Lerdahls Tonal Pitch Space (2001) combines music theory with current understanding of music perception and cognition creating of model of tonal pitch space. Lerdahls goals include quantification of areas of tension and relaxation perceived by listeners experienced in Western tonal music. Tension is associated with instability, distance, uncommon tones, and weak attractional force; relaxation with stability, proximity, common tones, and strong attractional force. Quantification requires creation of a time-span segmentation derived from the metrical grid and grouping analysis of the score. The time-span segmentation is necessary for creating the time-span reduction. The time-span reduction removes structurally less significant elements from the musical surface through a series of steps not unlike the layers of Schenkerian analysis. The ultimate goal is the prolongational reduction accompanied by prolongational tree.
Global tension is quantified by summing values obtained when considering the region in which an event occurs, distance between successive chords revealed by their position on the chordal circle-of-fifths, number of distinct pitch classes between successive chords, tension inherited by subordinate chords from superordinate chords, melodic and harmonic attraction, and surface dissonance. Lerdahls Surface Tension Rule assigns tension added values due to chord Inversion, chord note in the top voice (Melody), and nonharmonic chord tones. This study tested the validity of assigned tension added values for Inversion and Melody asking 82 participants familiar with Western tonal music to rate perceived tension of Major and minor four-note chords heard devoid of tonal and musical contexts.
Results showed Lerdahls tension added values required modification. Root position chords and chords with the root in the Melody require a tension added value greater than 0. Tension due to First Inversion is not the same as tension due to Second Inversion. Tension due to First and Second Inversion is greater than tension due to the third or fifth of a chord in Melody. Tension due to Second Inversion is not different from tension due to root in Melody. A new category, chord Quality, needed to be added. Expertise did not play a role. Lerdahls model and these results provide insight for performers, teachers, listeners, and composers
