Instruments specially constructed or adapted for performing music in microtonal tuning systems or to give accurate tuning in temperaments other than the ‘standard’ 12-note Equal temperament (ET). This article covers all such approaches, thus including not only unequal temperaments but also equal subdivisions of the octave that are more (occasionally less) than 12. Although some specialists limit the meaning of ‘microtonal’ to intervals that are less than a quarter-tone, others more logically apply it to all intervals that are smaller than the semitone, adopting the term ‘macrotonal’ for the few tunings that use larger intervals (primarily nine-, ten- and 11-note). This article deals only with Western instruments; instruments constructed in other parts of the world for the performance of music in systems of intonation other than 12-note ET are dealt with under their own headings.
Three main periods can be distinguished in the development of Western microtonal instruments: the work of theorists in the 16th and 17th centuries, acoustic research in the second half of the 19th century, and the explorations of composers, performers and researchers throughout the 20th century. Until the end of the 19th century there was little interest in microtonal composition based on more than 12 equal divisions of the octave; but this has been the main preoccupation in the 20th century in this area, and many composers who are not primarily concerned with microtonal systems have nonetheless included microtonal inflections in their works at some time, whether for traditional instruments or in electro-acoustic music.
In this article instruments are described as having a certain number of notes to the octave; ‘equal’ and ‘unequal’ temperaments are respectively those in which the octave is divided into equal or unequal intervals by the notes; ‘just’ indicates Just intonation, and ‘mean’ mean-tone temperament (both of which are unequal; see Temperaments). On some Enharmonic keyboard instruments and some instruments constructed since the 19th century certain pitches have duplicate keys for ease of fingering, so that there are more keys than notes to the octave. In other cases a single standard keyboard with 12 keys to the octave is used, together with switches, each of which assigns a specific intonation system to the keyboard.
HUGH DAVIES
Before the establishment of equal temperament in the course of the 18th century, a number of investigations were carried out into intonation and tuning systems, in many instances inspired by a renewal of interest in ancient Greece and the three genera (diatonic, chromatic and enharmonic) of the Greek modes. Those principally active in this area in the 16th century were the theorists Francisco de Salinas, who proposed the use of 19 notes to the octave and probably perfected mean-tone temperament, and Gioseffo Zarlino, who investigated systems of 17 and 19 notes to the octave and contributed significantly to the development of 12-note ET. In the 17th century Nicolaus Mercator suggested 53 equal divisions of the octave and Marin Mersenne and Christiaan Huygens 31; these result virtually in just intonation and mean-tone temperament respectively.
A few microtonal instruments with enharmonic keyboards were constructed during this period for the performance of music in specific intonations. In Venice Domenico da Pesaro built for Zarlino an enharmonic harpsichord with 19 notes to the octave (described in Zarlino's Le istitutioni harmoniche, 1558/R). Nicola Vicentino made instruments which he called the arcicembalo (by 1555, recently reconstructed by Marco Tiella) and arciorgano (by 1561); both had 31 notes to the octave with two manuals each having three terraces of keys, and they were designed to play in mean-tone systems. Around 1590 Elsasz built a clavicymbalum universale (19 notes, mean) for Carl Luython. Over the next 100 years several other enharmonic harpsichords were constructed, principally in Italy, including those of Vito Trasuntino, Fabio Colonna, G.P. Polizzino (for G.B. Doni), Francesco Nigetti, Galeazzo Sabbatini and Nicolaus (or Jacopo) Ramerini.
During the decades when 12-note equal temperament was becoming widespread in its use other intonation systems persisted, especially in solo performances on keyboard instruments; unaccompanied voices and string instrument players continued (and still continue) to adjust their intonation according to context. Special instruments, like Charles Clagget's 39-note grand piano called the Telio-chordon (patented in London in 1788), were rare in this period. By the time the majority of musicians and manufacturers had adopted equal temperament, in some cases as late as the middle of the 19th century, it was the turn of the practitioners of the new science of acoustics to explore different tuning systems. A number of pipe and reed organs were built or modified for this purpose, beginning with Henry Liston's 56-note ‘euharmonic’ pipe organ of about 1812. Some of them are described in Table 1. Instruments from this period that did not have a keyboard include General Thomas Perronet Thompson's enharmonic guitar (?1829; for illustration see Just intonation, fig.5), the 31-note ‘githárfa’ (Ger. ‘Guitharfe’) built by the Hungarian physicist József Petzval in Vienna in 1862, and a quarter-tone trumpet (1893, now in the Odessa Conservatory). In 1864 a piano tuned in just intonation was built for the Russian Prince Vladimir Fyodorovich Odoyevsky.
