Music Theory and Analysis

In the 18th century sectional binary form continued to appear in folk music and in chorales (for example in Bach’s chorale no.38, Straf mich nicht in deinem Zorn). It is most commonly found in arias, and may be understood retrospectively as a da capo form that unexpectedly fails to complete itself. This almost always occurs for dramatic reasons, as in Jonathan’s ‘No, no, cruel father, no!’ from Handel’s Saul, where a lamenting first section in B minor is succeeded by a G major Allegro. Both sections are harmonically closed, leaving the larger structure open; AB is clearly a more appropriate designation here. A more complex example is Iole’s aria ‘My father! ah! methinks I see’ from Handel’s Hercules. In the first section, beginning and ending in C minor, Iole relives the killing of her father by Hercules. The relative major is held in reserve for the second section, in which Iole bids her father rest in peace. Rather than finishing in E♭ major, though, the music clouds over into E♭ minor, implying that Iole’s remembrance of the violent death has invaded her thoughts. The close thus reverts to the mode of the first section and creates some sense of rounded shaping to the whole, if in the first instance for dramatic reasons; there are also some subtle thematic recollections from ...

Member of Calegari family

(b Padua, Feb 17, 1757; d Padua, July 22/28, 1828). Italian composer and theorist, brother of Giuseppe Calegari. He was probably not a nephew of Francesco Antonio Calegari; nor was he a son of Luigi Calegari (d ?1767), whose name has incorrectly been associated with Urbino Cathedral, but a younger son of Angelo Calegari and Anna Albanese, both native to Padua. He was often called ‘Il seniore’ to distinguish him from his nephew Luigi Antonio Calegari. His musical studies began with Jacopo Scalabrin (called Fantoncino) and possibly Fernando Turrini, and were continued in Venice under Ferdinando Bertoni. He conducted the first performance in Padua of Bertoni’s short opera Orfeo ed Euridice on May 2, 1776 at the Teatro Obizzi. His earliest surviving work is an oratorio, La risurrezione di Lazzaro (1779, Padua). His oratorio for women’s voices, Coronatio Salomonis, was performed by the choir of the Ospedale degli Incurabili in Venice in ...

(Florenz Friedrich)

(b Wittenberg, Nov 30, 1756; d Breslau [now Wrocław], April 3, 1827). German acoustician. He studied law at Leipzig University before turning to scientific studies. He invented two instruments, the ‘euphon’ and the ‘klavizylinder’, both of which were variants of the glass harmonica. However, he owes his fame to his celebrated experiments on the nodal patterns and corresponding frequencies of vibration plates. He showed that the vibration patterns, often called Chladni figures, could be made visible by sprinkling sand on the plate. The sand is thrown up on vibrating areas and collects around nodal lines. Chladni travelled through Europe playing on his instruments and demonstrating his experiments before many persons and institutions; he encountered Goethe, Lichtenberg, Olbers, Laplace, Napoleon and other notable men of the period. Chladni's experiments stimulated much early work on the vibration of plates and bars and indeed so impressed the Académie des Sciences, Paris, that it offered a prize for a successful explanation of his sand figures and the motion of elastic surfaces in general. His work helped to form the foundation of modern theories, capable of predicting precise vibration patterns for violin and guitar top plates and the soundboards of keyboard instruments....

(b Basle, April 4, 1707; d St Petersburg, Sept 18, 1783). Swiss mathematician, scientist and philosopher. He studied at Basle University under Johann Bernoulli. When he was 20, he took (at Daniel Bernoulli's suggestion) a post at the Academy of Sciences in St Petersburg; he held a post in Berlin (1741–66), then returned to St Petersburg. He won the Grand Prix of the Paris Académie des Sciences 12 times. The most prolific of scientists, he published some 800 memoirs and 50 books or pamphlets on various branches of mathematical science and some domains of engineering, music, philosophy and religion.

