The modulated adiabatic scanning calorimeter (MASC) described here is designed to work in both the time-domain (adiabatic-like step-scanning) and in the frequency domain (modulated temperature/power-scanning) operational modes. The cylindrical form of the cell and the controlled thermal environment in which the sample is located make it possible: (i) to write detailed and reliable equations to describe the heat flow; (ii) to derive analytical relations to calculate the energy release from the sample and the real and imaginary parts of the complex heat capacity at the modulation frequency; (iii) to study narrow phase transitions using the power modulated scanning mode; and (iv) to generate adiabatic-like conditions. The thermal environment is controlled by means of an active thermal shield which is kept at a temperature close to that of the sample cell in order to minimise the thermal gradients to which the sample is exposed. The temperature difference between the shield and the cell is set at the value required to control or cancel heat leakage from the cell. MASC can be used to carry out measurements on a single sample in different operational modes that can be made operative under the control of its built-in software. The parameters of interest can be automatically calculated by means of a program based on a model of the cell i sample system that will be described in a second paper. To test the performance of the calorimeter, samples of materials which undergo a first-order phase transition or a glass transition (indium, ice, and polystyrene) were studied. The specific features of the calorimetric cell, the calibration procedure, and the experimental results an reported and discussed,