'Ars Quatuor Coronatorum' are the Transactions of the Quatuor Coronati Lodge No. 2076 EC, which bills itself as 'the premier Lodge of masonic research'. It is very possible that your GL Library has a collection of the transactions, most do. From an electronic index of the Transactions 1886-1996 I have retrieved the following references for 'music':
Music & Masonry, [PL] (1988) (Pearmain, Andrew I.) 103:150-4.
Music & Songs, (Barrett, W.A.) Masonic musicians 4:90-6.
Music & Songs, (Gould, R.F.) The Entered Apprentice's song (1=B0) 4:169-71, 245.
Music & Songs (Masonic); Masonic Lodge and Chapter Music (1978) (A. Lewis Ltd.); Music for Masonic Ceremonies (1978) (Smith, E./Watson, D.M.), (Musical notation/sheets of music, for ceremonies), reviewed by (Smyth, Frederick) 90:323-4.
Music & Songs, (Poole, Herbert) Masonic songs and verse of the 18th-Century 40:7-29, 268-9.
Music & Songs, (Rabes, L.) Beethoven and his Masonic song "Maurerfragen" 80:144-50.
Music & Songs, (Sharp, Arthur) Masonic songs and song books of the late 18th-Century 65:84-95
Music & Songs, (Sharp, Arthur) Mozart's Masonic music 69:15-30.
Music & Songs, (Sharp, Arthur) Sibelius' Masonic Ritual music [SKA] 75:1-9.
Music & Songs, (Williams, W.J.) Mathew Birkhead, author of the Apprentice's song (1=B0) 42:130-1.
Music & Songs; See: Hymns, Plays & Operas, Composer (Masonic) Music at dinners 90:49, Music in the ceremonies 86:159-60, 168, 175 Music, Masonic Instrumental, of the 18th Century (Morehen) 89:176-81 Music, Vocal, in Craft Ceremonies and After-Proceedings (Hamill) 88:187-9 Musicians, as Serving Brethren 85:5-6 Musicians, well-known English (masonic), Samuel Wesley, William Boyce, and Thomas Attwood, Thomas Arne ('Rule Britannia'), Sterndale Bennett, Walter Parratt, Arthur Sullivan 103:152 Musicians, well-known European (masonic), Jean Sibelius, Mozart, Haydn, Beethoven? 103:152 Musik in Geschichte und Gegenwart, Die (1955), Kassel & Bassel, B=E4renreiter (general encyclopedia of music) 84:236, 236n2 Musiques Rituelles Maconniques du XVlIIe Si=E8cle (recording)(1970/1972), reviewed (Smyth) 84:234-6.
The numbering system is Volume Number: pages. Since the Index was compiled, another paper touching on the subject has been published. In Vol. 109, pages 244-247, there is a short piece on the background to the EAs Song and the FCs Song. This is probably outside your current research area.
There are also references, with very good illustrations, in the 'coffee table' format book 'A Celebration of the Craft', written by Hamill and Gilbert. A copy of this is also probably in your GL Library.