Around 1890 Carl Andreas Eitz began to explore quarter-tones (see Eitz method); similar interests were soon pursued by others, especially in Germany, and inaugurated a new phase in microtonal music. This was characterized by the appearance not only of a considerable number of compositions in various tuning systems, but also of a great variety of specially constructed instruments.
Before the 1890s only a few quarter-tone instruments were constructed; they included one inspired by the Greek modes and built around 1850 by Alexandre-Joseph Vincent and Bottée de Toulmon (for which Joseph Lubet d'Albiz wrote Création harmonique: étoile musicale composée pour piano ou orgue à quarts de ton, c1858), and a set of tuned glasses and an instrument with about 24 strings made around 1885 by George Ives (father of Charles). From 1890 a considerable number of quarter-tone pianos and reed organs were built (see Table 2), as well as a few in other tunings. Some of these instruments have two manuals tuned a quarter-tone apart; others have three manuals, the third duplicating the first to allow alternative fingerings (on the manual furthest from the player the white keys are the same size as the black ones). Those instruments with a single manual, including the harmoniums by Max F. Meyer and von Moellendorf, have unconventional keyboard lay-outs (see also Keyboard, §3).
Much of the quarter-tone music written in this period involves retuning or fingering differently existing instruments. The earliest composition to use quarter-tones appears to have been Halévy's Prométhée enchaîné (1849), in the string parts; in 1898 the British composer John Foulds wrote a string quartet (now lost) that used quarter-tones, and from 1905 he included microtones for bowed strings in other works. The first important quarter-tone composition, and perhaps the first fully microtonal work, was Charles Ives's Chorale for strings; this was variously dated 1903–14 and 1913–14 by the composer, and was probably based on experiments carried out with two pianos tuned a quarter-tone apart about 1900–01. The Chorale is also lost, but it was arranged for two pianos by Ives as the last of his Three Quarter-Tone Pieces for Two Pianos (1923–4), from which Alan Stout has reconstructed the original. Quarter-tones also occur in Ives's Symphony no.4 (c1912–18 and his unfinished Universe Symphony (c1915–28).
Other quarter-tone practitioners before 1930 included Julián Carrillo, who evolved the theory of el sonido trece (‘the 13th sound’) in 1895 (see Microtone), but wrote no microtonal music until 1922; Arthur Lourié, who between 1908 and about 1915 wrote a number of works, including a string quartet (1910), as well as a Prélude for quarter-tone piano (1915); Mikhail Vasil'yevich Matyushin included quarter-tones in his Futurist opera Pobeda nad solntsem (‘Victory over the Sun’, 1913); and several Soviet composers in the mid-1920s, including Georgy Mikhaylovich Rimsky-Korsakov, who founded the Petrograd society for quarter-tone music (1923) and directed its ensemble (1925–32), which included a quarter-tone harmonium, two pianos tuned a quarter-tone apart, re-tuned harp and, in 1932, the electronic Emiriton; Arseny Mikhaylovich Avraamov (who also devised an ‘ultrachromatic’ ⅛-tone ‘universal system of tones’), Nikolay Malakhovsky and Aleksandr Aleksandrovich Keneľ; and a number of musicians who developed or commissioned special instruments (see below). During this period quarter-tones were also briefly exploited in single works by Vittorio Gnecchi, Ernest Bloch and Alban Berg. Hans Barth featured his 1928 quarter-tone piano in several works, including a Concerto with string orchestra (1930), and many quarter-tone works were composed by Alois Hába and his students, and by Ivan Vischnegradsky.
Reed organs using other microtonal tunings were also constructed at about this time. Ferruccio Busoni, inspired in 1907 by reports of the second model of Thaddeus Cahill's Telharmonium (which had 36 notes to the octave in just intonation), experimented in New York (probably in 1910 or 1911) with a rebuilt three-manual harmonium tuned in 1/3-tones; a two-manual 1/6-tone instrument constructed for him by J. & P. Schiedmayer was completed only in 1925, several months after his death. In Cambridge Wilfrid Perrett built a harmonium in just intonation with 19 notes to the octave (c1925) which he called the ‘olympion’. An electric harmonium designed by Lev Termen around 1926 (but not completed) was tunable in subdivisions of up to 1/100-tones. Hába commissioned a 1/6-tone harmonium from August Förster in 1927. In 1932 Shôhei Tanaka, working in Tokyo, produced an instrument with 21 keys per octave (assignable to 46 notes) in just intonation. Around the same time the Polytone, a 60-key, 53-note harmonium with a special keyboard, consisting of ten rows of differently coloured keys, was constructed for the composer Arthur Fickénsher at the University of Virginia. From the early 1930s several 43-note harmoniums were constructed by Harry Partch under the names Ptolemy and Chromelodeon.
