Correct spelling for the English word "hauch" is [hˈɔːt͡ʃ], [hˈɔːtʃ], [h_ˈɔː_tʃ] (IPA phonetic alphabet).
The word "hauch" has its origins in the German language. It is derived from the Old High German word "huoh", which meant "breath" or "breeze". This ultimately traces back to the Proto-Germanic word "*xauxaz", which carried the sense of "exhalation" or "breath". Over time, the word evolved in different German dialects, leading to "hauch" in modern German. It has been loaned into English, often appearing in musical terminology to refer to a very light, delicate exhalation of breath or a gentle breeze.