a general rule proceed only in perfect Fourths or Fifths upwards or downwards.' Helmholtz defines it as 'the compound tone which represents the chord, as distinguished from its bass, that is, the tone which belongs to the lowest part.'
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FUX, Johann Joseph, born 1660 of a peasant family in the hamlet of Hirtenfeld, near Gratz in Styria. Nothing is known of his early life or studies, as he refused to give information on the subject even to Mattheson for his 'Grundlage einer Ehrenpforte' (Hamburg 1740; see p. 340, letter dated 1718). From 1696, however, all is clear. In that year he was appointed organist to the ecclesiastical foundation 'Zu den Schotten' in Vienna; and married a Viennese, by whom he had no children. In 1698 he became court composer, and in 1705 Capellmeister to the cathedral of St. Stephen. He was also appointed vice-Capellmeister to the court, and in 1713 Capellmeister to the Dowager Empress Wilhelmine Amalie. This post he resigned in 1718, as he had done that at the cathedral in 1715 upon his promotion to be head Capellmeister to the court. He received many proofs of court favour. To the King of the Romans—Arch-duke, afterwards Emperor, Joseph I—he dedicated his first opus 'Concentus musico-instrumentalis,' in 7 parts (Felsecker, Nuremberg 1701), and the 'Missa Canonica' (1718); and to the Emperor Charles VI his most important work 'Gradus ad Parnassum' (1725). In 1723, when laid up with gout, the Emperor Charles had him conveyed in a litter to Prague, that he might be present at the performance of his opera 'Costanza e Fortezza,' written for the coronation. Fux died at Vienna Feb. 13, 1741, and was buried at St. Stephen's. Among his best pupils were Zelenka, Muffat, Tuma, and Wagenseil. An oil-painting of him in the costume of the period is in the museum of the 'Gesellschaft der Musikfreunde' at Vienna. Fux considered his art in a serious light, and was held in general respect. He was courteous to all, and eminently kind and just in his dealings with the musicians under him. As a composer he was most industrious; 405 works by him are still in existence—50 masses; 3 requiems; 57 vespers and psalms; 22 litanies and completoria; 12 graduals; 14 offertoriums; 22 motets; 106 hymns; 2 Dies iræ; 1 Domine; 1 Libera (290 church-works in all); 10 oratorios; 18 operas (of which 6 were grand operas—'dramme per musica'—and the other 12 'componimenti per camera' and 'feste teatrali per musica'); 29 partitas and overtures; and 8 pieces for clavier. The greater part of these compositions, either copied or in autograph, are in the Imperial Library at Vienna; and the 'Gesellschaft der Musikfreunde' also possesses a considerable number.Of his works only few are printed: his 'Concentus,' already mentioned, 'Elisa,' festa teatrale (Jeane Roger, Amsterdam, 1719), and the 'Missa canonica' (see below). Proske's 'Musica divina,' vol. ii. and iii., contain seven church-works. 36 Trios for 2 violins and bass (published about 1700) are lost. His dramatic works are now valueless, though in their day they contributed much to the lustre of the court; while his oratorios, written for Lent, were still more quickly forgotten. Among his MSS. are 38 sacred 'Sonate a tre,' which were often played in Divine Service, and are masterpieces of freshness, invention, and variety. It is evident that Fux enjoyed 3-part writing, for in his 'Gradus' he says 'the master's hand may always be detected even in 3-part writing,' and 'I have often written in 3 parts, and not unsuccessfully,' a statement which even Mattheson endorses ('Critica Musica,' i. p. 131), though as a rule no friend to Fux. In his church music he was always reverent, and though polyphonic writing was second nature to him, he usually abstained from unnecessary subtleties in sacred music. One exception to this must however be made. His 'Missa canonica,' written throughout 'à capella,' a masterpiece containing every species of canon, is unique in its way. Here Fux displays his marvellous knowledge of counterpoint, combined with the richest modulation; and, as Marpurg says ('Abhandlung von der Fuge,' p. 130), speaking specially of the double canon in the 'Christe eleison,' 'his harmony is gorgeous, and at the same time thoroughly in keeping with the sacredness of the occasion.' The mass is dedicated to the Emperor as a proof 'that classic music, far from being extinct, has here gained one more step in advance' (see dedication in Italian). The Imperial Library at Vienna contains a copy of it by Michael Haydn (1757), and the Royal Library at Dresden another by Zelenka, Fux's pupil. It has been printed at Leipsic by Peters and Kühnel. The frequent performances of this mass at the cathedral and the court speak well for the efficiency of the singers. The most convincing proof of Fux's ability as a teacher is his 'Gradus ad Parnassum,' written in Latin in the form of a dialogue between master and pupil, and consisting of two parts, the first on the theory, and the second on the practice, of composition. It has passed through innumerable editions, and been translated into four languages. The dates of publication are as follows:—the original, in Latin, Vienna 1725; German edition, by Lorenz Mitzler, Leipsic, 1742; Italian, by Alessandro Manfredi, Carpi, 1761; French, by Sieur Pietro Denis, Paris, 1773; and English, anonymous, London, 1791. Its usefulness has been attested by such men as Piccinni, Durante, P. Martini, the Abbé Vogler, Paolucci, Gerbert, Cherubini, and in our own day by Heinrich Bellermann ('Der Contrapunct,' etc., Berlin 1862). Mozart used it in his contrapuntal exercises, and Haydn repeatedly studied it, and founded his teaching upon it. An exhaustive biography of the master, with a thematic catalogue of his compositions, has been drawn up with his usual accuracy by Dr. von Köchel from authentic information, with the title 'J. J. Fux, Hofcompositor und Hofkapellmeister der Kaiser Leopold I, Joseph I, und Karl VI, von 1698 bis 1740 (Hölder. Vienna 1872).
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