Biblical, Hellenistic, and Early Christian Music

Ancient Music History and Theory (General to Specific):

Ideas and Styles in the Western Musical Tradition by Douglass Seaton (Mayfield, 1991)
Antiquity and the Middle Ages: From Ancient Greece to the 15th Century edited by James McKinnon (Prentice Hall, 1991)
The Rise of Music in the Ancient World by Curt Sachs (Dover, 2018 [1943])
Ancient Greek Music by M.L. West (OUP, 1992)
Ancient Greek Music: A New Technical History by Stefan Hagel (CUP, 2015)

Musical Instruments:

The History of Musical Instruments by Curt Sachs (Dover, 2006 [1940])

Music in Early Christian Worship:

Worship in the Early Church by Ralph Martin (Eerdmans, 1975)
Music and Worship in Pagan and Christian Antiquity by Johannes Quasten (Pastoral, 1983)
The Search for the Origins of Christian Worship, 2nd Edition
by Paul Bradshaw (OUP, 2002)
Reconstructing Early Christian Worship by Paul Bradshaw (SPCK, 2009)
Early Christian Worship: A Basic Introduction to Ideas and Practice by Paul Bradshaw (SPCK, 2010)
Ancient Christian Worship: Early Church Practices in Social, Historical, and Theological Perspective by Andrew McGowan (Baker, 2014)
Rediscovering Worship: Past, Present, and Future, MNTS, edited by Wendy Porter (Pickwick, 2015)

Musical Writings Sourcebooks:

Documents of Ancient Greek Music edited by M.L. West and Egert Pohlmann (OUP, 2001)
Greek Musical Writings, Volume 1 edited by Andrew Barker (CUP, 1989)
Greek Musical Writings, Volume 2 edited by Andrew Barker (CUP, 2004)
Music in Early Christian Literature edited by James McKinnon (CUP, 1989)

Websites:

Michael Levy / Ancient Lyre