One of the earliest event, which shaped the development of music in the Muslim world, was the introduction of scholars of the Islam to ancient Greek treatises, many of which had probably been influenced previously by the legacies of ancient Egypt and Mesopotamia.
This contact was initiated during the ninth century under the Abbasid Caliph al-Ma’mun. This ruler established Bayt al-Hikmah, literally “the House of Wisdom,” a scholarly institution responsible for translating into Arabic a vast number of Greek classics, including musical treatises by major Pythagorean scholars and works by Plato, Aristotle, and Plotinus.
The outcome of this exposure to the classical past was profound and enduring. The Arabic language was enriched and expanded by a wealth of treatises and commentaries on music written by prominent philosophers, scientists, and physicians. Music emerged as a speculative discipline and as one of “the mathematical sciences,” which paralleled the Quatrivium (arithmetic, music, geometry, and astronomy) in the Latin West.
Ref: Professor Ali Jihad Racy, Ph.D. The Genius of Arab Civilization: Source of Renaissance, John Hayes, editor.
Ismailimail 
That’s a great article. I would also argue that the Shiite Renaissance that took place during the 8th century in and around Basra in present-day Iraq saw a comprehensive classification of the Sciences compiled by the Ikhwan al-Safa, a group of mostly Ismaili thinkers and arguably the earliest encyclopedists. This outstanding article from the Institute of Ismaili Studies by Professor Godefroid De Callatay shows how the Ikhwan al-Safa, or Brethern of Purity, classify Music as a Mathematical science along with Arithmetic, Geometry and Astronomy: see Table 2 of the Appendix under the title ‘The division of the Philosophical Sciences according to Epistle VII’:
http://www.iis.ac.uk/view_article.asp?ContentID=101199
LikeLike