Authors:Muzzulini; Daniel Abstract: Supplementary Materials for "Isaac Newton's Microtonal Approach to Just Intonation"Muzzulini, DanielIn 1665 Isaac Newton wrote a notebook in which he collected materials for a musical treatise which was never completed. He investigated ways of approximately representing just intonation scales by dividing the octave into many equally sized intervals. Strictly speaking, equal divisions of the octave are incompatible with just intonation, and just intonation intervals are audibly different from the intervals played on a modern equally tempered modern piano. By increasing the number of parts of an equal division, just intonation can be approximated arbitrarily well. Scales with more than 60 microtonal steps per octave, however, never gained wide acceptance in music theory or practice. Newton divided the octave into 612 equal parts so that he could represent the syntonic chromatic scale very accurately and he studied several equal divisions of the octave with fewer parts. His approximation problem is looked at in three ways: (1) A reconstruction of how he determined the many EDO-representations listed in the notebook is given. (2) Using computer programs Newton's tuning problem is solved "empirically" through calculating and evaluating the related approximations comprehensively. (3) The findings from the computer-assisted analysis are used to develop a more general geometric approach to the approximation problem. PubDate: 2021-01-01T00:00:00Z
Authors:Rector; Michael Abstract: Supplementary Materials for "Historical Trends in Expressive Timing Strategies: Chopin's Etude, Op. 25 no. 1"Rector, MichaelStudies of early 20th-century performance practice tend to focus on features that are alien to late 20th- and early 21st-century ears. Empirical analysis of timing in recordings of Chopin's Etude, Op. 25 no. 1—a piece for which performance style has remained relatively static—suggests how some foundational rules of phrasing and expressive nuance have changed over the history of recorded music. Melody note onsets were marked manually in 127 commercial recordings dating from 1909 to 2016. Overall, the data do not show an increase or decrease over time in the amount of tempo fluctuation. Independently of a tendency to use slower tempi, pianists changed the way they employ rubato. Several factors contribute to a trend whereby the fourth beat is lengthened at the expense of the second and third beats: an increase in phrase-final lengthening, an increase in the use of tempo arching for shorter groups of measures, and a tendency to delay the arrival of an accented dissonance or change of harmony instead of lengthening the melody inter-onset interval that contains it. The data illustrate nearly imperceptible shifts in interpretation and suggest that some practices thought to be the bedrock of expressive performance may be historically conditioned. PubDate: 2021-01-01T00:00:00Z