PHYSICS OF SOUND 725 



Musical Scale. A knowledge of the relations of different notes to 

 each other lies at the foundation of the science of music ; and without a 

 clear idea of certain of the fundamental laws of music, it is impossible to 

 comprehend thoroughly the mechanism of audition. 



It requires but little cultivation of the ear to enable one to compre- 

 hend the fact that the successions and combinations of notes must obey 

 certain laws ; and long before these laws were subjects of mathematical 

 demonstration, the relations of the different notes of the scale were estab- 

 lished, merely because certain successions and combinations were agree- 

 able to the ear, while others were discordant and apparently unnatural. 



The most convenient sounds for study are those produced by vibrat- 

 ing strings, and the phenomena here observed 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. 

 Take, to begin with, a string vibrating 48 times in a second. If this 

 string is divided into two equal parts, each part will vibrate 96 times in 

 a second. The note thus produced is the octave, or the 8th of the pri- 

 mary note, called the 8th, because the natural scale contains eight notes, 

 of which the first is the lowest, and the last, the highest. The half may 

 be divided again, producing a second octave, and so on, within the limits 

 of appreciation of musical sounds. If the string is divided so that | of 

 its length will vibrate, there are 72 vibrations in a second, and this note 

 is the 5th in the scale. If the string is divided again, so as to leave -| of 

 its length, there are 60 vibrations, which give the 3d note in the scale. 

 These are the most prominent subdivisions of the note; and the ist, 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 make 

 64 vibrations, and give the 4th note in the scale. With f of the string, 

 there are 54 vibrations, and the note is the 2d in the scale. With -| of 

 the string, there are 80 vibrations, or the 6th note in the scale. With T 8 ^ 

 of the string, there are 90 vibrations, or the 7th note in the scale. The 

 original note, which may be called C, is the key-note, or the tonic. In 

 this scale, which is called the natural, or diatonic, there is a regular mathe- 

 matical progression from the ist to the 8th. This is called the major 

 key. Melody consists in an agreeable succession of notes, which may 

 be assumed, for the sake of simplicity, to be pure. In a simple melody 

 every note must be one of those in the scale. When a different note is 

 sounded, the melody passes into a key that has a different fundamental 

 note, or tonic, with a different succession of 3ds, 5ths etc. Every key, 

 therefore, has its ist, 3d, 5th and 8th, as well as the intermediate notes. 

 If a note formed by a string | the length of the tonic instead of f , is sub- 

 stituted for the major 3d, the key is converted into the minor. The minor 



