Processing musical information is a task many of us perform effortlessly, and often, unconsciously. In order to gain a better understanding of this basic human cognitive ability, we propose a mathematical model for tonality, the underlying principles for tonal music. The model simultaneously incorporates pitch, interval, chord and key relations. It generates spatial counterparts for these musical entities by aggregating musical information. The model also serves as a framework on which to design algorithms that can mimic the human ability to organize musical input. One such skill is the ability to determine the key of a musical passage. This is equivalent to being able to pick out the most stable pitch in the passage, also known as "doh" in solfege. We propose a computational algorithm that mimics this human ability, and compare its performance to previous models. The algorithm is shown to predict the correct key with high accuracy. The proposed computational model serves as a research and pedagogical tool for putting forth and testing hypotheses about human perception and cognition in music. By designing efficient algorithms that mimic human cognitive abilities, we gain a better understanding of what it is that the human mind can do.