A: When it is a triangularly-based monochord called the "Trumpet of Marigni". It was designed 500 years ago to sound like a trumpet by virtue of the single string and the tremulations of the bridge. I'm not so sure what it sounds like (though it sounded like a trumpet) but it certainly is a beautiful thing seen in profile.
This appears in A Course of Lectures on Natural Philosophy and the Mechanical Arts, by the encyclopedic polymath, Thomas Young.
An 1845 version of the work and the engravings is available online--I'm using the engravings from the first edition that I have in hand, which are much cleaner than the later reprint. (I should say that the text is the same for the description of the illustrations so far as I can tell, though position and so on is different.)