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CHAPTER III. 

 EARLIEST STAGES OF HARMONICS. 



AMONG the ancients, the science of Music was 

 an application of Arithmetic, as Optics and 

 Mechanics were of Geometry. The story which is 

 told concerning the origin of their arithmetical 

 music, is the following, as it stands in the Arith- 

 metical Treatise of Nicomachus. 



Pythagoras, walking one day, meditating on the 

 means of measuring musical notes, happened to 

 pass near a blacksmith's shop, and had his atten- 

 tion arrested by hearing the hammers, as they 

 struck the anvil, produce sounds which had a mu- 

 sical relation to each other. On listening further, 

 he found that the intervals were a Fourth, a Fifth, 

 and an Octave; and on weighing the hammers, it 

 appeared that the one which gave the Octave was 

 one-half the heaviest, the one which gave the Fifth 

 was two-thirds, and the one which gave the Fourth 

 was three-quarters. He returned home, reflected 

 upon this phenomenon, made trials, and finally dis- 

 covered, that if he stretched musical strings of 

 equal length, by weights which have the proportion 

 of one-half, two-thirds, and three-fourths, they pro- 

 duced intervals which were an Octave, a Fifth, and 



