Tones of Overblown Organ Pipes. 7 3 



The action of the jet, however, is in reality not such a 

 simple matter as would appear from the above suggestion. 

 Helmholtz's theory fails to account for the initiation of the 

 vibration, for the well-known rise of pitch with wind 

 pressure, quantitative determinations of which have been 

 made by Blaikley, Rayleigh, and others, and also for the 

 jumping of the pitch to a higher frequency which results 

 from overblowing. 



A summary of subsequent work on the subject, with 

 full references, may be found in Winkelmann's IJand- 

 buch *. Attention may be drawn especially to the 

 investigations of Hensen f> Wachsmuth if, and others on 

 the behaviour of the air-jet, its breaking up into vortices, 

 and the relation of the tones of the pipe to the so-called 

 " edge-tones " resulting from the wiud-rush against a wedge- 

 shaped obstacle. Reference should also be made to a more 

 recent paper by A. 0. Lunn §, who has suggested that the 

 rise of pitch with wind-pressure may be due to the kinetic 

 stiffness or quasi-elasticity of the air-jet, and adduces mea- 

 surements in support of his theory. 



The character of the vibrations of the air in organ pipes 

 and the influence on it of the wind-pressure have been 

 studied experimentally by Raps || . The photographic records 

 which he obtained by an interference method show that the 

 vibration which at low pressures is comparatively simple 

 and consists mainly of the fundamental, develops overtones 

 as the pressure rises, the octave becoming more and more 

 pronounced as the fundamental diminishes and finally dis- 

 appears. In certain cases he noticed a peculiar " rolling " 

 tone produced at an intermediate stage, but did not pursue 

 his investigations in this direction. 



Now in its practical application for musical purposes, the 

 organ pipe has been developed exclusively as an instrument 

 for producing a steady tone, and any other condition', such 

 as the " rolling'''' or wavy tones noticed by Raps, is carefully 

 avoided in voicing, and previous investigations have been 

 conducted on the usual steady tones. But these wavy 

 tones so carefully avoided in practice are nevertheless 

 interesting from a theoretical aspect, as suggesting a 

 departure from the harmonic overtone relation in forced 

 vibrations and a comparison with the more familiar wolf- 

 note phenomenon in stringed instruments. In view of the 



* 2nd ed. vol. ii. pp. 435-446. 



t Ann. cler Phys. vol. xxi. p. 786 (1906). 



J Ibid. vol. xiv. p. 467 (1904). 



§ Physical Review, May 1920, p. 446. 



|| Ann. der Phys. vol. 1. p. 193 (1893). 