Microtonal instruments other than keyboards from the first half of the 20th century include the quarter-tone clarinet (c1906) of Richard Heinrich Stein; the ‘intonarumori’ (from 1913) of Luigi Russolo, in all of which divisions of at least ⅛-tone were possible; a quarter-tone violin (up to 1915) and a string instrument (1920) that combined features of the violin and balalaika, devised by Matyushin (who had published a quarter-tone violin tutor in 1912); Carrillo's ⅛-tone octavina (which resembled a bass guitar), his ⅛-tone arpa citera or ‘harmony harp’ (c1922), 14 other instruments in the same family tuned to subdivisions between 1/3- and 1/16-tones, and a quarter-tone trumpet and horn, all built during the 1920s; the six-string violins that formed part of a microtonal ensemble directed by Paul Specht in the mid-1920s; Eduardo Panach Ramos's 1/3-tone, citarina-like ‘triola’; and the quarter-tone instruments built for Hába (clarinets, 1924 and 1931, by F.W. Kohlert; trumpets with a fourth valve, 1931, by F.A. Haeckel; guitar, 1943). A 1/12-tone version of the ondes martenot was made in 1938 at the request of the Indian poet and composer Rabindranath Tagore for performing rāgas, and in the same year Messiaen composed two quarter-tone Monodies for solo ondes martenot. In 1930 Carrillo established the microtonal Orquesta Sonido Trece, which toured in Mexico during the next decade.
(i) Harry Partch and the California group.
Microtonal instruments, §4: After 1930
The first substantial range of less conventional microtonal instruments was constructed by the American composer Harry Partch from 1930; they employ a 43-note scale in just intonation. Besides inspiring a considerable number of instrumental inventions, including many later instruments in specific microtonal tunings, Partch's work has shown composers and performers that musicians who are reasonably skilful with tools can themselves create instruments appropriate to their ideas without much expense or assistance.
From the late 1940s Partch spent most of his time in California, where, as a result of his presence and ideas, a group of instrument makers concentrating on microtonal inventions has grown up. Ivor Darreg began to build and compose for new instruments in the mid-1930s (though initially he was probably unaware of Partch's work); he explored many equal and just systems. He re-fretted guitars in 17-, 19-, 22-, 24- and 31-note tunings and made several versions of three types of steel guitar with two or four separate sets of strings in different tunings (Kosmolyra, Hobnailed Newel Post and the bass Megalyra). The electrically amplified keyboard Megapsalterion (1971), which has 158 strings tuned to an overtone series, was based on his ‘amplifying clavichord’ (1940).
Ervin Wilson, working in West Hollywood from the early 1960s, has devised many lay-outs for keyboard and keyed percussion instruments in microtonal tunings, re-fretted guitars, and built several ‘Tubulongs’: tubular metallophones, usually tuned to give 31 equal divisions of the octave but sometimes in other equal or just tunings, including the 31-note Chromaphone and the 22-note Transcelest (1967), which has three rows of keys made from square brass tubing. The 19-note Hackleman-Wilson clavichord (1975) was built by Scott Hackleman to Wilson's keyboard design. Another 19-note clavichord was constructed at around the same time by Craig Hundley (now Huxley), a former student of Wilson's. Huxley's instruments also include a Tubulon (a large array of suspended aluminium tubes tuned in 53 equal divisions; fig.1) and the Blaster Beam; this is a water-filled aluminium beam 6 metres in length, along which 24 strings are stretched and amplified by means of movable magnetic and crystal pickups.
Another influential Californian is the composer Lou Harrison, who has constructed many instruments in 12-note ET and other equal and just tunings since around 1940, including his ‘tack piano’, clavichords and copies of oriental instruments. Later he collaborated with William Colvig, and together they constructed in the early 1970s what was probably the first American gamelan (see Gamelan, §II).
A younger group, who, unlike Partch did not restrict their work to a single tuning system, was centred on Jonathan Glasier and the Interval Foundation at San Diego (the Foundation published a quarterly journal from 1978 to 1987). In 1977 Glasier built a Harmonic Canon (modelled on that of Partch), which is tunable to any system; other instruments by him are an adaptation of a commercial Hawaiian guitar to create the microtonal ‘Fender four-neck steel’, and the Godzilla, which consists of tuned metal rods welded to a sawn-off oil drum. Glasier and others are also involved in improvisation, often with inventors of non-specifically tuned instruments, such as Prent Rodgers (who also built instruments that use 31-note equal or just intonation).
