“His orthography, or rather heterography, has been a subject of animadversion; and he has been charged with misspelling his own name.” A writer in Blackwoods Magazine in 1831 was referring to the painter William Hogarth (whose name, the writer alleged, should be spelled Hogart, to suit the family’s Westmorland origins).
In this period heterography referred to an individual’s idiosyncratic way of spelling that didn’t fit the conventions. (It’s a combination of Greek heteros, other, plus graphia, writing, the opposite of orthography, the correct or conventional spelling system of a language, from Greek orthos, correct.) In that sense, the word is long defunct. That’s a pity, you may feel, since there’s a lot of heterography about and it would be good to be able to describe a bad speller as a heterographer and be understood.
However, heterography is still with us. Linguists associate it with those languages in which the written form doesn’t properly reflect the way in which it’s spoken. Robert Trask explained in his Dictionary of Phonetics and Phonology that it’s a system of writing that “lacks a one-to-one correspondence between sounds and written symbols.” In systems of this kind, one letter or combination of letters can represent more than one sound. He goes on to note that “English orthography is, of course, a spectacular example of this.”
That’s the problem, as a lot of teachers tell us. Heterographers are that way because English is heterographic.