That work was translated from Arabic into Latin as the...

That work was translated from Arabic into Latin as the Secretum Secretorum about the year 530/1135, and won considerable popularity during the European Middle Ages.[^6] Following Pythagoras, the cosmic order of things was explained under the proposition that “everything is number,” and since mundane music was among the ectypes of numerical proportion, the harmonious order of things covered both melody and rhythm, the various genres of which could banish depression, assuage grief, halt passion and cure sickness.

The theory of numbers fascinated Muslim peoples because, unlike geometry, which depended on visual appreciation, it was purely mental sciences. The Pythagorean scale in music, which was based on the “theory of numbers,” was known quite early to the Persians and the Arabs, and the Khurasanians even improved on it. Islam, having no racial boundaries, the special musical characteristics of the Persian, Arab, Syrian, and Turkoman found open acceptance in the capitals and cities of the Caliphate.

Because of these national peculiarities it soon became evident that some sort of fixation of method and system was urgent, and this expediency was brought to fruition by an Arab named ibn Misjah (d. c. 97/715) who, having travelled in Syria and Persia and taken lessons from practitioners and theorists, conceived a system of music theory and a method of practice which were adaptable to existing conditions in Arabic-speaking lands.

These, we are told, were adopted generally.[^7] Thus were the eight Arabian melodic modes (asabi‘) classified in two groups of four each: the first in the course (majra) of the binsir , i.e. using the major third (408 cents), and the second in the course of wusta , i.e. using the minor third (294 cents).[^8] At the same time eight rhythmic modes (iqa‘at) were formulated, also in two groups of four each, those numbers being in accordance with cosmic theories.

All the song books of the period, from Yunus al-Katib (d. c. 148/765) to al-Isfahani (d. 356/967), specify the melodic and rhythmic modes of each song.[^9] Meanwhile, a neutral third (355 cents), i.e. an interval half-way between the major and minor third. It was introduced by a certain lutanist named Zalzal (d.