=Origin of the Church Scales=.—It is absolutely unknown when or by whom the system of scales, known as the Church Scales, was invented. The latest writer on the Greek System was =Claudius Ptolemy= (about 130 A. D.). In 330, =Pope Sylvester= established a school for training church singers, but we have no information as to the system he employed. The name of =Ambrose=, Bishop of Milan (333-397), has for centuries been associated with what are called the _Authentic_ Scales, but there is no valid evidence whatever that he had anything to do with their adoption. The name of =Pope Gregory= (540-604) has also been associated with another set of scales called _Plagal_, with as little authority as in the previous case. There does not appear to have existed any system of notation in the time of Ambrose or Gregory. The Greek notation by letters was forgotten, and the very insufficient system of notation by Neumes had not been invented. The only writer of any authority after Ptolemy was Boethius, and he did more to confuse the subject of music than to explain it. =Foundation of the Church Scales=.—But if we know nothing of the inventor of the Church Scales, or of the way in which they grew into their final form, we are, nevertheless, perfectly well informed of the fully-developed system which, it must be remarked, grew out of a misunderstanding of the Greek Scales. The Church Scales were founded on the Greater Perfect System of the Greeks, with this restriction, namely, that it was _not transposable_; whereas, we have seen that the various Greek modes were transpositions of either the Lesser or Greater Systems. [Music] This is the series of sounds from which the Church Scales were made. None of them might be _altered_ by sharp or flat, _except_ the _B_ in the second octave (and this was a later addition which was probably owing to a remembrance of the Lesser Perfect System in which the B was flat.) The Greek names were retained for the Church Scales, but as not one of the notes was inflected, it follows that the _halftones_ occur in _different_ places in every scale. The scales to which these names were given were called Authentic, those with the prefix _Hypo_ were called Plagal. In the table on the next page, the Greek and Church Scales, also the Greek _octaves_ are given side by side.