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12                                          MUSIC OF THE MIDDLE AGES.
Arithmetic, Geometry, and Astronomy. Sharon Turner remarks, that these comprised not only all that the Eomans knew, cultivated, or taught, but embodied " the -whole encyclopaedia of ancient knowledge." If we may trust the following jargon hexameters, which he quotes as " defining the subjects they comprised," Music was treated as an art rather than as a science, and a practical knowledge of it was all that was required:—
Gramm. loquitur; Dia. vera docet; Rhet. verba colorat Mus. canit; Ar. numerat; Geo. ponderat; Ast. colit astra. But the methods of teaching both the theory and the practice of music were so dark, difficult, and tedious, before its notation, measure, and harmonial laws were settled, that we cannot wonder when we hear of youth having spent nine or ten years in the study of scholastic music, and apparently to very little purpose.
In the latter part of the fourth century (a.d. 374 to 397), Ambrose, bishop of Milan, introduced a model of Church melody, in which he chose four series or successions of notes, and called them simply the first, second, third, and fourth tones, laying aside, as inapplicable, the Greek names of Doric, Phrygian, Lydian, iEolic, Ionic, &c. These successions distinguished themselves only by the posi­tion of the semitones in the degrees of the scale, and are said to be as follows:
These, Pope Gregory the Great (whose pontificate extended from 590 to 604) increased to eight. He retained the four above-mentioned of Ambrose, adding to them four others, which were produced by transposing those of Ambrose a fourth lower; so that the principal note (or key-note, as it may be called) which for­merly appeared as the first in that scale, now appeared in the middle, or strictly speaking, as the fourth note of the succession, the four additional scales being called the plagal, to distinguish them from the four more ancient, which received the name of authentic.
In this manner their order would of course be disarranged, and, instead of being the first, second, third, and fourth tones, they became the first, third, fifth, and seventh.
The following are the eight ecclesiastical tones (or scales) which still exist as such in the music of the Romish church, and are called Gregorian, after their founder :
It will be perceived at the first glance, that these Gregorian tones have only

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