and chromatic pitch will scarcely be worth while, and I will therefore merely add that the instruments were sometimes tuned differently, either to relieve the inevitable monotony of this purely diatonic scale or for purposes of modulation.  A Dorian tetrachord is composed of semitone, tone, tone; to make it chromatic, it was changed as follows:  [G:  e’ f’ g-’ a’] the lichanos, or index finger string, being lowered a semitone.

The enharmonic pitch consisted of tuning the lichanos down still further, almost a quarter-tone below the second string, or parhypate, thus making the tetrachord run quarter-tone, quarter-tone, two tones.  Besides this, even in the diatonic, the Greeks used what they called soft intervals; for example, when the tetrachord, instead of proceeding by semitone, tone, tone (which system was called the hard diatonic), was tuned to semitone, three-quarter-tone, and tone and a quarter.  The chromatic pitch also had several forms, necessitating the use of small fractional tones as well as semitones.

Our knowledge of the musical notation of the Greeks rests entirely on the authority of Alypius, and dates from about the fourth century A.D.  That we could not be absolutely sure of the readings of ancient Greek melodies, even if we possessed any, is evident from the fact that these note characters, which at first were derived from the signs of the zodiac, and later from the letters of the alphabet, indicate only the relative pitch of the sounds; the rhythm is left entirely to the metrical value of the words in the lines to be sung.  Two sets of signs were used for musical notation, the vocal system consisting of writing the letters of the alphabet in different positions, upside down, sideways, etc.

Of the instrumental system but little is known, and that not trustworthy.

[05] The fundamental doctrine of the Pythagorean philosophy
     was that the essence of all things rests upon musical
     relations, that numbers are the principle of all that
     exists, and that the world subsists by the rhythmical
     order of its elements.  The doctrine of the “Harmony of
     the spheres” was based on the idea that the celestial
     spheres were separated from each other by intervals
     corresponding with the relative length of strings
     arranged so as to produce harmonious tones.

[06] Dionysus, the same as the Roman Bacchus.

VII

THE MUSIC OF THE ROMANS—­THE EARLY CHURCH