Nabokov, Nicolas [Nikolay]

Nicolino.

See Cosimi, Nicola.

Nicoll, James

(fl early 18th century). Scottish publisher who inherited the firm established by John Forbes.

Nicolo.

The ‘Basset: Nicolo’ mentioned by Praetorius; see Crumhorn.

Nicolò [Nicolò de Malte].

See Isouard, Nicolò.

Nicolo da Perugia.

See Niccolò da Perugia.

Nicolson, Richard.

See Nicholson, Richard.

Nicomachus [Nikomachos] of Gerasa

(fl late 1st – early 2nd century ce). Greek mathematician and music theorist. His Introduction to Arithmetic (Arithmētikē eisagōgē) won him high praise and instant fame in antiquity. This work and the Manual of Harmonics (Harmonikon encheiridion) have survived in their entirety; ten extracts (Excerpta ex Nicomacho, ed. Jan, 266–82) remain from a longer treatise on music, and portions of another work, Theology of Arithmetic (Theologoumena arithmetikēs), are preserved in an anonymous treatise of the same title.

The Manual of Harmonics is the only work on Greek music to have come down from the long period between the appearance of the Harmonic Elements of Aristoxenus and the Euclidean Division of the Canon in the 4th century bce, and that of the Harmonics of Nicomachus’s celebrated younger contemporary Claudius Ptolemy in the 2nd century ce. The Manual is important for its influence on numerous later writers, and especially for the canonical material that it alone preserves. It is the first work in the literature to transmit the time-honoured story of Pythagoras’s momentous discovery that musical pitch is ruled by number. As Nicomachus tells it (chap.vi), Pythagoras’s revelation was inspired by the ringing sounds he chanced to hear issuing from a blacksmith’s anvil. Recognizing them to be the very concords – octave, 5th and 4th – that he could produce on the strings of his lyre, Pythagoras performed a series of experiments and found the elegantly simple truth about musical sound: the pitch from a plucked string depends on the length of the string, and the concords are produced by strings whose lengths are to each other as the ratios of the whole numbers: 6:8:9:12.

No less significant is Nicomachus’s detailed account of the first unified theory of the cosmos. It contains what may be the most ancient version of the distinctly Pythagorean-Platonic concept that the harmonic properties of music, discoverable in the ratios of the concords, are implicit in the orderly distribution of the heavenly planets (see Music of the spheres). Nicomachus’s discussion of this theory, along with Plato’s in the Timaeus, influenced astronomical thought for centuries, converging eventually with cosmic reality in the celestial physics of Johannes Kepler.

Nicomachus was the first writer on music to attribute the invention of the octachord (eight-string lyre) to Pythagoras (Manual, v); he is also the source (ibid., ix) of one of the oldest pieces of evidence on musical scales, a fragment of Philolaus’s On Nature, the first written document on the teachings of Pythagoras.

In his discussion of the inverse proportion that obtains between a sounding body and musical pitch (the higher the pitch, the smaller the body, and conversely) and the reciprocal relation between pitch and tension (the greater the tension, the higher the pitch, and conversely), Nicomachus provides (Manual, iv and x) valuable information on diverse musical instruments. The most exotic and obscure of the strings mentioned by him is the spadix, apparently a lyre-type instrument shaped like a palm frond. Equally interesting is his evidence on the pandoura, a lute of remote antiquity which he likens to the Pythagorean research instrument, the monochord.

Perhaps the most curious feature of the Manual is the incorporation (in chap.ii) into an otherwise strictly Pythagorean programme of a decidedly non-Pythagorean concept imported from the theory of Aristoxenus. For Aristoxenus’s theory is based on the notion of a tonal continuum (topos) whose division by the placement of pitches and intervals is under the sole governance of the human voice and ear. In the conventional Pythagorean approach, however, the division of musical space is determined solely by the mathematical laws of harmonic proportion. Thus, without citing him, Nicomachus spoke the language of Aristoxenus, and in his effort to credit the Pythagoreans with the invention of all things musical, he attributed to them the very doctrine that is contravened by their mathematically based harmonic principles.

See also Greece, §I, 6(i).

WRITINGS

C.E. Ruelle, trans.: Nicomaque de Gérase: Manuel d’harmonique et autres textes relatifs à la musique (Paris, 1881)

C. von Jan, ed.: Musici scriptores graeci (Leipzig, 1895/R), 209–82

A. Barker, ed.: Greek Musical Writings, ii: Harmonic and Acoustic Theory (Cambridge, 1989), 245–69

F. Levin, ed.: The Manual of Harmonics of Nicomachus the Pythagorean (Grand Rapids, MI, 1994)

FLORA R. LEVIN

Nicosia, Paulo Caracciolo da.

See Caracciolo, Paolo.

Niculescu, Ştefan

(b Moreni, Dâmboviţa, 31 July 1927). Romanian composer. He studied in Bucharest at the Royal Academy of Music (1941–6), the Polytechnic Institute (1946–50) and the Academy of Music (1951–7) under Andricu (composition), Jora (harmony) and Muza Ghermani-Ciomac (piano); he also attended the Darmstadt summer courses (1966–9) and Kagel's electronic music course in Munich (1966). In Bucharest Niculescu worked as a piano teacher (1958–60), researcher at the Institute of Art History (1960–63) and then lecturer in composition and analysis at the Academy of Music; he was made professor at the academy in 1993. He was composer-in-residence at the Deutscher Akademischer Austauschdienst in Berlin (1971–2), founder-director of the international Week of New Music, Bucharest, and guest lecturer at the Darmstadt summer courses in 1992.

