One of the simplest cases to visualise is a vibrating string, as in the illustration; the string has fixed points at each end, and each harmonic mode divides it into an integer number (1, 2, 3, 4, etc.) of equal-sized sections resonating at increasingly higher frequencies. Similar arguments apply to vibrating air columns in wind instruments (for example, "the French horn was originally a valveless instrument that could play only the notes of the harmonic series"), although these are complicated by having the possibility of anti-nodes (that is, the air column is closed at one end and open at the other), conical as opposed to cylindrical bores, or end-openings that run the gamut from no flare, cone flare, or exponentially shaped flares (such as in various bells).