Euler contributed more to theoretical acoustics as the subject is now known than has any other man. At the age of 19 he wrote Dissertatio physica de sono, in which he divided sounds into three kinds (the tremblings of solid bodies; the sudden release of compressed or rarefied air; and oscillations of air, either freely or confined). Acoustics was one of his favourite subjects. His notebooks show that as a boy of 19 he planned to write a treatise on all aspects of music, including form and composition as well as acoustics and harmony. The only part of this project to come to fruition was his ...

(b Turin, Jan 25, 1736; d Paris, April 10, 1813). French mathematician and physicist. He was largely self-trained and was encouraged by Euler and d'Alembert, whose protégé he became. He held positions in Berlin (from 1766) and Paris (from 1787). He is remembered as an acoustician for his work in 1759 on the transverse vibrations of the taut, massless cord loaded by n weights, equally spaced. He is credited with being the first to represent the string in this way and to calculate its normal mode patterns and frequencies, and for having established Euler's solution for the continuous monochord as being the result of taking the limit as n tends to infinity. In fact the discrete model was a very old one, and Lagrange's work on it is a straightforward extension of Euler's; further, as d'Alembert pointed out, Lagrange's passage to the limit is fallacious. In ...

(b Mulhouse, ?Aug 26, 1728; d Berlin, Sept 25, 1777). German scientist. From 1748 to 1758 he was tutor to the children of a Swiss noble family; in 1765 he managed to obtain a post at the Akademie der Wissenschaften in Berlin. He was one of those universal scientists characteristic of the 17th and 18th centuries, and was a figure of particular importance in several subjects mainly connected with physics and mathematics. He determined very precisely the frequencies of the first eight overtones of a bar in its clamped-free modes, correcting and extending Euler’s results; the results of Rayleigh and others, a century or more later, were less conclusive. Lambert projected a musical instrument, the ‘musique solitaire’, whereby a person might enjoy music through his teeth without awakening sleepers.

Member of Mozart family

(b Augsburg, Nov 14, 1719; d Salzburg, May 28, 1787). Composer, violinist and theorist.

He was the son of an Augsburg bookbinder, Johann Georg Mozart (1679–1736), and attended the Augsburg Gymnasium (1727–35) and the Lyceum adjoining the Jesuit school of St Salvator (1735–6), where he frequently performed as an actor and singer in various theatrical productions; he was also an accomplished organist and violinist. In 1737 Leopold broke with his family and matriculated at the Salzburg Benedictine University, studying philosophy and jurisprudence. He took the bachelor of philosophy degree the next year, with public commendation, but in September 1739 he was expelled for poor attendance and indifference. Shortly after, he became a valet and musician to Johann Baptist, Count of Thurn-Valsassina and Taxis, Salzburg canon and president of the consistory; it was to Thurn-Valsassina that Mozart dedicated his ...

(b Montpellier, Sept 14, 1723; d Montpellier, Nov 8, 1766). French dilettante and scientist. In December 1751 he announced his discovery of difference tones, which he had made by experiments with wind instruments. (Nearly three years later Tartini, evidently unaware of Romieu’s work, published his discovery of the same phenomenon observed in double stops on the violin.) Romieu’s ‘Mémoire théorique & practique sur les systèmes temperés de musique’, published in the 1758 Mémoires of the Académie Royale des Sciences, surveyed various regular tuning systems and expressed preference for ⅙-comma mean-tone temperament and its theoretical equivalent, the division of the octave into 55 equal parts.

(Fr. tonalité; Ger. Tonalität)

A term first used by Choron in 1810 to describe the arrangement of the dominant and subdominant above and below the tonic and thus to differentiate the harmonic organization of modern music (tonalité moderne) from that of earlier music (tonalité antique). One of the main conceptual categories in Western musical thought, the term most often refers to the orientation of melodies and harmonies towards a referential (or tonic) pitch class. In the broadest possible sense, however, it refers to systematic arrangements of pitch phenomena and relations between them.

A number of musical and discursive factors have contributed to a profusion of definitions for the term. There has been indecision about what musical domain the term covers: whether it applies to both Western and non-Western music, or whether, within Western musical traditions, it should be restricted to the harmonic organization of music from the so-called common practice (...