Cris Forster has made several instruments in 56-note just tuning: two of them, the Harmonic/Melodic Canon and Diamond Marimba, were inspired by Partch; a third, Chrysalis (fig.2), consists of a disc mounted vertically on a stand with 82 strings on each face, which radiate out from an off-centre circular bridge. The composer David Cope has constructed several percussion instruments tuned to 33-note just intonation. Other inventions to come out of California include Tillman H. Schafer's Undevigintivox, a 19-note metallophone (early 1960s), and a more recent 53-note metallophone built for Larry A. Hanson. Schafer (now based in Boston), Warren F. Kimball and others have refretted guitars. Kimball and Skip La Plante in New York have built microtonal ‘harmonic canons’ inspired by Partch.
In California there has also been some use of microtones in jazz. In the mid-1960s the Hindustani Jazz Sextet explored both microtones and complex time signatures (from 5/4 to 33/16). The Sextet included two musicians who went on to form their own bands in the late 1960s: the trumpeter Don Ellis, who commissioned from Frank Holton & Co. quarter-tone trumpets with a fourth valve for the whole of his trumpet section; and the percussionist Emil Richards, whose Microtonal Blues Band consisted of several electro-acoustic instruments and a wide range of percussion from many cultures, tuned microtonally to give, for instance, 22, 24, 31, 33 and 43 subdivisions of the octave.
Microtonal instruments, §4: After 1930
Since World War II, electronics have been widely applied to microtonal keyboard instruments, and electronic instruments have been used to perform microtonal music. In the late 1940s Percy Grainger, searching for means of producing ‘gliding tones’, simulated them by using 1/6- and ⅛-tone tunings respectively in the first two models of the Cross-Grainger free music machine. Between 1950 and 1957 Yevgeny Murzin developed the ANS, a photoelectric composition machine tuned to 72 equal octave divisions (1/12-tones). In the mid-1960s Robert Moog constructed three microtonal electronic keyboard instruments: one with 43 notes to the octave over a range of four octaves; one with 31 notes to the octave and a total of 479 keys for a range of seven octaves; and one with 137 keys. At about the same time a microtonal version of the Ondioline was produced for the composer Jean-Etienne Marie by Georges Jenny; this could be tuned in a variety of systems (e.g. divisions of the tone into between three and seven). On the basis of principles proposed by Alain Daniélou, Stephan Kudelski designed a 53-note unequally tempered keyboard instrument in the early 1960s in collaboration with the harpsichord builders Wayland Dobson and Jean Eicher; this was followed in the late 1970s by the S52, built by Claude Cellier and André Kudelski and tuned to 52 notes per octave, with a touch-sensitive keyboard the compass of which can be transposed within a total range of eight octaves. The 31-note Arcifoon was manufactured in Holland from 1971 (see §4 (iii) below). In the early 1970s George Secor and others developed the Scalatron (fig.3), in which each note is independently tunable; Kenneth Macfadyen's ‘detunable organ’ (1968–9, constructed by A.E. Davies & Son) is similarly conceived, though its tuning (including mean-tone) can be reset instantly while that of the Scalatron must by fixed one note at a time. An electronic organ constructed by Ivor Darreg in 1962 retunes itself automatically to any of several different systems. The ekmelische Orgel of Franz Richter Herf (1973–4), built with the assistance of Rolf Maedel, has three 84-note manuals tuned to 72 divisions of the octave; from 1971 Herf composed in this system.
Some synthesizer keyboards, which can be adjusted not only in range but also in compass, have been used to create any number of equal divisions of the octave. The American composer Easley Blackwood has used Moog and Polyfusion synthesizers and the Scalatron in this way, and John Eaton has performed on the Synket in a number of his microtonal compositions; La Monte Young has used a Moog synthesizer and Terry Riley a Yamaha electronic organ to play music in just intonation. The digital EGG synthesizer added a manual with three rows of keys tuned in quarter-tones (197 keys in all) to an 85-note standard equal-tempered manual. In the early 1950s composers working in the electronic music studio at the Nordwestdeutscher Rundfunk in Cologne used various equal subdivisions of the octave or of larger intervals in order to avoid 12-note equal temperament: in Stockhausen's Studie II (1954) 28 semitones (21/4 octaves) are divided into 25 equal intervals so that there are no octave relationships, and Gesang der Jünglinge (1955–6) uses up to 60 divisions of the octave with vocal material and 42 with electronic sounds.
