The diabolus in music ... ah.
Greek and Antiochian Orthodox Christians use this diabolus especially the Plagal of the 2nd or the 6th tone. This is what gives chant an exotic tone. Was this attempt by the Roman Catholic Church to outlaw the use of the diabolus in music just another slap at Eastern Orthodoxy?
The diabolus in musica is the tritone, NOT the minor second nor the diminished fifth.
The diminished fifth and the tritone are the same thing, at least in Western tonality (12 equal temperament). In other temperaments (19, 24, 31, etc.), though, this is not the case. In 24 equal temperament there is a minor fifth (approximating just ratio 16:11) which is wider than a tritone and narrower than the perfect fifth. In 31 equal temperament, like all odd temperaments, there is no
tritone or "diabolus", instead, the diminished fifth and augmented fourth approximate the ratios 10:7 and 7:5 respectively.
I'm not sure if there's a standard tuning for Byzantine chant, but from what I can gather, it cannot
be adapted to 12 equal-temperament and a different system is required, which is why it sounds so foreign to Western ears. The fact that it has eight tones/modes (instead of the seven in Western music theory) implies that. Larger temperaments (beginning with 19) would probably work. Which one is best probably varies by region (Slavic, Greek, Antiochian, etc.)
From what I've read, the Assyrian/Syriac church music is essentially quarter-tone (24 divisions of the octave) or can be approximated that way.