Quantitative Analysis of Tessitura and Density in Franz Schubert's Die schöne Müllerin.

Objective: Quantitative analysis of vocal compositions continues to be a topic of exploration in seeking methods that attempt to objectively match a singer's ability with musical difficulty. Work is needed to study the vocal demands of song cycles of Western classical art songs. The objective of this study is to assess the compositional range, musical tessitura, melodic directionality, vocal fold cycle dose, phonation time dose, and musical density of the 20 art songs comprising Die schöne Müllerin by Franz Schubert.

Methods: Vocal and piano pitches in each song were subdivided by the shortest universal rhythmic duration and converted to hertz for equal weighting. Musical density was determined by similarly subdividing each pitch in the piano part. Quartile analysis defined tessitura as the inclusive range between the first and third quartiles based on previous analysis models. The frequency difference between each pitch and summing time spent ascending, descending, or remaining stable in pitch determined vocal directionality.

Results: The overall tessitura of the composition varies but averages between 246.94 Hz (B₃) and 329.63 Hz (E₄) with an average pitch of 293.66 Hz (D₄). Textural density varies throughout the music and does not seem to correlate with either pitch range or tessitura. Melodic directionality throughout the cycle is primarily descending. The final number of the cycle (Des Baches Wiegenlied) contains some of the most challenging elements in the piece with a high compositional range and musical tessitura, and the highest vocal fold cycle dose, phonation time dose, and musical density of the entire cycle.

Conclusions: Quantitative musical analysis allows for a nuanced understanding of challenges in musical works. Vocal characteristics that individual singers might possess to navigate these works are described based on data interpretation. This research engages a new method of quantitatively evaluating musical density to assess effects on vocal production.