[1] See Michael Praetorius, De organographia (Wolfenbüttel, 1618), tab. viii., where crooks for lowering the key by one tone on trumpet and trombone are pictured.
[2] See Victor Mahillon, Les Éléments d’acoustique musicale et instrumentale (Brussels, 1874), pp. 96, 97, &c.; Friedrich Zamminer, Die Musik und die musikalischen Instrumente (Giessen, 1855), p. 310, where diagrams of the mouthpieces are given.
[3] See Joseph Fröhlich, Vollständige theoretisch-praktische Musikschule (Bonn, 1811), iii. 7, where diagrams of the two mouthpieces for first and second horn are given.
[4] See Gottfried Weber, “Zur Akustik der Blasinstrumente,” in Allgemeine musikalische Zeitung (Leipzig, 1816), p. 38.
[5] Les Instruments de musique au musée du Conservatoire royal de musique de Bruxelles, “Instruments à vent,” ii., “Le Cor, son histoire, sa théorie, sa construction” (Brussels and London, 1907), p. 28.
[6] Die Akustik (Leipzig, 1802), p. 86, § 72.
[7] Op. cit. p. 13, § 20, and p. 15, §§ 24 and 25. This apparent discrepancy between an early and a modern authority on the acoustics of wind instruments is easily explained. Chladni, when speaking of open and closed pipes, refers to the standard cylindrical and rectangular organ-pipes. Mahillon, on the other hand, draws a distinction in favour of the conical pipe, demonstrating in a practical manner how, given a certain calibre, the conical pipe must overblow the harmonics of the open pipe, whatever the method of producing the sound.
[8] See Gottfried Weber, loc. cit.
[9] See Ernst Heinrich and Wilhelm Weber, Wellenlehre (Leipzig, 1825), p. 519, § 281, and A Text-Book of Physics, part. ii., “Sound,” by J. H. Poynting and J. J. Thomson (London, 1906), pp. 104 and 105.
[10] See Sedley Taylor, Sound and Music (1896), p. 21.