A Treatise on Simple Counterpoint in Forty Lessons

In Short

Friedrich J. Lehmann’s A Treatise on Simple Counterpoint in Forty Lessons is a practical, step-by-step pedagogical manual written in 1907 for music students. The book systematically moves from basic two-part note-against-note exercises through increasingly complex rhythmic species, culminating in four-part florid counterpoint and the free harmonization of melodies. It has endured because it breaks down intricate compositional mechanics into forty digestible, clear assignments, bridging foundational harmonic theory and active melodic invention.

The Story

The book unfolds as a progressive pedagogical trajectory designed to guide a student from basic musical literacy to complete contrapuntal fluency. Lehmann opens by establishing the groundwork in Lesson I, defining simple counterpoint, harmonic and melodic intervals, and the foundational concept of the cantus firmus—the fixed melody around which all other voices are constructed. From there, the text embarks on two-part contrapuntal writing, meticulously introducing the traditional five species. It starts with First Species, where the added line matches the cantus firmus note for note, establishing strict rules around consonances, scale steps, and allowable skips. Step by step, the rhythmic complexity increases: Second Species introduces two notes against one, Third Species advances to four or six notes against one, Fourth Species introduces syncopation and suspensions, and Fifth Species weaves these elements into florid counterpoint.

Once the mechanics of two-part interaction are established, the book expands its scope to three-part writing. Lehmann re-introduces each species within this denser texture, challenging the student to balance voice leading across soprano, alto, tenor, and bass lines while maintaining full, resonant chords and managing non-harmonic embellishments. The rules adapt to accommodate the added density: incomplete chords, passing seventh chords, and subtle voice-crossing guidelines are methodically integrated.

The instruction then escalates to four-part counterpoint. In this section, the student orchestrates four distinct voices around a single given line, combining different species simultaneously—such as pairing syncopated lines with quarter-note motion over a steady baseline. The climax of this progression arrives in Lesson XXXII, where all four parts engage in florid counterpoint using imitation, with voices entering sequentially in response to one another.

In its final stretch, the treatise transitions from rigid, academic rules toward practical compositional freedom. Starting in Lesson XXXIII, fixed, static melodies give way to florid melodies and chorales as canti firmi. The strict distinction between harmonic chord-tones and foreign dissonances softens into free harmonization, allowing the student to shift harmonies at will, incorporate quarter-note suspensions, handle line endings with hold marks, and write original multi-measure phrases. The book ends not with abstract commentary, but with an assignment of pure creation: a full, thirty-two-measure original exercise in four-part counterpoint.

How It Unfolds

The foundation is laid Lehmann establishes the core terms, defining the cantus firmus, distinguishing between melodic and harmonic intervals, and setting down strict rules for two-part note-against-note motion.

Rhythm begins to move The lessons introduce faster note values and syncopations in two parts, forcing the student to navigate passing tones, embellishments, and suspended dissonances against a steady line.

Flowering into florid style The student combines half-notes, quarter-notes, eighth-notes, and ornamental resolutions into a single fluid line, learning to craft expressive, varied counterpoint against a fixed subject.

Adding the third voice The text scales up to three-part textures, detailing how to construct complete triads, manage voice spacing within a vocal compass, and balance mixed species simultaneously across multiple lines.

Four-part architecture and imitation Writing expands to four distinct voices, leading the student through complex species combinations and teaching them to introduce thematic material through staggered entries and imitation.

Freedom through free harmonization The book concludes by replacing rigid canti firmi with fluid chorales and original melodies, granting the student freedom in chord choices, rests, and structural phrasing across extended exercises.

The People

Because this is an instructional text, its key figures are the foundational concepts and structural roles that interact across every lesson.

• The Cantus Firmus wants to serve as an unyielding, solid anchor for every contrapuntal exercise. Standing in the way is the requirement that it must accept new, melodically independent voices above or below it without losing its shape. It ends up transformed from a isolated melodic phrase into the backbone of complex, multi-part harmony.
• The Counterpoint wants complete melodic individuality, continuous movement, and expressive contour. Standing in its way are strict rules against forbidden skips, parallel fifths, hidden octaves, and unresolved dissonances. It ends up evolving from a simple, rigid note-against-note companion into a free, florid line capable of imitation and independent expression.
• The Species want to organize rhythm systematically into manageable stages—from steady half-notes to complex syncopations and eighth-note groups. Standing in their way is the danger of monotony or broken rules when multiple rhythmic patterns are combined simultaneously. They end up merging seamlessly in the final lessons to form a unified, sophisticated contrapuntal texture.

In Its Own Voice

"Counterpoint is the art of combining two or more melodies of equal melodic individuality."

This foundational statement in Lesson I sets the goal for the entire treatise, establishing that every exercise is an exercise in building independent, equal musical voices.

"In this species the suspension may resolve ornamentally, that is, it may have some note or notes interpolated between the suspension and its resolution."

Writing on Fifth Species in Lesson IX, Lehmann demonstrates how strict contrapuntal constraints gradually yield to elegant decorative freedom.

"The solutions should be musical, and are to be written over and over again until such are secured."

This directive from Lesson IX highlights the author's insistence on practical practice, demanding that technical correctness must always serve artistic quality.

What It's Really About

At its core, A Treatise on Simple Counterpoint is about achieving artistic freedom through rigorous discipline. Lehmann’s underlying argument is that musical creativity is not hindered by strict constraints, but rather built upon them. By mastering the strict limits of step-by-step counterpoint—controlling every interval, resolving every dissonance, and balancing every line—a musician develops an intuitive sense of horizontal motion and vertical harmony. The book addresses how distinct, individual voices can maintain their own identities while contributing to a harmonious whole. It transforms abstract rules of voice leading into a practical, repeatable craft, showing that complex musical expressions are constructed systematically from simple, carefully governed relationships.

Why Read It Today

This textbook will deeply satisfy music theorists, student composers, arrangers, and classical music enthusiasts who want to understand the mechanical architecture behind polyphonic music. Reading it feels like sitting down at a workbench with a clear, concise master craftsman who wastes no time on fluff or vague theory. Lehmann offers immediate, practical instructions, explicit rules, and visual examples that demystify how complex musical textures are constructed piece by piece.

Modern readers should be prepared for its unapologetically dry, instructional format. It is a working manual, not a relaxed narrative, filled with technical terminology like inversions, six-four chords, and voice-leading restrictions. Because it presupposes a working knowledge of basic harmony, it expects the reader to engage directly with the mechanics of musical notation. For those willing to work through its forty lessons, it provides a remarkably clear window into the timeless discipline of classical composition.