Sperm whales (Physeter macrocephalus) typically produce sharp onset, broadband pulse sounds at varying repetition rates. Acoustic recordings of different social units of sperm whales in the Mediterranean Sea included apparent non-click sounds of tonal quality, termed ‘squeals’. Quantitative analysis of the spectral signal and waveform indicate that although squeals are perceived as tonal and appear spectrally as narrowband frequency-modulated structures with harmonics, they actually consist of pulses at high repetition rates exceeding 1600 clicks/s. Squeals contained energy at between 400 Hz and 22 kHz, with mean peak energy at the relatively low frequency of 700 Hz. Five spectral forms of squeal could be recognized, with the dominant form (45%) of squeals showing a decrease in frequency along the squeal contour. Mean click repetition rate ranged between 713 and 1385 clicks/s for individual squeals, and also varied within squeals at rates of between 64 and 444 clicks/s. Variation in click repetition rate was reflected in the frequency spacing of the spectral sidebands, in a statistically significant inverse relationship. Squeals were recorded only during bouts of sperm whale social behaviour, consistent with their having a communicative social function. Sperm whale squeals are structurally and audibly similar to the burst-pulse sounds produced by many smaller odontocete species, and might fall on the continuum between distinct click trains and pure-tone whistles.