When musical intervals are altered from their usual frequency ratios, listeners may experience a sensation of mistuning. We report results of experiments in which subjects judged degrees of mistuning of all intervals from unison to octave, as well as major tenth and twelfth. Using two simultaneous tones with fundamental frequencies between 250 and 800 Hz and 5 to 10 strong harmonics in each, we find: (1) just intervals, rather than tempered, are considered best in tune; (2) the range of mistunings considered acceptable generally becomes narrower when expressed in cents but wider when described by beat rate as we go from unison to octave, fifth and fourth; (3) whether that trend continues to sixths and thirds depends on individual listening strategies; and (4) the difficulty of judgment generally increases in going from the consonant toward the dissonant intervals, with the latter often eliciting only crude discrimination. Ability to judge mistuning with dichotic stimuli was also tested. We conclude that the beat rates of nearly coinciding harmonics provide an important clue to mistuning, but that a more abstract ability to judge interval size is also used; relative importance of the two strategies differs among subjects.