in PHONATION AND ARTICULATION 131 



Simple sounds or tones are composed of pendular vibrations, 

 i.e. to-and-fro movements of the vibrating molecules which follow 

 the same laws of motion as a pendulum. These vibrations only 

 differ in amplitude and duration : the amplitude is directly pro- 

 portional to the loudness of the sounds ; the duration is inversely 

 proportional to the number of vibrations per second, on which the 

 pitch of the sound depends. The form of the pendular vibrations 

 is constant and invariable. They can be graphically recorded 

 by making a tuning-fork trace its vibrations on a revolving 

 cylinder. 



Helmholtz distinguishes "simple tones" or sounds (Ton) from 

 " compound tones " (Klang), which are an aggregate of the simple 

 tones produced by simple, pendular vibrations. While the form 

 of vibration in simple tones is always the same, that of compound 

 tones varies considerably, and depends on the algebraic sum of the 

 component tones. The deepest of these tones is called the prime 

 tone, and the rest are the harmonics, or over-tones. The vibration 

 frequency of the prime tone to that of the partial tones is in the 

 ratio of 1 : 2 : 3, etc. 



The number of partials which make up a compound tone, and 

 their relative strength, differs considerably for different musical 

 instruments, even when the prime tone is the same. This difference 

 gives rise to the quality (timbre, Klangfarbe) of a note, which 

 depends on the particular form of the vibration of the tone, due to 

 the relative number and strength of its harmonic overtones. 



A compound tone can be resolved into its partial tones by 

 means of resonators. All sounding bodies have their own note ; 

 when made to vibrate, they invariably give out a note of a certain 

 pitch, which corresponds with a certain frequency of vibration per 

 second. When the surrounding 'air transmits to the sounding 

 body a number of vibrations corresponding to its proper note, it 

 begins to vibrate in unison. When, on the contrary, the vibration 

 frequency does not correspond with the frequency of its own note, 

 it remains at rest, or vibrates very feebly. Given a series of hollow 

 metal chambers (resonators) tuned to different notes of the musical 

 scale, it is possible to analyse compound tones into their partials. 

 When one ear is stopped, and the other is applied to the aperture 

 of a resonator, each resonator reinforces its own note and cuts 

 out all the rest (Helmholtz). Konig's manometric flame method, 

 described in text-books of physics, renders visible the partials 

 contained in a compound tone. 



Another mode of analysing complex sounds is based on the 

 phonautographic curves traced by means of the thin membranes 

 used in phonographs with a very light lever, or a small mirror 

 that reflects a beam of light on to a travelling sensitive surface 

 (Hermann's phonophotography'). 



Musical instruments can be classified according to the 



