Difficulties in comparing tempos and a new approach to their measurement

Abstract

Perception of the tempos is paradoxical: the same speed of the performance can be perceived as different tempos, and the hearer evaluates the relatively slower speed as “especially fast tempo” (F. Weingartner). A possible solution of the “Weingartner – Steglich paradox” may be a variety of musical scales, essential for the perception of rhythmic energy. The new European tempo is inseparately linked with the accented meter (German: ‘akzentuierende Metrik’). The peculiarity of the latter is the active role of visual perception, with the help of which notation signs (durations) turn from symbols of time intervals into markers of levels of accent structure. Each sign has its own “weight”, and the rhythmic masses are transmitted to the hearer in a live performance. The tempo of the European composition of the 18th and 19th centuries is the “kinetic momentum” (as defined by Miron Kharlap) — “the product of velocity and mass”. This article offers the author’s method of “weighing” of beats that allows to arrange the tempos on a 20-point scale.

Keywords

Bach, Beethoven, group theory (mathematics), isomorphism (mathematics), logarithm, scaling (psychology), “tempo transposition”