In this paper a simple method is proposed to carry out temperature-modulated calorimetry with multiple frequencies. The method is based on modulation with a complex sawtooth. The harmonics of the Fourier series of the measured heat-how rate and temperature are used to extract data pertaining to the frequencies of the 1st, 3rd, 5th, 7th and 9th harmonic. The complex sawtooth produces similar modulation amplitudes of the temperature of the first four harmonics. In temperature-modulated differential scanning calorimetry with a period of less than about 150 s, corrections by extrapolation to zero frequency are commonly needed. With the proposed method, these extrapolations can be done in a single experiment. Difficulties of baseline subtraction and other possible instrumentation and software problems are discussed.