the major-key formula IV–V–I.^[12:2] In loop-based popular music, competent listeners sometimes hear different notes as the tonic of the same song. Yust argues that, for at least some popular styles, identifying a single tonic is not part of understanding the music.^[4:5]

Shape-note, gospel and bluegrass singing

In the United States, a separate tradition of harmony grew out of rural shape-note singing. Thirty-eight tunebooks in four-shape ("fasola") notation appeared between 1798 and 1855. The 1844 Sacred Harp was still widely used in the 1930s.^[13:1]

In 1933 George Pullen Jackson described how Sacred Harp harmony struck listeners trained in urban music as discordant. He attributed this mainly to the arrangement of parts: men sang most of the melody, and women sang a high middle part. Others pointed to the songs' successive fifths. The Sacred Harp composer Whit Denson pointed instead to their reliance on tonic and dominant chords and neglect of the subdominant. Many of the songs have pentatonic melodies or are in minor keys.^[13:2]

Shape-note books also brought harmony into congregations that had sung without it. In a 1982 study, Brett Sutton found that conservative Primitive Baptists in the Blue Ridge rejected harmony, written music and instruments. In more moderate congregations that adopted shape-note tunebooks, the books encouraged harmony singing and new songs.^[14:1]

From the 1840s, seven-shape notation displaced the four-shape books. After the Civil War, a "gospel-hymn-tinged" sacred music in shape notation developed in the rural South. Jackson identifies the influences on it as Sunday-school gospel hymns, secular popular song, the glee-club manner and jazz, and above all the spread of seven-shape notation.^[13:1]

Seven-shape gospel publishing also produced the southern gospel quartet. From 1866 Aldine S. Kieffer's company promoted seven-shape notation through singing schools, periodicals and songbooks. The publisher James D. Vaughan later sent quartets of his singing teachers on tour, the origin of the classic southern gospel quartet of four men and a piano. White southern gospel is still associated with quartets and family groups singing in three- or four-part harmony.^[15:1] Close-harmony quartets were not only a white tradition: African American quartets were well established by 1890 and served as models for white quartets.^[16:1]

Brother duets and bluegrass

In 1930s hillbilly music, brother duets such as the Monroe Brothers, the Blue Sky Boys and the Delmore Brothers sang in harmony, accompanied by guitar and mandolin. James McDonald sees in them the stylistic development later embodied in bluegrass, and describes the Blue Sky Boys' harmony as the closest ever in country music.^[17:1]

Bluegrass made harmony singing in two, three and four parts a defining feature. In L. Mayne Smith's 1965 account, voices are added to the melody in a fixed order:

• Lead: the melody.
• Tenor: almost always above the lead.
• Third: usually a baritone below both, sometimes a "high tenor" above.
• Bass: the lowest part.

At most cadences the lead rests on the tonic, with the tenor a major third above, the baritone on the fifth below, and the bass on the tonic at the bottom. The conventions are fixed enough that a good singer can usually join in on a song they have not heard before.^[18:1] The accompanying harmony is simple: mostly I, IV and V triads without sevenths. The relative minor is almost the only minor chord, and ♭VII is added under pentatonic melodies.^[18:2]

In 1949 the Stanley Brothers reworked the standard trio of lead, tenor above and baritone below. Alongside the lead and tenor they added an even higher third part, the "high baritone".^[19:1] Smith traces bluegrass part singing to shape-note polyphony, filtered through earlier hillbilly music and influenced by African American gospel singers. Bill Monroe himself learned shape-note singing at local singing schools.^[18:3] Early bluegrass bands also borrowed gospel repertoire and quartet singing styles.^[15:1]

Extensions and limits

Late 19th-century composers often used chains of triads that confound conventional Roman numeral analysis. Neo-Riemannian theory explains such progressions through the common tones the chords share, rather than through their membership in a key.^[20:1]

Tymoczko proposes five features that characterize tonality in a broad sense, among them harmonic consistency and smooth voice leading. In various combinations, he argues, they define an "extended common practice" running from 11th-century polyphony to contemporary jazz. Reviewing the proposal, Julian Hook notes that centricity is the feature that most sharply separates 18th- and 19th-century common practice from the rest of this broader tradition.^[5:1]

Wikidata: Q3127530