have never since been equalled.

Before carrying our inquiries further, something must be said about the two main lines of musical development which led up to music as we know it to-day. These tendencies are designated by the terms Homophonic and Polyphonic. By homophonic,[10] from Greek words signifying a "single voice," is meant music consisting of a single melodic line, as in the whole field of folk-songs (which originally were always unaccompanied) or in the unison chants of the Greeks and the Gregorian tones of the early church, in which there is one melody though many voices may unite in singing it. Later we shall see what important principles for the growth of instrumental music were borrowed from the instinctive practise associated with the folk-song and folk-dance. But history makes clear that the fundamental principles of musical coherence were worked out in the field of music known as the Polyphonic. By this term, as the derivation implies, is meant music the fabric of which is made by the interweaving of several independent melodies. For many centuries the most reliable instrument was the human voice and the only art-music, i.e., music which was the result of conscious mental and artistic endeavor, was vocal music for groups of unaccompanied voices in the liturgy of the church. About the tenth century, musicians tried the crude experiment,[11] called Organum, of making two groups of singers move in parallel fifths e.g.,

Tu Patris sempiternus es Filius.

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but during the 13th and 14th centuries a method was worked out by which the introductory tune was made to generate its own subsequent tissue. It was found that a body of singers could announce a melody of a certain type and that, after they had proceeded so far, a second set of singers could repeat the opening melodic phrase—and so likewise often a third and a fourth set—and that all the voices could be made to blend together in a fairly harmonious whole.[12] A piece of music of this systematic structure is called a Round because the singers take up the melody in rotation and at regular rhythmic periods.[13] The earliest specimen of a Round is the famous one "Sumer is icumen in" circa 1225 (see Supplement of musical Examples No. 1), which shows to what a high point of perfection—considering those early days—musicians had brought their art. For, at any rate, by these systematic, imitative repetitions they had secured the first requisite of all music, coherence. This principle, once it was sanctioned by growing musical instinct, and approved by convention, was developed into such well-known types of polyphonic music as the Canon, the Invention and the Fugue; terms which will be fully explained later on. It is of more than passing interest to realize that these structural principles of music were worked out in the same locality—Northern France and the Netherlands, and by kindred intellects—as witnessed the growth of Gothic architecture; and there is a fundamental affinity between the interweavings of polyphonic or, as it is often called, contrapuntal[14] music and the stone traceries in medieval cathedrals. During the 13th and 14th centuries northern France, with Paris as its centre, was the most cultivated part of Europe, and the Flemish cities of Cambrai, Tournai, Louvain and Antwerp will always be renowned in the history of art, as the birthplace of Gothic architecture, of modern painting and of polyphonic music.[15] A great deal of the impetus towards the systematic repetition of the voice parts must have been caused by practical necessity (thus justifying the old adage); for, before the days of printed music, or even of a well-established tradition—when everything had to be laboriously written out or transmitted orally—whole compositions could be rendered by the singers through the simple device of remembering the introductory theme and joining in from memory whenever their turn came. Compositions in fact were often so recorded.[16] The following old English round (circa 1609) shows clearly how the voices entered in rotation.

1 Three blind mice, three blind mice
2 ran around thrice, ran around thrice; The
3 miller and his merry old wife ne'er laugh'd so much in all their life.

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For a Round in strict canonic imitation by the famous English composer William Byrd (1542-1623) see the Supplement, Example No. 2. In due time singers of that period became likewise very proficient in improvising free parts about a given melody or cantus firmus, a practice indicated by the term "musica ficta" which was beneficial in stimulating the imagination to a genuine musical activity.

We can now begin to realize the importance of polyphonic music. In fact, it is not too much to assert that systematic repetition in some form or other (several aspects of which we shall describe in due season) is the most important constructive principle in music, necessitated by the very nature of the material. This statement can be corroborated by a glance at almost any page of music considered merely as a pattern, quite regardless how the notes sound. We observe at once that some portions of the page look much or exactly like other portions. Frequently whole movements or long parts of a work are based entirely upon some terse and characteristic motive. Famous examples of this practise are the first movement of Beethoven's Fifth Symphony in C minor which, with certain subsidiary themes to afford contrast, is entirely based on the motive:

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the Finale of Wagner's opera The Valkyrie (see Supplement, Example No. 3) the chief