MUSICAL SCALE 



335 



A cent is the interval between any two tones whose frequency ratio 

 is the twelve hundredth root of two. 



For the practical production of music a so called equally tempered 

 scale has been found to be most satisfactory. The equally tempered scale 

 is a division of the octave into twelve equal intervals called equally tem- 

 pered half tones. 



The standard pitch for America is based on the frequency 440 cycles per 

 second for the tone A on the pianoforte keyboard. The frequencies of a 

 piano having an equally tempered scale are shown in Fig. 13.14. 



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Fig. 13.14. The piano keyboard and the frequencies of the equally tempered scale as used in 

 music according to the American Standard Pitch. 



The relative frequencies of the natural or diatonic or just scale and tem- 

 pered scale are shown below. 



Singers and players of instruments whose pitch can be varied by breath 

 or touch prefer the natural scale to the equally tempered scale because it 

 seems to be more artistic. Of course, the difference between the two scales 

 is small. However, in the case of chords it is said that the difference is 

 noticeable. 



Pianos and other fixed pitch instruments are tuned to the equally tem- 

 pered scale so that music may be played in various keys without retuning. 