Microtonal instruments, §4: After 1930
Microtonal keyboards have preoccupied inventors rather less in the period since World War II. The 31-note organ of Adriaan Fokker (1950) and its later electronic version the Arcifoon (1971) have a 31-note, equally divided octave, based on Christiaan Huygens's theories; they have a keyboard like that introduced by Bosanquet (see Table 1) with keys in three colours, blue, black and white (fig.4). A number of composers, including Hába and Vïshnegradsky, have written works for the 31-note organ. In Oslo the composer Eivind Groven built a non-tempered 36-note harmonium (1936), a small pipe organ (1954) and a 43-note electronic organ (1965), all in just intonation; around 1970 a similar complete pipe organ was constructed for him by Walcker. All four instruments use conventional keyboards with assignment facilities. In the 1940s A.R. McClure advocated tuning pianos and organs in mean-tone tuning, and an ‘extended meantone organ’ with 19 pipes to the octave was built to his specification in 1950; several mean-tone organs have been installed in the USA, especially those by Charles Fisk from about 1980 (his Stanford University organ has 17 pipes to the octave, and may be played either in mean-tone or well-tempered tuning). Arnold Dreyblatt's portable pipe organ in just intonation dates from around 1980, and Harold Waage's just intonation electronic organ from around 1985. Michael Harrison's modified ‘harmonic piano’ with 24 notes per octave, permits a choice of two different just intonation tunings.
A series of pianos metamorfoseadores (microtonal upright pianos with conventional keyboards), each in a different tuning from 1/3- to 1/16-tones, was planned by Carrillo in 1927; a 1/3-tone grand was built in 1947 and the uprights (by the Carl Sauter Pianofortefabrik in Spaichingen, Baden-Württemberg) in 1957–8. The range of these pianos becomes smaller as the number of subdivisions of the octave is increased, so that the 1/16-tone instrument has a compass of a single octave, in the middle range, with 97 keys. Many of Carrillo's instruments are housed in the Carrillo Museum in Santismo. From the 1930s Augusto Novaro, a former pupil of Carrillo's, built pianos that sounded less percussive than normal and were tuned in 14, 15 and 16 divisions of the octave in a system based on beats; he also constructed Novares, asymmetrical plucked string instruments in 15, 16, 53 and 72 equal divisions.
Activities in building microtonal instruments without keyboards have been largely concentrated in California; elsewhere developments have been sporadic. Since 1977 Dean Drummond in New York has built a family of Zoomoozophones: aluminium tube metallophones in 31-note just intonation, as well as the one-octave set of just intonation Juststrokerods. In Toronto the composer Gayle Young produced Columbine in 1977–8, a 61-note steel tube metallophone covering nearly three octaves in a 23-note unequal temperament based on frequency ratios; she followed it in 1980 with Amaranth, a koto-like instrument with 24 strings and movable bridges, which is tuned in various systems and can be plucked, struck and bowed. The Six-Xen was constructed for Xenakis's Pléïades (1979), written for Les Percussions de Strasbourg; this is a set of six 19-note metallophones, each of which provides different pitches in an unequal scale of 21 notes to the octave, consisting of alternate 1/4- and 1/3-tones. John Grayson in Vancouver employed non-equal tunings in some of his instruments, such as the Pyrex Marimba (1967) which has 24 notes in a compass of about one and a half octaves. Since Carrillo's death in 1965 the arpa citera has been redesigned in Cuernavaca by Oscar Vargas Leal and the composer David Espejo Avilés; several large arpas armónicas with 400 notes to the octave have been built, as well as smaller models, including a three-octave version with 100 notes in ET played by Pepe Aton Estevane since the late 1970s. Péter Eötvös has performed on a ‘55-chord’, a specially built Hungarian citera tuned in intervals based on the golden section, which results in a logarithmic scale lacking any integral frequency ratios or interval steps of identical size. Pierre-Jean Croset's 18-string amplified ‘lyre harmonique’ (1976), tuned to natural harmonics, is based on the ‘harmonic canon’. Since 1983 the composer James Wood has constructed keyed percussion instruments for use in his own compositions, including a quarter-tone marimba and the microxyl (microtonally-tuned stroked rods). Warren Burt wrote several works from 1985 for his four-octave set of aluminium tuning-forks tuned in 19-note just intonation. Markus Stockhausen's quarter-tone flügelhorn is a specially-modified Besson instrument. Eva Kingma of Groloo, the Netherlands, has patented a ‘Key-on-key’ mechanism for quarter-tone alto and bass flutes; based on her patent, quarter-tone flutes and piccolos have been built by Brannen Brothers Flutemakers in Woburn, Massachusetts.
