54 PRACTICAL LESSONS IN SCIENCE. 



damental and its octave form a series of eight tones called the 

 natural or diatonic scale. Sounds resulting from the same num- 

 ber of vibrations are said to be in unison. When two notes differ 

 in pitch, but their combination is agreeable to the ear, they are 

 said to be consonant; when disagreeable, dissonant. This scale 

 repeated eleven times includes all sounds within the range of the 

 human ear. The capacity of the ear to appreciate vibrations 

 varies greatly. Some cannot appreciate one-half as many as 

 others can. Only about seven octaves are used in music. By the 

 English standard of pitch the note A of the treble clef is made 

 up of 400 vibrations in a second ; by the French standard the 

 rate for the same note is 435 vibrations per second. The tones 

 in the scale have definite relations to each other. If we represent 

 the number of vibrations for a fundamental note by one, then 

 the several notes of the scale will be made by the following 

 ratios: C 1, D 9-8, E 5-4, F 4-3, G 3-2, A 5-3, B 15-8, C 2. Now, 

 from this scale of fractions, and the fact that A is made up of 

 440 vibrations, the number for the others may be found; as. 

 for example, the number of vibrations to give the fundamental 

 C would be 3-5 of 440, equal to 264. 



The intensity of sound is that which distinguishes it as being 

 loud or soft. It depends entirely upon the amplitude or width of 

 the vibrations which produce it. The greater the amplitude the 

 louder the sound will be. 



Whenever a piano wire, or the cord of any stringed instrument 

 is struck, it vibrates as a whole and in segments at the same 

 time. The vibrations as a whole yield the fundamental note of 

 the cord; the vibrations in segments yield higher tones called 

 overtones or sometimes harmonics. 



By quality we refer to that peculiarity of sound by which we 

 may distinguish notes of the same pitch and intensity made on 

 different instruments. The pitch or intensity of tones made on a 

 violin and on a piano may not differ and yet how easy to tell the 

 sounds apart. We recognize the voices of friends, not by their 

 pitch or intensity but by their quality. The various stringed 

 instruments, as the piano, harp, violin, depend for their value 



