Voice leading

Voice leading (from the German Stimmführung) is the way the individual parts, or voices, of a musical texture move from note to note as one chord follows another. Music theory traditionally divides the "rules of harmony" into two groups: rules of harmonic progression, which govern the choice and order of chords, and rules of voice leading, which govern how each part moves between successive sonorities. Many theorists have held that the main purpose of voice leading is to create perceptually independent musical lines.^[1:1]

Dmitri Tymoczko describes Western music as lying at the intersection of harmony and counterpoint, using "counterpoint" and "voice leading" as synonyms for the technique of connecting the notes of successive chords so that they form simultaneous melodies. In his account, chords are usually connected so that the voices move independently, efficiently (by short distances) and without crossing. These features make the music easier to perform, follow explicit aesthetic norms, and help listeners tell the simultaneous melodies apart.^[2:1]

Conventional rules

There is no single, fixed set of voice-leading rules, and treatises differ in detail. David Huron identifies a core of about a dozen rules found in nearly every pedagogical text. These include:

• Range and spacing: keeping to a set registral range and limiting the spacing between voices.
• Smooth motion: keeping common tones in the same voice, moving to the nearest chord tone, and preferring stepwise motion to leaps.
• Separate parts: avoiding unisons, and avoiding crossing or overlapping parts.
• Parallels: avoiding parallel or consecutive unisons, fifths and octaves, and avoiding "exposed" (also called hidden or direct) octaves and fifths.^[1:2]

The prohibition of parallel fifths is among the rules regarded as valid throughout the history of tonal music. If two voices form a fifth in one chord, the same two voices should not form a fifth in the next; similar rules apply to octaves and unisons. François Pachet and Pierre Roy note that such rules mainly list forbidden combinations of notes rather than giving a complete method for composing.^[3:1]

Species counterpoint

Voice leading is commonly taught through species counterpoint, a step-by-step method for writing melodies and combining them. Open Music Theory's version follows Johann Joseph Fux's Gradus ad Parnassum (1725), and composers from the 18th to the 21st centuries have used the method or variants of it. Species counterpoint distinguishes four kinds of motion between two parts:

• Contrary: the parts move in opposite directions.
• Similar: both parts move in the same direction.
• Parallel: both parts move in the same direction by the same interval.
• Oblique: one part moves while the other holds its pitch.^[4:1]

Students are told to avoid parallel fifths and octaves. They should also try to avoid direct fifths and octaves, in which two parts move in the same direction into one of those intervals.^[4:2]

Textbooks justify these rules in terms of the independence of the lines. Parallel fifths and octaves promote tonal fusion at the expense of melodic independence. Contrary motion best preserves independence. Voice crossing makes the lines harder to tell apart by ear.^[5:1]

Four-part writing

In harmony teaching, compositions are often reduced to four parts named after the voices of a choir: soprano, alto, tenor and bass ("SATB"). Strict SATB style gives each voice a conventional range. Adjacent upper voices are kept within an octave of each other, and the tenor and bass within a twelfth. Voices do not cross. The leading tone and other tendency tones, such as chordal sevenths, are not doubled.^[6:1] Conventions vary between sources. Huron's summary of the traditional rules, for example, places no limit on the distance between tenor and bass.^[1:2]

Perceptual explanations

Earlier theorists tended to treat the voice-leading rules as fixed, universal laws. More recent theorists have treated them as a description of one historically specific convention.^[1:3] In a 2001 study, Huron derived the traditional rules from experimentally established principles of auditory perception, drawing mainly on research into auditory stream segregation. Six core principles account for most of the traditional rules:

• toneness
• temporal continuity
• minimum masking
• tonal fusion
• pitch proximity
• pitch co-modulation

Huron also derived new rules that traditional theory does not state, and found that musical practice is consistent with them. Four further principles act as optional choices that distinguish styles of part writing such as polyphony, homophony and close harmony:

• onset synchrony
• limited density
• timbral differentiation
• source location^[1:4]

Tonal fusion is the tendency of some simultaneous tones to merge into a single sound image. The unison fuses most strongly, followed by the octave and then the perfect fifth. In J. S. Bach's polyphonic writing, these intervals are avoided in proportion to how strongly they fuse. This avoidance is separate from the rule against parallel motion.^[1:5]

In a study of 143 works, the degree to which notes in different voices start together (onset synchrony) was the strongest factor distinguishing homophonic from polyphonic textures. In Bach's polyphonic works, most perfect intervals are approached with staggered note onsets. In his homophonic chorales, most are approached with simultaneous onsets.^[1:6]

Huron notes that his account does not explain the sense of direction, or "leading", in successions of pitches. He also leaves open whether the principles are universal features of human hearing or the product of culture-specific learning.^[1:7]

Geometric and transformational theories

Diagrams of efficient voice leading have a long history. The circle of fifths, first published in 1728, shows efficient voice leadings among the 12 major scales. The Tonnetz, which originates with Euler in 1739, shows efficient voice leadings among the 24 major and minor triads.^[2:2]

Late 19th-century composers often used triadic progressions that do not fit conventional Roman numeral analysis. Neo-Riemannian theory explains such progressions by the common tones that chords share, rather than by their membership in a key. Its three basic transformations each keep two notes of a triad and move the third:

• Parallel: C major ↔ C minor.
• Relative: C major ↔ A minor.
• Leading-tone exchange: C major ↔ E minor.

The progressions of most interest use "parsimonious" voice leading, in which no voice moves by more than a step.^[7:1]

In a 2006 paper in Science, Tymoczko represented chords as points in geometric spaces called orbifolds, in which line segments represent voice leadings. The space of unordered pairs of pitch classes, for example, forms a Möbius strip. Efficient voice leading between chords of the same type is possible only when the chords are nearly symmetrical under transposition, inversion or reordering of their notes.^[2:3] The consonant chords of Western music divide the octave nearly evenly, so they lie near the centre of these spaces. As a result, they can be linked by efficient, independent voice leading. Tymoczko argues that this central feature of Western counterpoint follows from composers' interest in acoustic consonance.^[2:4]

Callender, Quinn and Tymoczko later generalised the model into what are sometimes called "OPTIC" spaces. The name comes from five ways of treating chords as equivalent: octave shifts, permutation, transposition, inversion and changes in the number of notes. A voice leading is a path through such a space, and the distance between two chords reflects how smoothly they can be connected. Reviewing Tymoczko's 2011 book A Geometry of Music, Julian Hook described the model as drawing together several strands of music theory: set theory, scale theory, neo-Riemannian theory and earlier work on voice leading.^[8:1]

In computation

Because the conventional rules mainly list forbidden combinations of notes, Pachet and Roy's survey of automatic harmonisation treats them as constraints for a computer to satisfy. It reviews systems that harmonise melodies and figured basses this way.^[3:1][3]

Wikidata: Q2027877