Many of the new acoustic and electronic instruments produced by musicians and sound sculptors use non-tempered tunings that are microtonal but do not adhere to any specific system. Examples include some of the work of Mario Bertoncini and the Sonambient series of Harry Bertoia, which produce constellations of microtonal intervals. Microtonal systems are equally feasible with the techniques of Drawn sound.
However, composers and performers more often prefer to use conventional instruments that are retuned or specially fingered (see Instrument modifications and extended performing techniques ); works for microtonal piano have often been played on two adjacent instruments tuned a quarter-tone apart. Ben Johnston's Sonata/Grindlemusic (1965) requires a piano tuned in a just system in which only seven pairs of keys, mostly several octaves apart, give octave relationships. Just intonation is also used in La Monte Young's The Well-Tuned Piano (1964), which has been revived effectively since 1974 with a Bösendorfer piano. Serge Cordier has specialized in tuning pianos to equal temperament with justly tuned 5ths. Bjørn Fongaard wrote several works from the mid-1960s involving quarter-tone guitars, and the guitarist John Schneider performs in mean-tone, just and Pythagorean tunings. In the 1950s and 1960s Maurice Ohana used zithers tuned in 1/4- and 1/3-tones in several works. Henri Pousseur adopted a 19-note tuning in his solo cello piece Racine 19 (1975), and quarter-tones have been used, primarily but not exclusively with bowed string instruments, in works by Boulez, Ligeti, Penderecki, Xenakis, Per Nørgård, Heinz Holliger, Alain Bancquart and others. Jean-Etienne Marie composed for some of Carrillo's instruments (several of which were in his possession), for the microtonal Ondioline and for synthesizers such as an Oberheim. Pavel Blatný wrote a Study for quarter-tone trumpet and jazz orchestra in 1964. Microtonal inflections and beats are featured in works by Giacinto Scelsi, Phill Niblock, Kenneth Gaburo, George Crumb, Sergey Slonimsky, Peter Sculthorpe and Alvin Lucier. Manfred Stahnke's orchestral Metallic Spaces (1978) uses 1/12-tone tuning, and he has specialised in just intonation and beats. Larry Polansky has also concentrated on just intonation. Since 1989 Klaus Huber has composed several works that include bowed and plucked string instruments in 1/3-tones.
In New York a variety of conventional instruments have been played microtonally, especially in the series of concerts given since 1981 under the title American Festival of Microtonal Music; these are organized by a leading participant, the bassoonist Johnny Reinhard. Refretted guitars and the Scalatron have also appeared in these concerts. Tui St George Tucker has specialized in quarter-tones since the 1950s, especially in her compositions for members of the recorder family. A number of microtonal ensembles have been active in the USA, including the Interval Players, The Newband, Sonora and John Catler's 31-note rock group, J.C. and the Microtones.
GroveA (‘Tuning Systems’; D. Leedy)
MersenneHU
MGG2 (‘Mikrotöne’, B. Barthelmes; also ‘Intervall’, M. Ruhnke and H.-P. Hesse)
N. Vicentino: L'antica musica ridotta alla moderna prattica (Rome, 1555, 2/1557; ed. in DM, 1st ser., Druckschriften-Faksimiles, xvii, 1959; Eng. trans., 1996)
G. Zarlino: Le istitutioni harmoniche (Venice, 1558/R, 3/1573/R; Eng. trans. of pt iii, 1968/R, as The Art of Counterpoint; Eng. trans. of pt iv, 1983, as On the Modes)
N. Vicentino: Descrizione dell'arciorgano (Venice, 1561); Eng. trans. in H.W. Kaufmann: ‘Vicentino's Arciorgano: an Annotated Translation’, JMT, v (1961), 32–53
