Greek and Roman Musical Studies 6 (2018) 339-358 brill.com/grms An Experimental Investigation of Rhythmic Irrationality Stelios Psaroudakēs Department of Music Studies, National & Kapodistrian University of Athens
[email protected] Fotis Moschos Laboratory of Musical Acoustics, Department of Music Studies, National & Kapodistrian University of Athens
[email protected] Abstract The present paper investigates ‘rhythmic irrationality’ in the medium of recited ‘word’, as this is defined by Aristoxenos and Dionysios Halikarnasseus in three rhythmic con- texts: that of the anapaest, of the dactyl, and of the trochee (choreios). For this purpose, computer experiments have been devised, one for each of the aforementioned irratio- nalities: against the background of a monitored metronome, a line in each rhythm is initially recited in the rational mode. The line is subsequently recited another seven times, with the podic duration which is to suffer diminution or augmentation, in steps of eighths of the time unit. The eight vocal renderings of each line are then assessed psychoacoustically, in order to locate: (a) the point at which our hearing detects the onset of irrationality, and (b) the point at which a shift from the original rhythm to another is sensed. Keywords rhythmic theory – rhythmic irrationality – cyclic anapaest – irrational dactyl – alogos choreios © koninklijke brill nv, leiden, 2018 | doi:10.1163/22129758-12341326Downloaded from Brill.com09/30/2021 10:48:23AM via free access 340 Psaroudakēs and Moschos 1 Rhythmic Rationality1 It has been established in the scholarship of ancient Hellenic music that a ‘simple rational foot’ (ῥητὸς ἀσύνθετος/ἁπλοῦς πούς) is defined as the temporal structure2 π = (Χl: Ẋ f) or (Ẋl: Xf), where3 π stands for simple rational foot; Xl stands for the ‘leading part of the foot’ (καθηγούμενος ποδικὸς χρόνος),4 hereafter the ‘leader’, which is a multiple of the ‘unit of time’ (πρῶτος χρόνος).5 Thus, Χl = kυ with k ϵ {1, 2, 3}, i.e.