Tension is a complex multidimensional concept that is not easily quantified. This research proposes three methods for quantifying aspects of tonal tension based on the spiral array, a model for tonality. The cloud diameter measures the dispersion of clusters of notes in tonal space; the cloud momentum measures the movement of pitch sets in the spiral array; finally, tensile strain measures the distance between the local and global tonal context. The three methods are implemented in a system that displays the results as tension ribbons over the music score to allow for ease of interpretation. All three methods are extensively tested on data ranging from small snippets to phrases with the Tristan chord and larger sections from Beethoven and Schubert piano sonatas. They are further compared to results from an existing empirical experiment.