To begin with the most banal:  the music must have extramusical
associations, preferably intended by the composer.  These associations
schould be metaphysical (if not necessarily theological) in intent; &
(apparently...  the negative case doesn't seem to make an awful lot of
artistic sense, although there's nothing conceptually amiss with idea)
benign-to-transcendental.

(One should, however, clearly differentiate between a mystical composer
& a mystical composition)

A sense of mystery is also pretty much essential:  a straight setting of
the Latin mass will generally not be described as mystical (although
elements within the setting might be); though a choral vocalise quoting the
Deus Irae could.

Technically, a mystical piece would try to use compositional devices that
achieve the above effects.  Absence of obvious form is an (equally) obvious
start; so getting rid of clear tonal centers & adopting a loose, rhapsodic
structure would generally be the way to go.  Another popular device -
extremely slow tempos - solves two problems simultaneously:  firstly, they
give a cathedral spin to a piece (if only because _slow_ as the sound
metaphor for historical religion has been imprinted in our brains by other
media); while also making it more difficult to perceive connections within
the score.  As mentioned above:  quoting of archaic melodies may also be
used to reinforce associations of mysticism.

All of this probably sounds incredibly mechanical; but if the intent
is communication (as most of the modern mystical composers (Hovhaness,
Tavener, Paert, etc) seem to believe, it makes sense for their works to
speak clearly (& they do:  which is why these three composers sell so
well).  In spite of - or perhaps:  because - of their soaring ideas,
all three have shared something of a form-follows-function approach to
composition...  an approach which makes as much sense than any contemporary
aesthetics....

All the best,

Robert Clements <[log in to unmask]>
<http://www.ausnet.net.au/~clemensr/welcome.htm>