Works such as the String Trio, Cantata II and Symphonies for 15 Soloists placed Niculescu at the forefront of the Romanian avant garde during the 1950s. Subsequently, he embarked on a study of heterophony. This led to a radical rethink of his composition technique and the application of modern mathematics (e.g. the theories of graphs and sets) in works such as Cantata III, Hétérophony and Heraclit's Aphorisms. During the 1970s and 80s he developed this interest further by creating new heterophonic shapes, but in a diatonic language dramatically opposed to the serial chromaticism of his earlier works. During the 1990s he attempted to fuse diverse trends, such as diatonicism and chromaticism; the natural harmonic scale and scales not built around octaves; heterophony and polyphony; homophony and melody; and the continuity and discontinuity of speech. His later works are often monumental in scale and have veered towards a new kind of sacred music, in which aspects of the Romanian Byzantine and similar traditions of the world are integrated and transfigured.

Niculescu is one of the most original Romanian contemporary composers of his generation. He has received many awards from the Romanian Composers' Union and Romanian Academy, and was made a member of the latter in 1993. Outside Romania he has received the International Record Critics Award (1985), the Herder Prize, Vienna (1994), and an award from the French Academy (1972 Prix d’Académie des Beaux Arts).

WORKS

(selective list)

Stage: Cartea cu Apolodor (children's op, 2, G. Naum), 1974; Cluj-Napoca, 13 April 1975

Orch: Ison II, wind, perc, 1957; Scènes, suite, wind, perc and db, 1962; Syms. for 15 Soloists, 1963; Hétérophony, 1967; Formanti, 1968; Unisonos I, 1970; Unisonos II, 1971; Ison Ia, 14 soloists, 1973; Ison Ib, 1973; Sym. no.1, 1975; Sym. no.2 ‘Opus Dacicum’, 1980; Synchrony II ‘Omaggio a Enescu e Bartók’, 1981; Sym. no.3 ‘Cantos’, 1984; Sym. no.4 ‘Deisis’, 1995; Sym. no.5, ‘Litanies’, 1997; Umdecimum, fl, ob, cl, bn, hn, tr, trb, 2 vn, va, vl, 1998

Vocal: Cantata I (N. Cassian), female/children's chorus, orch, 1959; Cantata II (G. Naum), T, mixed chorus, orch, 1960; Cantata III ‘Răscrucee’ (T. Arghezi), Mez, 5 wind, 1965; Heraclit's Aphorisms, 20 vv, 1969; Invocatio, 12 vv, 1989; Axion, female chorus, sax, 1992; Psalm xii, 6 male vv, 1993

Chbr and solo inst: Sonata, cl, pf, 1955; Str Trio, 1957; Inventions, cl, pf, 1965; Tastenspiel, pf, 1968; Wind Sextet, 1969; Triplum I, fl, vc, pf, 1971; Triplum II, cl, vc, pf, 1973; Echos I, vn, 1977; Synchrony I, 2–12 insts, 1979; Echos II, vn, synth, 1984; Ricercare in uno, cl, vn, synth, 1984; Duplum, vl, pf and synth, 1984; Synchrony III, 3 wind, 1985; Hétérophonies for Montreux, 5 wind, 1986; Synchrony IV, cl, perc, pf, 1987; Incantations, 6 perc, 1991; Sextuplum, wind, perc, vn, vc, 1993; Sequentia, fl, vn, va, vln, perc, 1994

Principal publishers Muzicală (Bucharest), Salabert, Schott

WRITINGS

with others: George Enescu, ii (Bucharest, 1971)

Reflecţii despre muzică [Remarks on music] (Bucharest, 1980)

‘Planetarische Grammatik’, MusikTexte, no.45 (1992), 54–56

BIBLIOGRAPHY

A. Stroe: ‘Simfonia de Ştefan Niculescu’, Muzica, x/6 (1960), 42 only

V. Cosma: Muzicieni romani: lexicon (1970) 330–32

V. Cosma: Corul “Madrigal” al Conservatorului (1971)

I. Sava: Ştefan Niculescu si galaxiile muzicale ale secolului XX [Ştefan Niculescu and the musical galaxies of the 20th century] (Bucharest, 1991)

H. Halbreich: ‘Roumanie, terre du neuvième siècle’ (Bucharest, 1992)

L. Knessel: ‘Stefan Niculescu’, Wien Modern … ein internationales Festival mit Musik des 20. Jahrhunderts, Vienna, 1992, 129

R. Kager: ‘Rumäniens Musikavangarde’, Suddeütsche Zeitung (21 Jan 1993)

R. Steinitz: ‘Profile: Ştefan Niculescu’, Huddersfield Contemporary Music Festival, November, 1993

‘Fatǎ în fatǎ: György Ligeti et Stefan Niculescu intro convortire coordonatâ de Karsten Witt. Viena, 1992’, Muzica, new ser. iv/2 (1993), 58–81 [incl. Eng. trans., 70–81]

‘Von Heterophonie und verschobenen Blöcken: György Ligeti analysiert gesprächs weise die Musik von Ştefan Niculescu’, Ton (1993–4), wint., 17–19

L. Knessel: ‘Stefan Niculescu’, Wien Modern … ein internationales Festival mit Musik des 20. Jahrhunderts, Vienna, 1998, 69–70

VIOREL COSMA