Number, indeed, has two proper kinds (ιδια ειδη), odd and even, and a third mixed together from both, the even-odd(αρτιοπέριττον). Of each of the two kinds there are many shapes, of which each thing itself gives signs.
(Philolaus F5 = Stobaeus, Eclogae 1.21.7c; tr. Huffman 1993)
The quote is from Horky's Plato and Pythagoreanism, 2013, (p.141), it is commented twice further in text. On p185 the author writes " the so-called even-odd (αρτιοπέριττον), which appears to refer to the “one.” Aristotle, too, knew this fragment, and he is explicit in associating the “one” with the “even-odd” class and stating that it is derived from the “even” and the “odd.” On p190, disappointingly, he says "however It is beyond the scope of this study to examine in more detail the significance of the concept of “mixture” of Forms or classes".
The “one” is not the number preceding two which Ancient greeks apparently did not accept as a number. Philolaos quote might suggest that it is set apart as it has no shape but I am tempted to read it as suggesting that the mixed numbers have multiple shapes, while the numbers from the proper kinds have each just one.
So what are the 3 kinds of numbers? The odd numbers are perhaps the ones that we also call odd, (starting with 3), while the even numbers are seen as, so to say, 'strictly even', the powers of 2, that is 2,4,8,16 and the rest, that is 6,10,12 etc. as even-odd. References and comments (or should this be moved to Philosophy SE)?