The hypothesis that pairs of appropriate inharmonic sounds can evoke perceptions similar to conventional consonance and dissonance is examined. The inharmonicity considered is not the relatively small displacement of frequency components seen in conventional musical instruments (e.g., piano), but rather large, deliberate shifting of frequencies by a number of semitones. The hypothesis states that if there is a match between upper‐frequency components of two such inharmonic sounds, consonance should be perceived. If near misses occur between upper‐frequency components of the two sounds, causing audible beats, then dissonance should be perceived. The individual inharmonic sounds should have reasonably wide component spacing to avoid a noiselike timbre. This hypothesis was confirmed by experiments in which subjects chose which of two different inharmonic sound pairs was the more consonant. The sound pairs with matching frequency components were chosen more often than those with near misses. The difference was significant for the experimental subjects as a whole and was pronounced for subjects with musical experience. This last fact is important since the sound pairs with matching components were arranged to have conventionally dissonant relationships between their fundamentals, and vice versa for the pairs with near misses. It is speculated that the structures in music which have their origins in the harmonic series (intervals, chords, scales) may be alterable by electronically relocating the harmonics to inharmonic positions.