Faà di Bruno, Giovanni Matteo [Horatio, Orazio] 83

Fokine [Fokin], Mikhail Mikhailovich

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Fokine [Fokin], Mikhail Mikhailovich

(b St Petersburg, 13/25 April 1880; d New York, 22 Aug 1942). Russian dancer and choreographer; see Ballet, §3(i).

Fokker, Adriaan Daniel

(b Buitenzorg [now Bogor], Java, 17 Aug 1887; d Beekbergen, 24 Sept 1972). Dutch physicist and acoustician. He took the doctorate in physics in 1913 at the University of Leiden, and studied with Einstein in Zürich, Rutherford in Manchester and Bragg in Leeds. He taught physics at Delft Gymnasium (1921–3) and Technical College (1923–7), and was Lorentz's assistant (1927) and director of the physics section (1928–55) at Teyler’s Stichting, Haarlem, concurrently occupying the chair founded by this institute at Leiden (1928–55). During these years Fokker became one of the foremost physicists in the Netherlands, and with the suspension of academic activity under the German occupation he turned to problems of musical aesthetics, his chief interests being the theories of Euler and Christiaan Huygens. He constructed two pipe organs, one (1943) with just intonation scales according to the principles of Euler’s genera musica, and another (1950) that realized Huygens’s theories of the pure 3rd, secured by a scale of 31 5th-tones. He described this scale in his several books and articles on harmony and temperament.

Fokker became an ardent promoter of the use of the 31-tone system in musical performance (especially on the 31-tone organ at Haarlem) and in composition. He composed a number of musical works, including Preludium chromaticum (1948), Nine Bagatellen (1950–52) and In generibus Leonhardi Euler (1956–7), for the tuning systems and instruments he devised. Other composers who adopted the 31-tone system under his influence include Henk Badings, Jan van Dijk, Anton de Beer, Hans Kox, Alan Ridout and Joel Mandelbaum. In 1970 Fokker founded the Stichting Nauwluisterendheid (Foundation for Listening Accuracy), later Stichting Huygens-Fokker, to take charge of the application and dissemination of his ideas on music.


Rekenkundige bespiegeling der muziek (Gorinchem, 1944)

‘Les mathématiques et la musique’, Archives du Musée Teyler, 3rd ser., x (1947) 1–32

‘Expériences musicales avec les genres musicaux de Leonhard Euler contenant la septième harmonique’, IMSCR IV: Basle 1949, 113–14

Just Intonation and the Combination of Harmonic Diatonic Melodic Groups (The Hague, 1949)

Recherches musicales, théoretiques et pratiques (The Hague, 1951)

‘The Qualities of the Equal Temperament of 31 Fifths of a Tone in the Octave’, IMSCR V: Utrecht 1952, 191–2

‘Les cinquièmes de tons: les subtilités lignes mélodiques et l’enrichissement des harmonies’, Acoustique musicale: Marseilles 1958, ed. M.F. Caine (Paris, 1959), 29–37

‘Multiple antinairesis’, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, ser. B, lxvi (1963), 1–6

‘Wozu und warum? Fragen zur neuen Musik’, Die Reihe, viii (1962), 62–72; Eng. trans. (1968), 68–79

Neue Musik mit 31 Tönen (Düsseldorf, 1966; Eng. trans., 1975)

‘On the Expansion of the Musician’s Realm of Harmony’, AcM, xxxviii (1966), 197–202

‘Selections from the Harmonic Lattice of Perfect Fifths and Major Thirds containing 12, 19, 22, 31, 41 or 53 Notes’, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, ser. B, lxxi (1968), 251–66

‘Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7-) Harmonic Lattice of Notes’, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, ser. B, lxxii (1969), 153–68


B. Lemkes: ‘Over zuivere intonatie: het levenswerk van prof. dr. A.D. Fokker’, Mens en melodie, xxiii (1968), 37–42

R. Rasch: Introduction to Adriaan Daniel Fokker: Selected Musical Compositions (1948–1972), Corpus Microtonale, i (Utrecht, 1987)

R. Rasch: ‘Adriaan Daniël Fokker (1887–1972): musicus tricesimoprimalis’, Jaarboek van de Stichting Huygens-Fokker (1988), 5–17

R. Rasch: ‘The Theories of Adriaan Fokker’, 1/1: Quarterly Journal of the Just Intonation Network, iv (1988), no.1, pp.4–7, 14; no.2, pp.6, 10–12


Fokkerod, Gottfried.

See Vockerodt, Gottfried.

Folc de Marseille.

See Folquet de marseille.

Foldes [Főldes], Andor

(b Budapest, 21 Dec 1913; d Herrliberg, nr Zürich, 9 Feb 1992). American pianist and conductor of Hungarian birth. He inherited musicianship through his mother (née Ipoly), and was educated at home, studying the piano with Tibor Szatmari. In May 1922, aged eight, Foldes made his début playing Mozart’s k450 Concerto with the Budapest PO. A year later he entered the Liszt Academy of Music, studying composition with Leo Weiner and conducting with Ernst Unger; he graduated from Dohnányi’s masterclass in 1932. He had made his début in Vienna in 1929, and that year he met Bartók and at once began to study his piano music under his supervision, continuing until Bartók’s death. Dohnányi’s conducting of concertos from the keyboard fired Foldes with the ambition to do the same, though he did not do so until 1960, after when he also pursued a side-career as a symphonic conductor.

Foldes first toured Europe in 1933, but retired for a while to replace childish intuition with adult reasoning in musical interpretation through study of other arts, language and philosophy. He soon resumed his career though he did not consider himself an adult pianist until 1939 when he played Beethoven’s Second Concerto under Erich Kleiber. After his New York début in 1940 he remained in the USA, taking American nationality and marrying the Hungarian journalist Lily Rendy. In 1948 the Foldes returned to Europe; from 1958 to 1965 he took masterclasses in Saarbrücken. At that time he concentrated on the Viennese Classics from Haydn to Schubert, adding Bartók when he recognized that his earlier, pugnacious interpretations were no longer apt to a modern Classical master. He never lost his early virtuoso technique. In the early 1960s his playing was exuberant, outward-going and bright-toned, always attentive to articulation and rhythm. After then he became more concerned with softer shades, and subtle phrasing, perhaps through his study of the late works of Mozart, Beethoven and Schubert, as well as Schumann and Debussy. He composed a number of works and made keyboard transcriptions of three numbers from Kodály’s Háry János.


Keys to the Keyboard (New York, 1948)

Gibt es einen zeitgenössischen Beethoven-Stil? und andere Aufsätze (Wiesbaden, 1963)


L. Foldes: Two on a Continent (New York, 1947)

W.-E. von Lewinski: Andor Foldes (Berlin, 1970)


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