Quarter-Tone Harmony/History and Praxis

Quarter tones have been used relatively sparsely in Western music history, but it gained use in twentieth-century music and continues to gain use (along with other microtonal systems) with computers and modern music technology.

Though almost all Western instruments are not designed to produce quarter tones, there are ways to play them.

Though not technically quarter tones, intervals of similarly small sizes have appeared in some music traditions.

Traditional Arabic music, which pervades throughout the Arab world, uses quarter tones melodically, in a system of "scales" called maqam. The maqam system creates maqamat (singular maqam) out of sets of three to five notes called ajnas (singular jins); though the tunings of ajnas and maqamat are very loose, many include intervals not unlike quarter tones.

For example, the popular Maqam Rast is very similar to a normal C major scale with a neutral third and neutral seventh rather than their major counterparts. This is because Maqam Rast is made up of two connected Jins Rast:

This system in turn is derived from ancient Greek music, which feature similar sets of notes—formally called tetrachords—in a system of musical genera. These feature microtones in the form of pure frequency ratios, many of which can be approximated quartertonally.

For instance, the enharmonic genus (a cousin to the diatonic genus which produces our diatonic scale) produces a scale that can be approximated like so:

Before the standardization of 12-tone equal temperament, quarter-comma meantone was the common Western tuning system, which did not feature a neat, closed circle of fifths with twelve pitches. However, as some composers found out, when extended, quarter-comma meantone could produce a near-perfect circle of thirty-one fifths, producing a system with even smaller intervals than the quarter-tone: 31-tone equal temperament.

Sixteenth-century composer Nicolà Vicentino famously constructed a complex, two-manual harpsichord instrument called the archicembalo, which featured thirty-six keys per octave capable of producing microtonal intervals. Vicentino also composed several pieces featuring these intervals as part of his music treatise, demonstrating them in combination with typical compositional styles of the time. Among these are Musica prisca caput, a madrigal in which he musically demonstrates diatonicism, chromaticism, and enharmonicism (his name for the use of these intervals) in series.

Quarter tones and quartertonal theory (as seen in this book) emerged in the twentieth century along with the other new theories and compositional trends of that time. Many very famous composers of the century experimented with quarter tones, among which are Iannis Xenakis, Pierre Boulez, Gérard Grisey, Tristan Murail, Karlheinz Stockhausen, and Charles Ives.

Some composers were far more involved in quartertonal composition and theory, namely:

• Julián Carrillo, who wrote Sonido 13 and experimented with other very small microtonal intervals
• Ivan Wyschengradsky, who wrote the Manual of Quarter-Tone Harmony and wrote the 24 significant preludes in quartertonal scales
• Alois Hába, who produced numerous quarter-tone pieces in his career

For acoustic instruments, two copies of any instrument that can be tuned and can produce all twelve tones of the conventional system can produce quarter tones when one of them is tuned one quarter tone away from the other.

For instance, a very common scheme for the production of quarter tones consists of two pianos, one of which is tuned normally and the other of which is tuned up a quarter tone (or down a quarter tone to reduce tension on the strings). This scheme is used for the performance of Ivan Wyschnegradsky's 24 Preludes, with scores written as if it were a duet for two pianos.

Still, some instruments are capable of playing quarter tones on their own: trombones and orchestral string instruments are capable of playing any pitch degradation, and many woodwinds are capable of playing some microtonal pitches through unconventional fingerings.

Of course, quarter tones and other microtones have been recently popularized due to the capabilities of synthesizers, computers, and modern music technology, which allow for any pitch to be produced by nearly any timbre through virtual means.