MUSICAL SCALE. 177 



served are essentially the same for all musical sounds ; for it 

 is by means of vibrations communicated to the air that the 

 waves of sound find their way to the auditory apparatus. 

 Let us take, to begin with, a string vibrating 24 times in a 

 second. If this string be divided into two equal parts, each 

 part will vibrate 48 times in a second. The note thus pro- 

 duced is the octave, or the 8th of the primary note, called the 

 8th, because the natural scale, as we shall see, contains eight 

 notes, of which the first is the lowest and the last, the high- 

 est. We may divide the half again, producing a second 

 octave, and so on, within the limits of our appreciation of 

 musical tones. If we divide the string so that f of its length 

 will vibrate, we have 36 vibrations in a second, and this note 

 is the 5th in the scale. If we divide the string again, so as 

 to leave f of its length, we have 30 vibrations, which gives 

 the 3d note in the scale. These are the most natural subdi- 

 visions of the tone ; and the 1st, 3d, 5th, and 8th, when 

 sounded together, make what is known as the common major 

 chord. Three-fourths of the length of the original string 

 makes 32 vibrations, and gives the 4th note in the scale. If 

 we take f of the string, we have 27 vibrations, and the note 

 is the 2d in the scale. With f of the string, we have 40 vi- 

 brations in a second, or the 6th note in the scale. With -f% 

 of the string, we have 45 vibrations in a second, or the 7th 

 note in the scale. 



It will be observed that we have started with a note, 

 which we call C. This is the key-note, or the tonic. In this 

 scale, which is called the natural, or diatonic key, we have a 

 regular mathematical progression from the 1st to the 8th. 

 This is called the major key of C. Melody consists in an 

 agreeable succession of tones, which we may assume, for sake 

 of simplicity, to be pure. We cannot, in a simple melody, 

 sound any note but one of those in the scale. When a differ- 

 ent note is sounded, we pass into a key which has a different 

 fundamental note, or tonic, with a different succession of 

 3ds, 5ths, etc. Every key, therefore, has its 1st, 3d, 5th, 



