1 Marchetto of Padua’s Theory of Modal Ranges Jay Rahn, York University (Toronto) Marchetto of Padua’s formulation of modal ranges in the Lucidarium (1317-18) ranks among his most important innovations as a music theorist. Like earlier writers, Marchetto distinguished between melodies (cantus) that, relative to their final tones (finales), ranged relatively high (tonus authenticus: authentic mode) and low (tonus plagalis or subiugalis: plagal mode). Unlike previous theorists, Marchetto also allowed for the possibility that a melody’s range might be ‘mixed’ (mixtus), i.e., by virtue of comprising substantial parts of both a high-ranging authentic mode and its low-ranging plagal counterpart. Moreover, within the authentic and plagal categories, Marchetto defined ranges he termed ‘perfect’ (perfectus: lit. ‘complete’), ‘imperfect’ (imperfectus: relatively narrow), and ‘pluperfect’ (plusquamperfectus: relatively wide-ranging). Also, Marchetto contrived a way to specify whether an individual melody with a very narrow range (e.g., spanning a sixth or less) should be considered authentic or plagal. In comparison with earlier accounts, Marchetto’s formulation of modal ranges was remarkably comprehensive, tidy and consistent. As well, Marchetto’s formulation of melodic ranges can be considered ‘deep’—in something like the modern mathematical sense—for it jibes clearly with contrapuntal cadence structures of his era, thus transcending his own important distinction between monophonic chant and polyphonic discant. Figure 1. Marchetto’s formulation of perfect ranges. For perfect authentic modes, the final and lowest notes are underlined; for perfect plagal modes, the confinal and highest notes are underlined. mode final lowest note highest note confinal 1 authentic D C d a 2 plagal D A b-flat a 3 authentic E D e b 4 plagal E B c b 5 authentic F F f c 6 plagal F C d c 7 authentic G F g d 8 plagal G D e d Perfect Modes Figure 1 displays part of Marchetto’s highly ramified account of the modal ranges. In Marchetto’s account, an authentic perfect melody extends upward to the note a perfect octave above the final, but its lowest note is not the final—instead its lowest note is a