Dissonance Treatment in Counterpoint: 15th Century to Fux

Posted on Feb 16, 2025 in Music

Question 1: Describe the treatment of dissonance in counterpoint treatises from the late fifteenth century through Fux, Gradus ad Parnassum.

Counterpoint is a set of context-dependent rules: rhythm, melodic contour, harmonic relation to other voices. Harmony is incidental to independent melodic lines, perspective, and order of composition. Stylistic and technical considerations include imitation, motivic concerns, mode, and text. Different parts have different roles; for example, Tenor first, cantus second, contratenor as filler. Counterpoint emerges in the 14th century (Cum notum sit) and by the 15th century, Prosdocimo establishes 6 rules.

Tinctoris: Liber de arte contrapuncti, 1477

Tinctoris makes a distinction between composed polyphony (res facta) and extemporized counterpoint (super librum). He emphasizes the importance of varietas in good composition and uses the work of contemporaries as stylistic models. The first part focuses on contrapunctus simplex (limiting melodic intervals, consonances), and the second part on diminutions (several notes). Dissonance depends on rhythmic and melodic position, and Mensura directio (measure, tactus).

Dissonances on the beat resolve by step, all held over; no neighbor motion unless lower rhythmic value.

Syncopated dissonance with a leap of a third. Perfections in mode.

16th Century Developments

  1. Drawing together of contrapunctus simplex, contrapunctus diminutus, and composition for more than two voices (often still separate in the 15th century).
  2. Expansion of matters treated to include modes, techniques of imitation and inversion, text, and music.
  3. More precise rules for the use of dissonance (Ramis (1482 Musca Practica M6-8), Gaffurius 1496 – most to closest Imperfect consonance, Aaron Compendiolo 1545 to points in a row if voice crossing, Zarlino Le istitutioni 1558).

Zarlino’s Le istitutioni harmoniche (1558)

Part III discusses composition technique used in sacred music, Willaert, Zarlino’s teacher. It surpasses fellow student Nicola Vicentino’s very similar L’antica musica ridotta alla moderna prattica (1555). Topics include soggetto (theme and imitation), fuga (equal interval pattern), imitatione (differing interval pattern), and harmonia perfetta (triad). Zarlino (IV, 33) discusses text setting and underlay according to the natural rhythm and accent of speech. Dissonance is stepwise, accented resolves down by step. Suspensions require consonance preparation, and the dot must be consonant.

Vicentino used chromatic madrigals as examples and recognized liberties (in progression, harmony, and mode) justified by text meaning or the affect of the words. Galilei allowed freer uses of dissonance (with exceptions: conjunct sequence of four semiminims, two can be dissonant in any position, and occasionally three can be consecutively dissonant). Suspensions can be resolved by leap to a consonance (ex.15c), by progression to a new dissonance (ex.15d), by ascent to a consonance (ex.15e), and, apart from the form in ex.14b, simultaneously with a chromatically progressing added part (ex.15f); they can occur several at once (ex.15g). Dissonances can also sometimes occur in the stressed position without syncopated preparation if a regular resolution follows (ex.15h, i).

Fux, Johann Joseph (Gradus Ad Parnassum, 1725)

Fux describes species counterpoint as “strict,” with fewer types of freedom than other types of counterpoint. It is a pedagogical tool, with species increasing in complexity, starting from cantus firmus.

Types of Species Counterpoint

  1. Note against note
  2. Two notes against one
  3. Four (modified by others to include three, six, etc.) notes against one
  4. Notes offset against each other (as suspensions)
  5. All the first four species together, as florid counterpoint

Rules for All Species

  • The final is approached by step from above, semitone from below.
  • Melodic intervals: P4, P5, 8va, Mm2, Mm3, m6 (ascending only, must be followed by a downward motion).
  • Two skips in the same direction: use rarely; if so, the second skip must be smaller than the first, with a consonant interval between the first and third note. Try to keep notes from the same triad. Proceed with different direction after a skip. Avoid motion of tritone and seventh between three notes.
  • There must be a climax or high point in the line countering the cantus firmus, must occur on a strong beat, usually somewhere in the middle.
  • Must begin and end on a perfect consonance.
  • Contrary motion should predominate.
  • Perfect consonances may be approached by any type of motion.
  • The interval of a 10th should not be exceeded between to adjacent parts unless by necessity.
  • Build from the bass upward.