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