In this study, the relationship between the degree of tempering of musical intervals and the subjective purity of these intervals was investigated. Subjective purity was determined for fifths and major thirds. The intervals were presented in isolation, that is, they were not given in a musical context. For two simultaneous complex tones the relationship between subjective purity and tempering could be described by exponential functions. These functions were obtained both for ratings on a 10-point equal-interval scale and for subjective distances derived from preference data collected by means of the method of paired comparisons. To verify to what extent subjective purity had been determined by interference of nearby harmonics, the spectral content of the tones was varied. For both the fifths and the major thirds, interference of the various pairs of nearly coinciding harmonics was canceled by deletion of the even harmonics of the higher tone. This deletion resulted in higher purity ratings, the effect being most prominent for the major third. A further reduction of the potential interference between harmonics was still more effective: for simultaneous sinusoidal tones, subjective differences between pure and tempered intervals were much smaller than for complex tones. Purity ratings for simultaneous sinusoids presented at a low sound level were about equal to the ratings for successive tones. The purity ratings were compared with dissonance patterns predicted by models for tonal consonance/dissonance. Only in a few conditions do the patterns predicted by the model of Plomp and Levelt resemble the rating patterns obtained, and the dissonance patterns predicted by the model of Kameoka and Kuriyagawa are at variance with the purity ratings in all conditions. Suggestions for revision of the models are given.