This study aims to characterize distinctive acoustic features of Mandarin tones based on a corpus of 1025 monosyllabic words produced by 21 native Mandarin speakers. For each tone, 22 acoustic cues were extracted. Besides standard F0, duration, and intensity measures, further cues were determined by fitting two mathematical functions to the pitch contours. The first function is a parabola, which gives three parameters: a mean F0, an F0 slope, and an F0 second derivative. The second is a broken-line function, which models the contour as a continuous curve consisting of two lines with a single breakpoint. Cohen's d, sparse Principal Component Analysis, and other statistical measures are used to identify which of the cues, and which combinations of the cues, are important for distinguishing each tone from each other among all the speakers. Although the specific cues that best characterize the tone contours depend on the particular tone and the statistical measure used, this paper shows that the three cues obtained by fitting a parabola to the tone contour are broadly effective. This research suggests using these three cues as a canonical choice for defining tone characteristics.