I came across this quote and was intrigued by its grammar: "The soul would have no rainbow, had the eyes no tears"
At first glance, "had the eyes no tears" this seems like a type II conditional sentence being inverted (I can vaguely make out the conditional clause to mean "If the eyes had no tears"), therefore shouldn't the conditional clause be "Were the eyes to have no tears"?
Even if it were a mixed conditional sentence, the conditional clause would still be "Had the eyes had no tears", correct?
How and why is "had the eyes no tears" used here? I have never seen this of inversion being used ever before. Is it missing "if" (if i reordered it, would it be "The eyes had no tears")? Is it even correct? Any and all help is greatly appreciated. Thanks in advance!