296 COMPOSITION OF SOUND WAVES. 



vibrations per second; its octave will have 512; the fifth 

 of its octave will have 512 x f = 768. If F be given 352 

 vibrations, G will have 352 -i- f = 264. Thus, knowing (7, 

 any given tone may have its number of vibrations deter- 

 mined by multiplying by the proper ratio. 



459. Absolute Pitch. The number of vibrations 

 constituting the tone called C is purely arbitrary. The 

 assignment of 256 complete vibrations to middle C is com- 

 mon, but the practice of musicians is not uniform. A 

 certain tuning-fork deposited in the Conservatory of Music 

 at Paris is the standard for France; it assigns 261 vibra- 

 tions per second to middle C. The standard tuning-fork 

 adopted by English musicians and deposited with the 

 Society of Arts in London, gives 264 vibrations to middle 

 C. Multiplying the numbers in the last line of 457 by 

 11, we shall have the absolute numbers of vibration for 

 the several tones of the gamut corresponding to this 

 standard. 



(a.) Whatever be the standard thus adopted, an instrument will 

 be in tune when the relative number of vibrations is correct. The 

 string that produces the tone G must always vibrate three times 

 while the one producing C vibrates twice, or 36 times, while the 

 latter vibrates 24 times. While the string yielding D vibrates 27 

 times, the string yielding B must vibrate 45 times ; and so on. 



(&.) Middle C is the tone sounded by the key of a piano at the left 

 of the two black keys near the middle of the key-board. It is 

 designated by C\. Its octaves below and above are designated as 

 follows : 



cu, a.,, <?, a, c a, c 4 . 



460. Fundamental Tones and Overtones. 



A string may vibrate transversely as a whole, or as inde- 

 pendent segments. Such segments will be aliquot parts 

 of the whole string, and separated from each other by points 



