Sunday, 9:00 am–12:00
pm
(John Hothby (ca. 1410–1487), often regarded as a conservative theorist because of his support for Pythagorean tuning and Guidonian solmization, can in fact be credited with important conceptual innovations that greatly expanded the medieval pitch system. These include (a) the first systematic 17-step gamut, (b) a system of 12 hexachords allowing for the solmization of all 17 pitches, and (c) the classification of Bf with other flats rather than as an essential note of the Guidonian musica recta.
In La Calliopea legale, Hothby presents the complete gamut of pitches that may be derived through chromatic extensions of the Guidonian hand without redundancy. Hothby’s expansion of the gamut, hexachordal solmization and mutation offers a groundbreaking theoretical and pedagogical response to the increasingly chromatic music of the late 15th century. However, these innovations have largely been overlooked because Hothby’s idiosyncratic pitch nomenclature is difficult to understand. Once the basis of his reasoning is understood, the system’s inherent logic becomes clear.
Hothby’s basic set of pitches consists of the seven notes of the Guidonian gamut, excluding Bf. He derives additional pitches (our modern “sharps” and “flats”) by dividing each diatonic whole-step into two pairs of unequal semitones, the Pythagorean limma and apothome.
Karol Berger explains Hothby’s system as moving toward conceptualizing pitches in terms of the keyboard rather than of Guidonian solmization. In fact, Hothby’s system is based on the Pythagorean monochord and Guidonian solmization. Its orientation is aural, not visual.
It has been argued that the metaphoric concept of verticality in music (in the West) originated with the development of staff notation, but this paper presents evidence that tells a different story. Atkinson (1995) traces the development of staff notation back to the accent signs of Donatus, but a conceptualization of vocal sounds in terms of verticality, consistent with our modern conception, emerges prior to that in Ancient Greece: in the explicit reference to the “upper” (ano) and “lower” (kato) notes of the voice in the Aristotelian Problemata; in the conceptualization of poetic feet in terms of “raising” (aeirein) and “lowering” (tithenai); and by way of the conceptual metaphor GREATER IS HIGHER, where hypate meant not only literally “highest” but also metaphorically “most important.” Donatus adopted the prosodic concepts (as arsis and thesis) and thereby perpetuated the metaphoric verticality of vocal sounds, and this paper suggests that the design of his accent signs (acutus, gravis, and circumflexus) was motivated and constrained by a preexisting metaphoric concept; that vocal experience first motivated the metaphor, and that this metaphor in turn determined the verticality in the shape of the accent signs. The evidence presented thus invites us to reconsider both the history and the basis of one of our most fundamental musical concepts.
Chapter 17, section 6, of Johann Joachim Quantz's Versuch einer Anweisung die Flöte traversiere zu spielen (1752) concerns the duties of the keyboardist in accompaniment, and includes a short original composition entitled “Affettuoso di molto.” This piece features an unprecedented variety of musical dynamics — alternating abruptly from loud to soft extremes and utilizing every intermediate gradation. The extreme density of dynamic surprises is remarkable: most comparable pieces from the period were published without any dynamic indications whatsoever, and no other eighteenth-century treatise spells out dynamic prescriptions as explicitly. Quantz’s dynamics are seemingly intended to document an ideal concept of dynamic shaping, and may also be taken as an indication of contemporary performance practice. Most suggestively, Quantz’s discussion of this example provides an analytic rationale for the various dynamic levels specified in the musical score: specific levels of relative amplitude are prescribed for particular classes of harmonic events, depending on their relative dissonance. Quantz defines his categories in the language of the thoroughbass theorists of the time, but his categorization of dissonant chords speaks to a harmonic understanding related to or derived from emerging Rameauvian ideas of chordal structure. Quantz’s categories implicitly anticipate Kirnberger's distinction between essential and inessential dissonance; further, his judgments of chordal dissonance closely coincide with even later conceptions, as indicated by the various chords' spans on the Oettingen-Riemann Tonnetz and on David Temperley’s “line of fifths.”
The paper will incorporate a live period performance of the piece in question.
The French accompaniment treatises written between 1660 through the 1720s are filled with “unwritten” information about the evolution and eventual development of a harmonic theory. The aspects of a harmonic theory are “unwritten” because the treatise authors were not necessarily “theorists.” They were musicians trying to develop a practical method for teaching others how to improvise accompaniments from an unfigured bass. The authors were teaching accompanists chord progressions without the benefit of having a harmonic theory to use as a teaching tool. They developed a system known as “Harmony by Interval.” This system provided the accompanist with a method for choosing chord structures based solely on the intervallic motion of the bass. By combining the prescribed intervals of thirds, fifths, sixths, and, sometimes, sevenths for a given bass motion, such as up a P4, up a m2, down a M2, etc., the accompanist would play chord structures suitable for that bass motion. The accompaniment treatise authors did not have the theoretical vocabulary—because a harmonic theory did not yet exist—to tell the accompanist to play a dominant seventh to a tonic triad or a leading tone triad in first inversion to a tonic triad. However, by examining their written rules and analyzing their musical examples, one can “read between the lines” and discover the “unwritten” aspects of a harmonic theory as it was—unknowingly—being fashioned. Their rules consistently assigned specific harmonic functions to certain scale degrees in certain situations. It is this consistency of rules and results that made it possible to eventually formulate a harmonic theory.