Byzantine scales were used in the early Greek Church, and are described in Bryennius’s Harmonicon (c. 1320). This work may be found in the third volume of John Wallis’ Opera Mathmetica (1699), and a further description is given in Paranikas’ Aids to Byzantine Literature.
The scales were four in number, with four Plagals, situated, like Greek Plagals, a fifth below the Authentics. Byzantine scales were reckoned downwards and were as follows:
all without chromatic notes.
The notes were named after the first seven letters of the Greek alphabet, but the A was placed where our C is. The method of using the Greek letters was introduced into the Western Church by Ambrose, and , when afterwards the first seven letters of the Latin alphabet were substituted for the Greek, the old pitch meaning was retained, and it was not till about 900 that the note which we call C was so named.
The original name appears to have been A in both Eastern and Western churches. It will be noticed that by the use of B flat instead of B natural the Plagals become simply transposed copies of their Authentics (this is true of all Plagals that are a fifth below their Authentics); when the Plagals are, as in the Western church scales, a fifth above (usually called a fourth below) the Authtentic, the use of B flat produces the Plagal without transposition.
The pitch meanings of the letters in Byzantine scales afterwards rose one degree, so that what had hitherto been called B was now A (using modern letters, but not modern meaning): thus Byzantine A = modern D, so that the Byzantine fourth Authentic = Church Dorian (not to be confused with Greek Dorian), but as the Byzantine 1st Authentic was called by the title a (alpha), it is easy to see how confusion arose when the change from Greek to Latin lettering took place.
The pitch meaning of the letters was somewhat arbitrary until the 10th century; and it is possible that some of our names for the church scales are erroneous.