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| double second | |
|---|---|
| Name | Double second |
| Classification | Microtonal interval / comma-based interval |
| Cents 12TET | ~200* |
| Cents just intonation | variable |
| Notation | specialized accidentals, cent markings |
| Common instruments | violin, saxophone, voice, sitar |
| Notable in repertoire | Messiaen, Scelsi, Partch |
double second The double second is a microtonal interval used in various tuning systems and performance traditions to denote an interval approximately twice the size of a traditional chromatic or diatonic second as conceived in a particular temperament. It appears across theoretical writings, compositional practice, and oral traditions where small-step inflections—often measured in commas or cents—are doubled to create expressive or structural pitch relationships. Its treatment varies by context: from the acoustical ratios discussed in Pythagoras-inspired schemata to the practical fingerings applied by Niccolò Paganini-influenced virtuosi, and the notation practices advocated by Heinrich Schenker-era theorists and 20th-century microtonalists.
In scholarly descriptions the double second is defined relative to a reference second: for example, twice a chromatic semitone in a meantone temperament or twice a diatonic semitone in a unequal division of the octave. Writers contrast it with terms like the "diesis" used by Gioseffo Zarlino and later by Werckmeister, and with commas such as the Pythagorean comma or syntonic comma that quantify the small discrepancies between tuning systems. Composers and theorists from Johann Sebastian Bach-era temperaments to Adriaan Fokker's 31-tone equal temperament have treated the double second as a tool for voice-leading, modulation, and coloristic effect. Performance guides by figures associated with Christofori-era keyboard practice or with Franz Liszt-era Romanticism sometimes adapt the term when translating historical compromise tunings to modern instruments like the piano and harpsichord.
Conceptual roots trace to ancient Greek ratio theory credited to Pythagoras and mathematical secularity in works connected to Boethius, which explored interval multiplication and subtraction. Renaissance theoreticians such as Zarlino and Gioseffo Zarlino's contemporaries cataloged commas and minute intervals that later writers aggregated to form "double" intervals. The Baroque temperaments described by Andreas Werckmeister and polemics around tuning by Giovanni Battista Doni provided practical frameworks for doubling small intervals in keyboard temperament tables. In the 19th and 20th centuries the expansion of microtonal thought in publications by Sethares, Ivan Wyschnegradsky, and practitioners like Harry Partch and Alois Hába led to explicit naming and systematization of double-size subdivisions, especially within unequal and extended equal temperaments championed by Adriaan Fokker and Julian Carrillo.
Theoretical treatments express the double second either as a rational ratio—often composed of two successive commas—or as a cent value in equal temperaments such as 19-TET, 31-TET, or 53-TET where step sizes approximate the target. Analytical discourse connects this interval to contrapuntal constraints in writings influenced by Heinrich Schenker and to scale construction strategies in Olivier Messiaen's modes of limited transposition. Notation practices vary: 19th-century accidentals used by Hermann von Helmholtz-influenced theorists coexist with 20th-century cent-number annotation preferred by Erwin Stein and microtonal editors working with Harry Partch's custom staff. Editions of contemporary scores sometimes borrow accidentals from the Ben Johnston system or invent hybrids combining arrows, commas, and numeric cent labels to communicate double-second inflections to performers.
Instrumentalists approach the double second differently according to technique and tradition. Bowed-string players influenced by schools associated with Niccolò Paganini and the Ysaÿe lineage use subtle left-hand adjustments and portamento to realize doubled micro-intervals. Wind players in the lineages of Adolphe Sax and Giacinto Scelsi exploit alternate fingerings and embouchure to produce steps approximating double seconds. Vocalists trained in the traditions exemplified by Enrico Caruso or by modern extended-voice pedagogues incorporate microtonal inflections into ornamentation and ornament cadences. Keyboardists either retune instruments—following the practice of Andreas Werckmeister-style temperaments—or rely on instruments built for microtonal systems, as with the instruments commissioned by Harry Partch or the 31-TET pianos promoted by Adriaan Fokker.
Closely related concepts include the diesis and various named commas: the syntonic comma, the Pythagorean comma, and system-specific intervals in Meantone temperament and in equal temperaments like 19-tone equal temperament and 31-tone equal temperament. Techniques that produce similar sonic results include portamento, pitch bending in the electric guitar tradition represented by Jimi Hendrix-style approaches, and blue-note inflection practices traced through W.C. Handy and Bessie Smith in blues singing. Contemporary composers combine double-second manipulation with spectral techniques associated with Giacinto Scelsi and spectralism linked to Gérard Grisey and Tristan Murail to explore beating patterns and overtone alignments.
Repertoire explicitly exploiting double-second relationships appears in the works of microtonal and modernist composers such as Harry Partch's ensemble pieces, Ben Johnston's string quartets, Iannis Xenakis's exploratory works, and selected pieces by Olivier Messiaen that require precise microtonal registrational control. Solo repertoire for sitar and koto traditions often implies doubled small-scale inflections in ornamentation, while contemporary works by Giacinto Scelsi and La Monte Young foreground minute pitch shifts that can be interpreted through the double-second lens. Editions and recordings from ensembles associated with IRCAM, Kronos Quartet, and microtonal workshops at institutions like Royal Conservatory of The Hague provide documented realizations and pedagogical models for the interval.
Category:Microtonal music