TREATISE ON COUNTERPOINT AND FUGUE (Parts 4&5)

Parts IV and V analyze the theoretical systematization of Counterpoint and the species of counterpoint, addressing historical treatises, consonances, dissonances, rules, the cantus firmus, and their pedagogical relevance.

PART IV – Theoretical Systematization of Counterpoint

IV.1 Emergence of normative treatises
IV.2 Codification of intervals
IV.3 Classification of consonances
IV.4 Classification of dissonances
IV.5 Rules of preparation and resolution
IV.6 Contrary, oblique, and direct motion
IV.7 Avoidance of parallels
IV.8 Rhythmic proportion
IV.9 Formal balance
IV.10 Counterpoint as an academic discipline
IV.11 Pedagogical transmission
IV.12 Normative authority
IV.13 Foundations of the species of Counterpoint

PART V – The species of Counterpoint: general foundations

V.1 Concept of species
V.2 Counterpoint as a progressive exercise
V.3 The cantus firmus voice
V.4 Note-against-note relationship
V.5 Didactic function
V.6 Hierarchy of difficulty
V.7 Gradual control of dissonances
V.8 Melodic motion
V.9 Modal stability
V.10 Formative value
V.11 Actual historical use
V.12 Difference between exercise and work
V.13 Pedagogical relevance

PART IV – Theoretical Systematization of Counterpoint

IV.1 Emergence of Normative Treatises

The systematization of Counterpoint developed gradually between the fifteenth and eighteenth centuries through treatises that transformed compositional practices into explicit norms. Johannes Tinctoris completed De arte contrapuncti in 1477, establishing intervallic rules observed in real repertoires. Gioseffo Zarlino published Le Istitutioni harmoniche in 1558, integrating mathematical theory, vocal practice, and normative Counterpoint. Giovanni Maria Artusi disseminated L’arte del contraponto in parts between 1586 and 1589, reinforcing strict control of dissonance. Johann Joseph Fux published Gradus ad Parnassum in 1725, consolidating the teaching of Counterpoint through species.

IV.2 Codification of Intervals

Treatises codify intervals according to stability, motion, and function within Counterpoint. Tinctoris enumerates acceptable combinations and preferred successions. Zarlino organizes consonances and dissonances into a coherent theoretical system. Fux reduces variables through the cantus firmus, facilitating repeatable intervallic decisions in strict Counterpoint.

IV.3 Classification of Consonances

Tradition distinguishes perfect and imperfect consonances to order hierarchies in Counterpoint. Fifths and octaves sustain structural stability, while thirds and sixths provide mobility and color. Zarlino formalizes these categories for systematic pedagogical application.

IV.4 Classification of Dissonances

Dissonance is accepted only under strictly controlled conditions in normative Counterpoint. Artusi emphasizes rigorous criteria, especially regarding suspensions. Historical theory legitimizes dissonance through rhythmic context and structural function.

IV.5 Rules of Preparation and Resolution

The suspension articulates three normative phases: consonant preparation, retained dissonance, and resolution by stepwise motion. This model organizes the use of dissonance in Renaissance Counterpoint. Fux integrates it as an essential formative core.

IV.6 Contrary, Oblique, and Direct Motion

Treatises classify motions to preserve the independence of voices in Counterpoint. Contrary motion maximizes polyphonic clarity, oblique motion stabilizes, and direct motion demands constant technical control.

IV.7 Avoidance of Parallels

The avoidance of parallel fifths and octaves constitutes a central rule of strict Counterpoint. The justification is pedagogical and perceptual, since parallels reduce the independence of lines. Historical practice admits exceptions, but the scholastic norm remains.

IV.8 Rhythmic Proportion

Rhythmic control regulates the admission of dissonances in Counterpoint. Dissonances typically occur on weak beats or prepared syncopations. Fux grades rhythmic proportion to increase complexity progressively.

IV.9 Formal Balance

Normative Counterpoint seeks balance between tension and repose. Exercises favor stable openings, controlled development, and clear cadences. Simple form trains structural foresight.

IV.10 Counterpoint as an Academic Discipline

The discipline consolidates when rules are institutionalized within formal curricula. Zarlino grounds the theory–practice relationship. Fux consolidates the most influential pedagogical manual. Counterpoint becomes a criterion of professional competence.

IV.11 Pedagogical Transmission

The teaching of Counterpoint combines systematic example and rigorous correction. The species create a shared evaluative language. The method fosters transferable technical habits.

IV.12 Normative Authority

The authority of a treatise is historical and institutional. Zarlino, Artusi, and Fux gain weight through educational adoption and circulation. The norm describes a formative ideal, not a universal law of Counterpoint.

IV.13 Basis of the Species of Counterpoint

The species isolate specific difficulties of Counterpoint. The cantus firmus stabilizes the sonic environment. Rhythmic progression allows complexity to be mastered gradually.

PART V – The Species of Counterpoint: General Foundations

V.1 Concept of Species

A species is a pedagogical category of Counterpoint, not an autonomous historical genre. It defines controlled rhythmic relationships with the cantus firmus.

V.2 Counterpoint as a Progressive Exercise

Learning progresses by reducing variables and increasing decisional density. Species-based Counterpoint automates correct choices before expressive freedom.

V.3 The Cantus Firmus Voice

The cantus firmus functions as a fixed axis of scholastic Counterpoint. It limits ambiguity and focuses structural attention.

V.4 Note-against-Note Relationship

Note-against-note defines the first species of Counterpoint. Transparency reveals parallels, excessive leaps, and melodic weaknesses.

V.5 Didactic Function

The didactic function of Counterpoint is to train the ear and technical judgment. Each species introduces a specific difficulty in cumulative order.

V.6 Hierarchy of Difficulty

Difficulty increases through rhythmic density and progressive control of dissonance. Counterpoint advances toward complex integration.

V.7 Gradual Control of Dissonances

The early species restrict dissonance. The fourth introduces regulated suspension. Counterpoint integrates dissonance only after prior mastery.

V.8 Melodic Motion

Successful Counterpoint produces singable, independent lines. Stepwise motion and compensated leaps are favored.

V.9 Modal Stability

Pedagogical Counterpoint operates within simplified modal frameworks. Stability reduces harmonic variables during learning.

V.10 Formative Value

The formative value of Counterpoint is technical and perceptual. It trains tension, repose, and coherent voice-leading; therefore, it remains current.

V.11 Actual Historical Use

The method summarizes historical practices without reproducing them in full. Real Counterpoint shows greater flexibility than the school model.

V.12 Difference Between Exercise and Work

The exercise verifies technical control, while the work pursues artistic expression. Scholastic Counterpoint functions as structural grammar.

V.13 Pedagogical Relevance

The pedagogical relevance of species-based Counterpoint lies in its diagnostic clarity. It detects typical errors and creates shared vocabulary between teacher and student.