F. de Salinas: De musica libri septem (Salamanca, 1577); Eng. trans. in A.M. Daniels: The ‘De musica libri VII’ of Francisco de Salinas (diss., U. of Southern California, 1962)
F. Colonna: La sambuca lincea, overo dell'istromento musico perfetto (Naples, 1618/R)
C. Huygens: ‘Novus cyclus harmonicus’, Opera varia (Leiden, 1724), 747–54; ed. in Oeuvres complètes, xx (The Hague, 1940; Eng. and Dutch trans., 1986)
H.W. Poole: ‘An Essay on Perfect Intonation in the Organ’, American Journal of Science and Arts, 2nd ser., ix (1850), 68–83, 199–216
H. von Helmholtz: ‘Über musikalische Temperatur’, Naturhistorische-Medizinischer Verein Heidelberg (23 Nov 1860); rev. in Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Brunswick, 1863, 6/1913/R), 501, 664, 669; Eng. trans., 1875, as On the Sensations of Tone, 2/1885/R), 310–30, 422–93
A.J. Ellis: ‘On the Temperament of Instruments with Fixed Tones’, Proceedings of the Royal Society of London, xiii (1863–4), 404–22
T.P. Thompson: On the Principles and Practices of Just Intonation (London, 9/1866)
H.W. Poole: ‘On Perfect Harmony in Music, the Double Diatonic Scale, and an Enharmonic Key-Board for Organs, Piano-Fortes, etc.’, American Journal of Science and Arts, 2nd ser., xliv (1867), 1–22
R.H.M. Bosanquet: An Elementary Treatise on Musical Intervals and Temperament (London, 1876/R)
W.H. Stone: The Scientific Basis of Music (London, 1878), 49–71
G. Engel: Das mathematische Harmonium: ein Hilfsmittel zur Veranschaulichung der reinen Tonverhältnisse (Berlin, 1881)
C. Brown: Music in Common Things (London, 1885)
S. Tanaka: ‘Studien im Gebiete der reinen Stimmung’, VMw, vi (1890), 1–90; partial Eng. trans. in D.J. Wolf: ‘Studies in the Realm of Just Intonation’, Xenharmonikôn, xvi (1995), 118–25
C.A. Eitz: Das mathematisch-reine Tonsystem (Leipzig, 1891)
G.A. Behren-Senegalden: Die Vierteltöne in der Musik: Begleitschrift zu der Erfindung eines achromatischen Klaviers und Entwurf zur Darstellung der Vierteltöne als Notenschrift (Berlin, 1892)
J.W. Hinton: Organ Construction (London, 2/1902, 3/1910/R), 164–73 [first pubd 1900]
F. Busoni: Entwurf einer neuen Ästhetik der Tonkunst (Trieste, 1907, 2/1916/R; Eng. trans., 1911/R)
J. Mager: Vierteltonmusik (Aschaffenburg, 1915)
W. von Möllendorf: Musik mit Vierteltönen (Leipzig, 1917)
A.M. Avraamov: ‘Jenseits von Temperierung und Tonalität’, Melos, i (1920), 131–4, 160–66, 184–8
F. Busoni: ‘Bericht über Dritteltöne’, Melos, iii (1922), 198–9; Eng. trans. in The Essence of Music and Other Papers (New York, 1957), 50–51
R.H. Stein: ‘Vierteltonmusik’, Die Musik, xv (1923), 510–16, 741–6
J. Mager: Eine neue Epoche der Musik durch Radio (Berlin, 1924)
E.H. Pierce: ‘A Colossal Experiment in “Just Intonation”’, MO, x (1924), 326–32
S. Baglioni: Udito e voce: elementi fisiologici della parola e della musica (Rome, 1925)
C. Ives: ‘Some “Quarter-Tone” Impressions’, Franco-American Music Society Bulletin, xxv/3 (1925), 24–33; repr. in Essays Before a Sonata and Other Writings, ed. H. Boatwright (New York, 2/1962), 105–19
G.M. Rimsky-Korsakov: ‘Obosnovaniye chetvyortitonovoy muzïkal'noy sistemï’ [Basis of the quarter-tone musical system], De musica, i (1925), 52–78
L. Kallenbach-Greller: ‘Die historischen Grundlagen der Vierteltöne’, AMw, viii (1926), 473–85
W. Perrett: Some Questions of Musical Theory (Cambridge, 1926)
G. Overmyer: ‘Quarter-Tones – and Less’, American Mercury, xii (1927), 207–10
G. Rimsky-Korsakov: ‘Theorie und Praxis der Reintonsysteme in Sowjet-Russland’, Melos, vii (1928), 15–17
M.F. Meyer: The Musician's Arithmetic: Drill Problems for an Introduction to the Scientific Study of Musical Composition, University of Missouri Studies, iv/1 (Boston, 1929)
J. Yasser: A Theory of Evolving Tonality (New York, 1932/R)
J. Foulds: Music Today: its Heritage from the Past, and Legacy to the Future (London, 1934), 59–65
