1 History and cultural roots

1.1 Early theoretical foundations

1.1.1 Ancient Greek tetrachords

The earliest documented exploration of intervals smaller than a semitone occurred in ancient Greek music theory. Theorists such as Pythagoras and later Aristoxenus described the tetrachord, a four‑note framework spanning a perfect fourth. Within this framework, the genera *diatonic*, *chromatic*, and *enharmonic* used varying interval sizes, with the enharmonic genus employing a quarter‑tone (a diesis) as the smallest step. These theoretical systems laid the groundwork for later microtonal speculation.

1.1.2 Medieval and Renaissance speculative tunings

Medieval theorists, building on Boethius’s translations of Greek sources, continued to debate the mathematical division of the monochord. The Renaissance saw renewed interest in just intonation and meantone temperament, which produced intervals slightly different from equal temperament. Some theorists, such as Gioseffo Zarlino, advocated for intervals derived from the harmonic series, inadvertently opening the door to pitches outside the standard twelve‑note gamut.

1.2 Non‑Western historical traditions

1.2.1 Indian microtones (shruti)

Indian classical music uses a concept of *shruti*—the smallest distinguishable pitch interval. Ancient treatises such as the *Natya Shastra* (c. 200 BCE–200 CE) describe twenty‑two *shrutis* within an octave. While different *raga* systems select from these microtones, the precise tuning varies among schools, giving Indian music a fluid microtonal character distinct from fixed equal temperament.

1.2.2 Arabic maqam and quarter‑tones

Arabic music theory, particularly the *maqam* system, traditionally employs quarter‑tones (e.g., half‑flats and half‑sharps) as integral scale degrees. The 24‑tone “quarter‑tone scale” codified in the 20th century for pedagogical purposes draws on this heritage, though many traditional maqamat use neutral intervals that do not align perfectly with equal‑tempered quarter‑tones.

1.2.3 Indonesian gamelan (Slendro and Pelog)

Javanese and Balinese gamelan orchestras use two chief tuning systems: *slendro*, a five‑note scale with roughly equidistant pitches, and *pelog*, a seven‑note scale with uneven intervals. Neither system corresponds to Western equal temperament; the specific frequencies vary among gamelan sets. Western listeners often perceive slendro and pelog as microtonally different from familiar scales.

1.3 Western experimental revival (19th–20th centuries)

1.3.1 Hermann von Helmholtz and just intonation

In *On the Sensations of Tone* (1863), physicist Hermann von Helmholtz analyzed the physical basis of consonance and dissonance, advocating for just intonation based on simple frequency ratios. His work inspired later composers to explore intervals beyond the 12‑note chromatic scale, although practical instruments for just intonation remained rare.

1.3.2 Julian Carrillo’s “Sonido 13”

Mexican composer Julián Carrillo (1875–1965) developed a system he called *Sonido 13*, dividing the octave into 16, 24, 36, 48, 60, 72, or 96 equal parts. He built specially designed pianos and wrote a large body of microtonal works, treating the traditional twelve‑note system as only one of many possible subdivisions.

1.3.3 Harry Partch and his instrumentarium

American composer Harry Partch (1901–1974) rejected equal temperament entirely, basing his music on a 43‑tone just intonation scale. He built unique instruments—such as the chromelodeon, cloud chamber bowls, and the diamond marimba—to realize his microtonal vision. Partch’s theoretical writings and performances established him as a central figure in microtonal music.

2 Tuning systems and theory

2.1 Equal temperaments beyond 12

2.1.1 19‑TET

19‑tone equal temperament divides the octave into 19 equal steps, each approximately 63.16 cents. It offers closer approximations to just‑intonation thirds and fifths than 12‑TET, while still maintaining complete transpositional symmetry. It has been used by composers such as Easley Blackwood Jr. and in some recent electronic works.

2.1.2 24‑TET (quarter‑tone)

24‑TET splits each semitone into two equal quarter‑tones, producing 24 steps of exactly 50 cents each. This system is the most familiar microtonal equal temperament, widely adopted in Arab music theory and 20th‑century Western art music (e.g., Alois Hába, Ivan Wyschnegradsky). Quarter‑tone pianos and notation conventions exist.

2.1.3 31‑TET and 53‑TET

31‑TET, with steps of about 38.71 cents, provides exceptionally accurate just‑intonation approximations for thirds, fifths, and sevenths. It was championed by theorist Adriaan Fokker and used by a few Dutch composers. 53‑TET, with steps of approximately 22.64 cents, virtually reproduces Pythagorean and meantone intervals; it has historical roots in ancient Chinese and Greek theory. Both systems remain largely experimental.

