Psychophysics of musical elements in the discrete-time representation of sound

Notes, ornaments and intervals are examples of basic musical elements. Their representation as discrete-time digital audio plays a central role in software for music creation and design. Nevertheless, there is no systematic relation, in analytical terms, of these musical elements to the sonic samples. Such a compendium enables scientific experiments in precise and trustful ways, among educational and artistic uses. This paper presents a comprehensive description of music in digital audio, within an unified approach. Musical elements, like pitch, duration and timbre are expressed by equations on sample level. This quantitatively relates characteristics of the discrete-time signal to musical qualities. Internal variations, e.g. tremolos, vibratos and spectral fluctuations, are also considered to operate within a note. Moreover, the generation of musical structures such as rhythmic meter, pitch intervals and cycles, are attained canonically with notes. The availability of these resources in scripts is provided in public domain within the massa toolbox Music and Audio in Sequences and Samples. Authors observe that the implementation of sample-domain analytical results as open source can encourage concise research. As further illustrated in the paper, massa has already been employed by users for diverse purposes, including acoustics experimentation, art and education. The efficacy of these physical descriptions was confirmed by the synthesis of small musical pieces. As shown, it is possible to synthesize whole albums through collage of scripts and parametrization.