HARMONIC ORIGINS The latent harmonic sense of the Greeks is shown in the fact that their diatonic scale was amenable to the Pythagorean science of harmonic ratios. And we cannot suppose that no notice was taken of the combined sounds resulting from reverbe'ration in halls and caverns, or from striking several strings of the lyre at once. Yet the fact remains that outside the orbit of our own Western music of the last six centuries we know of no harmonic system that has advanced beyond drones below the melody and cymbals (our Authorized Version is right in reading "tinkling cymbal") or bells above it.
Music, as we now understand it, consists in the interaction of three elements as inseparable (but not as interchangeable) as the three dimensions of Newtonian space. The Greeks knew two, rhythm and melody, which are as ancient as human consciousness and evidently have their meaning for some other animals. But non-harmonic melody is a very different thing from melody that implies harmony. (See MELODY exs. r and 2 with their discus sion.) When we hear an unaccompanied folk-song we involun tarily think of it as the top line of a series of harmonies. If it is really pre-harmonic it will prove unamenable to that interpreta tion, and then we shall think it quaint. Neither the quaintness nor the harmonic interpretation ever entered into its intention. Life is too short for Western musicians to devote much of it to the violent mental gymnastics of thinking away the harmonic ideas that have made Western music enjoyable throughout five centuries. We may perhaps widen our experience by going back another two centuries; for it was agreed by all the musicians in Vienna that a concert of "Gothic" music was their most inter esting musical experience of the year 1928.
In the article HARMONY the main steps are indicated by which mediaeval musicians advanced from doubling melodies in 4ths and 5ths (as the unoccidentalised Japanese are said to be doing now) to an aesthetic system of polyphony that demands com plete independence in its melodic threads and forbids consecutive 5ths and fives as barbarous. The details of this evolution are abstruse ; but two main issues may be mentioned here. Polyphony could not have been established without fixed scales and a reposi tory of known melody for composers to work upon.
The scale was set in order in Graeco-Roman times by Ptolemy the astronomer, who flourished A.D. 13o and from whose time the history of the "ecclesiastical modes" becomes continuously trace able until the records of music are secured by the art of printing.
"tones" was set in order by St. Ambrose. According to a tradition accepted, after some "historic doubts," by good authorities, St. Gregory revised and enlarged the Ambrosian collection; and the whole corpus of Gregorian music undoubtedly familiarizes Roman Catholics of to-day with a music enormously more ancient in its origin than any harmony. This music forms the principal melodic foundation of Palestrina's polyphony; but by his time it had become corrupted, and we must look to the Solesmes edition of 1904 for the text and method of singing plain-song in the per fection it is held to have attained shortly after the death of St. Gregory. The essential difference between the Ratisbon tradi tion (which we may loosely call Palestrinian) and that of Soles mes is that the Palestrinians impatiently curtailed the flourishes of the plain-song much as Palestrina did with the Gregorian themes he used in polyphony ; whereas the Solesmes method re stores the free speech-rhythm which makes the flourishes (or melismata) possible in a rapid delivery. Some of these melismata are very extensive, and the Palestrinians (who gradually devel oped the modem organist's habit of providing each note of a Gregorian melody with a separate chord) had some excuse for mistaking them for corruptions of style.
The Gregorian tradition did not stand alone. There was an ancient Visigoth (or "Spanish") tradition; and there are the traditions of the Eastern Church. Professor J. J. W. Tillyard has shed much light on Byzantine music (q.v.), including a prom ising opening in the deciphering of the earliest Neumae, dia critical signs above the words, supposed to indicate musical notes.
He uses the method of interpreting the past from vestiges of primitive usage in the present. Controversies as to the number of modes, whether 8 or 12, raged till late in the i6th century. The Dodecacliordon of Glareanus settled the question in favour of twelve, as its name implies. Meanwhile composers developed polyphony by ear and got no help whatever from the theorist. Quite independent of modes and entirely practical was the hexa chord scheme (see HEXACHORD) developed in the i i th century by Guido d'Arrezzo (q.v.).
The general reader may learn something of the hexachord sys tem very pleasantly from the music-lesson in The Taming of the Shrew. Hortensio's gamut says "Gamut am I, the ground of all accord . . . D sol re, one clef [i.e., sign, or key], two notes have I: E la mi: show pity or I die." "Gamut" is a survival of Greek tradition; for the bottom note of the Greek scale was iden tified with the bass G, and this "ground of all accord" is an octave below the Ut of the hard hexachord. Hence it is Gamma ut. D is Sol in the hard hexachord k I and