José Manuel López López’s Chart for managing tempi

Abstract

In 2003, Spanish composer José Manuel López López (b. Madrid 1956) wrote his Estudio II sobre la modulación métrica for four percussionists, commissioned by the Portuguese ensemble Drumming. As the title of the percussion quartet reveals, Elliott Carter’s metric modulation was a key concept for López López during the compositional process. Nevertheless, his theoretical and aesthetic position up to this time was rather close to Karlheinz Stockhausen and to the French spectral composers. López López conceived a chart of tempi in order to reconcile the metric modulation with some ideas he borrowed from Stockhausen, in particular from his famous article “ . . . wie die Zeit vergeht . . . .” In the columns, López López calculated a series of metric modulations among basic notes – from a whole note to a 16th-note – and their dotted counterparts. Conversely, for each row, given a starting value, the cells were filled by iteratively multiplying this value by 12 √ 2, which is the frequency ratio of an equally tempered semitone. López López lastly rounded the obtained values to the nearest integer, giving rise in each row to a series of “chromatic tempi.” This chart puts in evidence a double analogy for understanding tempo relationships as tuning ones. On the one hand, the vertical rational proportions are equivalent to those of the partials of the harmonic series, which are concomitants of just intonation. On the other hand, the horizontal irrational proportions reflect those of the chromatic scale in the equal temperament. Notice that, although not present within the table, López López took also into account subdivisions based on tuplets for his metric modulations, as evident in several calculations below the charted values. This device is a significant milestone in López López’s creative development. Estudio II sobre la modulación métrica is an unpitched score, but this temporal conception was also present in the next piece he composed: Entrance-Exit. For this kind of pianistic tombeau for his dear friend Fausto Romitelli, López López paired tempi with spectral fundamentals by means of these methods. Next, López López implemented and refined his table via Excel, a platform allowing him to remap values as fast as possible. This choice also led him to choose new frequency ratios beyond 12 √ 2 – and therefore related to further tuning systems – for analogous purposes.