The Waves of the House Military were the generations of their War Era troops.
Instead of dividing their military into legions, or by purpose, the Great Houses primarily organised the House Military into a sequence of generations called Waves. The War took the form of a cycle between the instantaneous deployment of an entire Wave, and a long lull of entrenchment as the Houses concentrated their effort on the design and gathering of biodata for the next. Each Wave tended to curb its predecessor's excesses, while emphasising the traits that had lead to success. Instead of numbering campaigns in order, the Houses numbered them based on Wave: the Third Retro-War was named for the Wave involved, not for the number of Retro-Wars preceding it.
The First Wave of the House Military was comprised of normal House members, many originally part of the ceremonial guard. They were the only Wave not designed specifically for War, although some were fitted with the few militarily-applicable augmentations available at the time. The First Wave only met with any success because the enemy's early forces were equally unready. Few to no First Wave soldiers who fought in the War's first battle, on Dronid, survived.
The Second Wave was the first created specifically for war, by a Homeworld with only received knowledge of what war entailed. It was extreme by any measure, a crusade which committed frequent acts of genocide, wiping out any species or culture which opposed or even rivalled the Homeworld. Its comprehensive destruction of Faction Paradox sites like Ordifica crippled the Faction for years and ruined the lines of communication between the Faction and the Remote, leaving the Remote unbound by the Protocols of Linearity.
Third Wave troops were created in hominid forms, but they became non-hominid with each life to a far greater extent than the Second Wave.
House Xianthellipse took initiative with the Fourth Wave, introducing foreign biodata (including that of humanity) to the breeding engines (much to House Mirraflex's chagrin). Compared to the Homeworld's traditional values, the Fourth Wave was chaotic — its soldiers were undisciplined (best suited to guerrilla warfare), tended to prod the boundaries of the Houses' Protocols, and even had sexual tendencies. Robert Scarrat was the most high-profile (and arguably most successful) of the Fourth Wave.
The Fifth Wave was stable and standardised. The Houses incorporated the military cell-codes of the Second and Third Waves and the "mongrel" biodata techniques of the Fourth Wave, but were more careful to keep those Waves' more extreme tendencies under control. It was the first Wave to be created without any political drama.
Officially, no Sixth Wave ever existed — the number was simply skipped. However, there was a suspiciously long gap between the Fifth and Seventh Waves, and The Book of the War referred to a non-existent entry on "Sixth Wave Defections". It is possible that the enemy expunged the entry because they retro-compromised this wave, causing them to have never been created or born supporting the enemy.
The Seventh Wave was created when Fifth Wave troops were still plentiful, so rather than a general fighting force, it was used for specific tactical methods. It was overseen by House Xianthellipse, and combined the savagery of the Second Wave with the subtler, less culturally acceptable techniques of the Fourth to psychologically degrade its targets. The Seventh Wave was used in the Seventh Time Assault, a "morally questionable" campaign which took place on Earth and was inspired by apportation. After the enemy became involved, the Assault eventually (or inevitably) devolved into the Seventh Retro-War.
The Eighth Wave was defensive, designed only to reinforce the troops already in use.
The Ninth Wave was odd in multiple ways: the non-military House Tracolix was instrumental in its creation, even though it had never previously been involved in breeding, and claimed a "surprise" was in the works. It could have had something to do with House Lolita, which was allied with Tracolix (PROSE: The Book of the War) and the only member of which (Lolita) was a timeship (PROSE: Toy Story) who spread her own children throughout history. (AUDIO: In the Year of the Cat)