2.2 Just intonation and extended rational intervals

2.2.1 Harmonic series and sub‑harmonics

Just intonation constructs intervals from rational frequency ratios, often derived from the harmonic series (overtones). A major third is 5:4 instead of the equal‑tempered 2^(4/12):1. Sub‑harmonic series produce descending intervals by integer division. Both approaches yield intervals that are pure but not equally spaced, requiring careful management of commas and enharmonic spelling.

2.2.2 Otonality and Utonality (Harry Partch)

Harry Partch coined the terms *otonality* and *utonality* to describe chords built respectively from the harmonic series (overtones) and the sub‑harmonic series (undertones). An otonal chord uses ratios whose numerators are multiples of a common fundamental; an utonal chord uses denominators. This framework systematizes just‑intonation harmony and appears in Partch’s compositions and instrument designs.

2.3 Non‑octave and octave‑repeating scales

2.3.1 Bohlen–Pierce scale

The Bohlen–Pierce scale is based on the 13th harmonic, dividing the tritave (3:1, an octave plus a fifth) into 13 equal steps. It does not repeat at the octave, emphasizing the interval of a twelfth instead. Designed independently by Heinz Bohlen, John Pierce, and others, it produces a distinctive, unfamiliar harmonic landscape used in some experimental electronic music.

2.3.2 Wendy Carlos’ alpha, beta, gamma scales

Composer and electronic musician Wendy Carlos devised three non‑octave scales—alpha, beta, and gamma—each dividing the octave into a non‑integer number of steps. These scales were created to approximate just intervals while preserving a degree of transpositional uniformity. She employed them in works such as *Beauty in the Beast* (1986).

2.4 Microtonal notation and conventions

2.4.1 Standard accidentals with additional symbols

No single notation system is universally adopted. Common symbols include arrows attached to accidentals (e.g., ♯↑, ♭↓), modified sharps and flats (e.g., half‑sharp , half‑flat ), and numbers indicating cents deviation. Some composers use staff lines extended by additional leger lines or color‑coded staves.

2.4.2 Cent‑based annotation (1200 cents per octave)

The cent, dividing the octave into 1200 equal units, offers a precise logarithmic measure of interval size. Microtonal works frequently specify pitches in cents relative to a reference (e.g., A4 = 440 Hz). Tuning tables and scale‑file formats (such as .scl files) rely on cent values for exact description.

3 Instruments and performance

3.1 Traditional instruments adapted for microtonality

3.1.1 Fretted string instruments (e.g., custom guitars)

Fretted instruments can be refretted to a microtonal scale, or equipped with movable, scalloped, or multi‑scale frets. Luthiers have built guitars with up to 36 frets per octave, and some designs allow for on‑the‑fly retuning. Electric guitars with pitch‑bend systems (e.g., the EBow or fretless variants) also facilitate microtonal playing.

3.1.2 Keyboards with split manuals or extra keys

A few keyboard instruments have been built with split manuals (two keyboards tuned differently) or extra keys to produce quarter‑tones or other microtones. Examples include the quarter‑tone piano built for Alois Hába and the “enharmonic” organ by Adriaan Fokker. Such instruments are rare due to mechanical complexity.

3.2 Specially built microtonal instruments

3.2.1 Harry Partch’s cloud chamber bowls and chromelodeon

Partch constructed the cloud chamber bowls from the tops of Pyrex carboys, tuned to specific just‑intonation pitches and played by striking with mallets. The chromelodeon is a retuned reed organ capable of producing his 43‑tone scale. These instruments are iconic in the microtonal canon.

3.2.2 The microtonal guitar (e.g., Tolgahan Çoğulu’s adjustable fret model)

Turkish luthier Tolgahan Çoğulu developed an adjustable‑fret guitar in which each fret is a movable segment, allowing the player to reconfigure the scale for different microtonal systems (e.g., maqam or 24‑TET). Similar designs have been adopted by other builders and composers.

3.3 Electronic and digital instruments

3.3.1 Synthesizers with pitch‑bend and micro‑tuning

Modern synthesizers (both hardware and software) often include pitch‑bend wheels, aftertouch, and micro‑tuning tables that allow any equal temperament or custom scale. Analog synthesizers with voltage‑controlled oscillators can be calibrated to non‑standard tuning voltages.

3.3.2 Software (e.g., Scala, microtonal plug‑ins)

Scala is a free, widely used program for creating, editing, and converting microtonal scale files. Many digital audio workstations (DAWs) support micro‑tuning via plug‑ins such as MTS (MIDI Tuning Standard) or custom scripts. These tools let composers apply any tuning system to virtual instruments and MIDI controllers.