W. Dupont: Geschichte der musikalischen Temperatur (Kassel, 1935/R)
A. Fickénsher: ‘The “Polytone” and the Potentialities of a Purer Intonation’, MQ, xxvii (1941), 356–70
E.W. Tipple and R.M. Frye: A Graphic Introduction to the Harmon (Boston, 1942)
J. Carrillo: ‘Sonido 13’: fundamento científico e histórico (Mexico City, 1948; Eng. trans. in Soundings, no.5 (1973), 64–125)
E. Groven: Temperering og renstemning [Temperament and just tuning] (Oslo, 1948; Eng. trans., 1970)
A.D. Fokker: Just Intonation and the Combination of Harmonic Diatonic Melodic Groups (The Hague, 1949), 195–319
H. Partch: Genesis of a Music (Madison, WI, 1949, enlarged 2/1974), 361–457
A.R. McClure: ‘An Extended Mean-Tone Organ’, The Organ, xxx (1950–51), 139–49
J.M. Barbour: Tuning and Temperament: a Historical Survey (East Lansing, MI, 1951/R, 2/1953/R)
M.J. Mandelbaum: Multiple Division of the Octave and the Tonal Resources of 19-Tone Equal Temperament (diss., Indiana U., 1961)
Ll.S. Lloyd: Intervals, Scales and Temperaments, ed. H. Boyle (London, 1963, 2/1978)
A.D. Fokker: Neue Musik mit 31 Tönen (Düsseldorf, 1966; Eng. trans., 1975)
H.W. Kaufmann: The Life and Works of Nicola Vicentino (1511–c.1576), MSD, xi (1966), 163 only
L.A. Hiller and others: ‘Microtonal Music in America’, Proceedings of the American Society of University Composers, ii (1967), 77–122 [forum]
E. Groven: Renstemningsautomaten [A machine for just tuning] (Oslo, 1968)
K.A. Macfadyen and D. Greer: ‘A Detunable Organ’, MT, cx (1969), 612–13
A. Hába: Mein Weg zur Viertel- und Sechstel- Tonmusik (Düsseldorf, 1971)
Xenharmonikôn (1974–) [incl. I. Darreg: ‘Xenharmonic Bulletin nos.1–9’, i–viii (1974–9)]
W. Colvig: ‘A Western Gamelan’, Sound Sculpture: a Collection of Essays by Artists Surveying the Techniques, Applications, and Future Directions of Sound Sculpture, ed. J. Grayson (Vancouver, 1975), 162–9
D. Ellis: Quarter Tones: a Text with Musical Examples, Exercises and Etudes (New York, 1975)
F.R. Herf: Die ekmelische Orgel: eine elektronische Feinstufenorgel mit 72 Tonstufen in der Oktave (Salzburg, 1975)
S. Schneider: Mikrotöne in der Musik des 20. Jahrhunderts: Untersuchungen zu Theorie und Gestaltungsprinzipien moderner Kompositionen mit Mikrotönen (Bonn-Bad Godesberg, 1975)
J.-E. Marie: L'homme musical (Paris, 1976), 25–94
Interval: Exploring the Sonic Spectrum (1978–87)
K. Terry: ‘La Monte Young: Avant-Garde Visionary Composer and Pianist’, Contemporary Keyboard, vi/8 (1980), 12–18
E. Blackwood: ‘Discovering the Microtonal Resources of the Synthesizer’, Keyboard, viii/5 (1982), 26–38
‘Microtonal Music’, Ear Magazine East, vii/5 (1982–3)
1/1: the Journal of the Just Intonation Network (1985–)
Interface, xiv/1–2 (1985)
E. Blackwood: The Structure of Recognizable Diatonic Tunings (Princeton, NJ, 1985)
Pitch for the International Microtonalist, i/1–4 (1986–90) [i/2 incl. bibliography compiled by J. Reinhard; i/3 is a cassette]
J. Wood: ‘Microtonality: Aesthetics and Practicality’, MT, cxxvii (1986), 328–30
D. Keislar: ‘History and Principles of Microtonal Keyboards’, Computer Music Journal, xi/1 (1987), 18–28
S.R. Wilkinson: Tuning In: Microtonality in Electronic Music: a Basic Guide to Alternate Scales, Temperaments and Microtuning using Synthesizers (Milwaukee, 1988)
D. Devie: Le tempérament musical: philosophie, histoire, théorie et pratique (Béziers, 1990) [incl. bibliography]
G. Read: 20th-Century Microtonal Notation (New York, 1990)
‘Forum: Microtonality Today’, PNM, xxix/1 (1991), 172–262
J.H. Chalmers: Divisions of the Tetrachord: a Prolegomenon to the Construction of Musical Scales (Hanover, NH, 1993)
B. McLaren and others: Microtonal Bibliography (1998) 〈www.ixpres.com/interval/mclaren/biblio.htm〉