Aside from the already mentioned de La Motte....
Zarlino: "Bicinia" on the twelve modes, precisely twelve short example compositions created by the Renaissance theorist and included in his Istitutioni Harmoniche as exemplifications of the twelve modes presented and explained therein.
I stumbled upon this PDF that I am reading
http://www.lucaverzulli.it/files/il_flauto_militare.pdf
It is certainly OT [Off-Topic] but there is an abundant bibliography and a snippet of the introduction to Borstein's work:
The third mode, or Phrygian mode, is practically a scale that starts from E and returns to E, but using only natural sounds.
Borstein, in the introduction to Zarlino's Bicinia, gives a detailed explanation of Renaissance modality. Regarding the third mode, he writes:
The 3rd authentic mode, spanning from E to E, has its regular cadences in E, G, B. In this mode, two particular cadences appear because they lack a leading tone: this makes it sound somewhat harsh, and Zarlino explains, in this regard, that its regular cadence in B, due to its harshness, is often replaced by the cadence in A, also for very precise harmonic reasons, since B lacks an upper fifth, as the B-F interval is a diminished fifth, i.e., a tritone to be avoided both melodically and harmonically. Regarding the practical substitution of the regular cadence in B with that in A, it happens that the 3rd mode loses its natural structure, mixing with the 9th mode: "If this did not mix with the Ninth, and were heard simply, it would have a somewhat harsh harmony: but because it is tempered by the Diapente [the fifth] of the Ninth, and by its cadence which occurs in A, which is greatly used in it; therefore [for this reason] some have held the opinion that it has a nature to move one to tears; wherefore they willingly accommodate to it those words that are mournful and full of lamentation".
Probably it is precisely this "harsh" mode characteristic that makes it preferred in music for war.