4 Genres and repertoire

4.1 Contemporary classical and avant‑garde

4.1.1 Works of Alois Hába and Ivan Wyschnegradsky

Czech composer Alois Hába (1893–1973) wrote extensively in quarter‑tone and sixth‑tone systems, including his opera *Matka* (Mother, 1929). Russian‑born Ivan Wyschnegradsky (1893–1979) composed in quarter‑tone and 24‑tone harmony, exploring “pansonority” and building a quarter‑tone piano. Both are key figures in early 20th‑century microtonal art music.

4.1.2 Spectral music (Gérard Grisey, Tristan Murail)

Spectral composers of the 1970s onward derived harmonic structures from the overtone series, often using microtonal intervals as byproducts of natural resonance. Gérard Grisey’s *Les espaces acoustiques* and Tristan Murail’s *Gondwana* exemplify this approach, employing subtle pitch shifts and just‑intonation chords.

4.2.1 Microtonal jazz (e.g., Joe Maneri, Bill Frisell)

Saxophonist Joe Maneri developed a microtonal improvisational language based on 12‑tone and just‑intonation principles. Guitarist Bill Frisell occasionally uses microtonal bends and alternate tunings in his jazz‑fusion works. The microtonal tradition in jazz remains niche but persistent.

4.2.2 Progressive rock and metal (e.g., King Gizzard & the Lizard Wizard)

The Australian band King Gizzard & the Lizard Wizard released the album *Flying Microtonal Banana* (2017), featuring custom‑tuned microtonal guitars. Other metal and experimental rock acts have explored 19‑TET, quarter‑tones, and just intonation to create unusual harmonic textures.

4.3 Electronic and ambient music

4.3.1 Use of microtonal scales in sound design

Electronic composers and ambient artists frequently use microtonal scales to evoke unfamiliar or “alien” atmospheres. Software synthesizers and digital samplers make it easy to import custom tuning files. Artists such as Wendy Carlos, Eliane Radigue, and newer sound designers employ microtonality to generate drones and evolving harmonic fields.

5 Notable composers and practitioners

5.1 Pioneers (early 20th century)

5.1.1 Charles Ives

American composer Charles Ives (1874–1954) experimented with quarter‑tones in several works, most notably the *Three Quarter‑Tone Pieces* (1923–24) for two pianos tuned a quarter‑tone apart. His theoretical openness influenced later microtonal exploration.

5.1.2 Julián Carrillo

Carrillo’s “Sonido 13” system and his dozens of microtonal compositions (including symphonies and concertos) established him as a pioneering advocate for new pitch resources. His writings promoted the idea that any subdivision of the octave is musically valid.

5.2 Mid‑20th century innovators

5.2.1 Harry Partch

Partch’s instruments, notations, and compositions (e.g., *Delusion of the Fury*) form a unique corpus of microtonal music rooted in just intonation and theatrical ritual. His book *Genesis of a Music* remains a foundational text.

5.2.2 Lou Harrison

Lou Harrison (1917–2003) combined just intonation with world music influences, constructing his own “American gamelan” and composing works for it. He developed a “tack piano” and used the “harmonic canon” as a compositional tool.

5.3 Contemporary figures

5.3.1 La Monte Young

La Monte Young (b. 1935) is a key figure in minimalism and just‑intonation composition. His works, such as *The Well‑Tuned Piano* (1964–present), employ extended microtonal drones and rational intervals, often performed over many hours.

5.3.2 Ben Johnston

Ben Johnston (1926–2019) composed in extended just intonation, notably his string quartets and the suite *Sonata for Microtonal Piano*. His system of notation uses accidentals with arrows to indicate comma‑level adjustments.

5.3.3 Easley Blackwood Jr.

Easley Blackwood (1933–2023) composed *Twelve Microtonal Etudes* for electronic music, each exploring a different equal temperament (13‑TET through 24‑TET). He also authored a treatise on microtonal theory and built a custom 19‑TET pipe organ.

6 Impact and cultural relevance

6.1 Influence on music education and pedagogy

Microtonal concepts appear increasingly in university music curricula, often within courses on acoustics, composition techniques, and world music. The availability of software and affordable hardware has enabled students to experiment with tunings. Some conservatories offer dedicated microtonal performance workshops.

6.2 Interaction with digital audio workstations and MIDI

MIDI Tuning Standard (MTS) allows keyboard controllers and synthesizers to load arbitrary microtonal scales. Many DAWs support MTS or third‑party plug‑ins for micro‑tuning, making microtonal composition accessible to a broader community. This has spurred a resurgence of interest since the 1990s.

6.3 Future directions in composition and performance

Microtonal music continues to evolve with advances in digital signal processing, machine learning, and new instrument design. Composers explore dynamic tuning systems that change over time, algorithmic microtonality, and interactive performance with real‑time pitch bending. The boundaries between microtonal and macrotonal (e.g., equal temperaments with fewer than 12 notes) are also being reexamined, promising a diverse future for pitch‑centric experimentation.