Cleonides identified the species by what 'the ancients' supposedly called them

Yep - ever since Aristoxenus, music theory has been a game of Chinese Whispers attributing ideas to predecessors that they would never have recognized as their own. It's only been in very recent decades that people have been able to get closer to what ancient music theorists really intended to say.

Some of the thoroughly unhelpful factors that distorted our perceptions of the history of music theory have been

* the near-deification of Pythagoras in pagan times, which meant that his own ideas got buried in a farrago of myth

* the tendency of theorists like Aristoxenus to act like the drunk searching for his watch under the streetlight, by ignoring ubiquitous kinds of music they didn't know how to theorize about

* 2500 years of ignorance about music theory preceding classical Greece, which has only been interpreted quite recently by scholars like Anne Kilmer. (The Greeks didn't invent the tetrachord - players of aulos-type instruments would have known about it 1000 years before the Greeks ever produced a theory of anything).