Hamsphire rhymes with:
foxfire, backfire, brushfire, foxfire, hellfire, sunfire, abshire, backfire, barkshire, biedermeier, blackshire, brushfire, dannemeyer, darbyshire, devonshire, elvire, esquire, fesmire, foxfire, foxmeyer, gardenhire, goldwire, haywire, hehmeyer, hellfire, jurgensmeyer, kastenmeier, lancashire, macintyre, mcintire, mcintyre, newswire, obermaier, ohlmeyer, proxmire, pugmire, racamier, retemeyer, rightmire, rothmeier, settlemire, settlemyre, shropshire, stegemeier, stiegemeier, stoudemire, stoudenmire, sunfire, suttmeier, tietmeyer, untermeyer, waymire, whitmire, wilshire, wiltshire
Hamsphire sounds like:
hangover, hansberry, hansbury, hemisphere