6 DYNAMICAL THEORY OF SOUND 



The names given to the various intervals are in a sense 

 accidental, and refer to the relative positions of the notes on 

 the ordinary " diatonic scale." This is based on the " major 

 chord," which is a combination of three notes forming a Major 

 and a Minor Third ; i.e. their frequencies are as 4 : 5 : 6. If we 

 start from any arbitrary note, which we will call C, as keynote, 

 the two notes which lie a Fifth above and below it are called 

 the " dominant" (G) and the " subdominant " (F,) respectively. 

 If we form the major chord from C we get the notes E = f C, 

 and G = | C. Again if we form the major chord from G we get 

 the notes B = f G = - 1 /- C, and d = f G = f C. The latter falls 

 outside the octave beginning with C ; the corresponding note 

 within the octave is D = f C. Lastly, forming the major chord 

 from F, we get A, = f F = f x f C = f C, the octave of which is 

 A = -| C, and C itself. We thus obtain the scale of seven notes 

 whose frequencies are proportional to the numbers here given : 

 C D E F G A B 



i I I f f S 



24 27 30 32 36 40 45 



This is continued upwards and downwards in octaves ; the same 

 letters are repeated as the names of the notes, but the various 

 octaves may be distinguished by difference of type, and by 

 accents or suffixes. The precise pitch of the key-note is so far 

 arbitrary; it determines, and is determined by, that of any 

 other note in the scale. Among musicians the standard has 

 varied in different places and at different times, the general 

 tendency being in the direction of a rise. German physical 

 writers, including Helmholtz, have followed a standard which 

 assigns to a certain A a frequency of 440*. On this basis we 

 have the following frequencies for a certain range of the 

 scale : 



* This makes c' = 264. Physical instrument makers now often take c' = 256, 

 which is convenient on account of its continued divisibility by 2. 



