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INTRODUCTION.
1. A certain amount of elementary knowledge of music will be necessary to the student before beginning the study of the present work. It will be assumed that he is acquainted with the names of the notes, the meanings of the various musical signs (accidentals, &c.), the relative time values of notes of different lengths, and such other matters as are treated of in ordinary textbooks on the Elements of Music.

2. A musical sound is produced by the periodic vibration of the air, that is to say, its motion at a uniform rate. When the air moving at a uniform rate comes in contact with the nerves of hearing, there is produced, provided the motion is sufficiently rapid, what is called a musical sound, or note. The pitch of a sound (that is, its being what is called a high or a low note), depends upon the rapidity of the vibration. This will be seen later (see Chapter II., § 35); all that is needed now is that the student shall understand what is meant when we speak of a musical sound.

3. If sounds of different pitch are heard one after another, we get what is called ; if sounds of different pitch are heard together, we get. It is the laws of harmony that we shall explain in this book; but it will be seen as we proceed that the question of melody is often so closely connected with that of harmony, that it is impossible to treat of one without also paying some attention to the other.

4. If two different notes are sounded, either in succession or together, it is clear that one of the two must be the higher, and the other the lower. The difference in pitch between two sounds is called the Interval between them. This difference may be so small as to be hardly recognisable by the ear; or it may be as great as between the lowest and highest notes in a large organ, or anything between the two. An infinite number of intervals is possible; but in music we make a selection, the nature of which will be explained later. For the present we are merely defining the meaning of the word "Interval."