Harmonic Weave

🎭 Melodic Interaction First

While the term "counterpoint" can sometimes refer to a single voice or even an entire composition, its primary focus is on the dynamic interaction between melodies. The resulting harmonies are a secondary, albeit crucial, outcome of this melodic interplay.^[3]

➕ Mathematical Foundations

Modern theoretical work, notably by Guerino Mazzola, has provided a rigorous mathematical framework for counterpoint theory. This model offers a structural basis for understanding traditional prohibitions, such as parallel fifths and the dissonant fourth.^[4][5] Octavio Agustin has further extended this model to microtonal contexts. Earlier, Sergei Taneyev, inspired by Spinoza, developed an algebraic theory that generalized advanced contrapuntal phenomena, including invertible counterpoint, using his own specialized terminology.^[6][7]

🚫 Voice Independence

A paramount concern in counterpoint is the functional independence of each voice. Violations of this principle lead to specific effects that are generally avoided. For instance, in organ registers, certain interval combinations can be activated by a single key, resulting in parallel voice leading. These parallel voices lose their independence, fusing into a single perceived timbre. Counterpoint prohibits such parallelisms to preserve the distinctiveness and heterogeneity of the musical texture.^[8][9]

👑 Bach: Master of Counterpoint

Johann Sebastian Bach is widely regarded as one of the supreme masters of counterpoint. His works exemplify the profound depth and complexity achievable through this technique. For instance, in the opening subject of the Fugue in G-sharp minor from Book II of The Well-Tempered Clavier, the implied harmony takes on new subtleties when a second voice is introduced. This contrapuntal addition in bars 5-8 illuminates the subject's tonality in an unexpected way.^[11] Similarly, Bach's 3-part Invention in F minor masterfully combines three independent melodies, each contributing to a cohesive yet intricate whole.

🏛️ Beethoven & Mozart

Bach's contrapuntal mastery significantly influenced later composers such as Wolfgang Amadeus Mozart and Ludwig van Beethoven. Pianist András Schiff highlights this influence in the development section of the opening movement of Beethoven's Piano Sonata in E minor, where Beethoven introduces "a wonderful counterpoint" to one of the main themes.^[12] In Beethoven's Symphony No. 9, the finale's first orchestral variation on the "Ode to Joy" theme (bars 116–123) showcases fluid counterpoint, with violas and cellos carrying the theme, basses adding a spontaneously improvised bass-line, and a solo bassoon contributing an impromptu counterpoint.^[13] Mozart's Symphony No. 41 ("Jupiter" Symphony) finale presents a spectacular example of 5-voice counterpoint, where five distinct tunes combine simultaneously to form a "rich tapestry of dialogue."^[16]>

🎭 Wagner's Virtuosity

Richard Wagner's Prelude to his opera Die Meistersinger von Nürnberg features a remarkable instance of three themes from the opera being combined simultaneously. Gordon Jacob lauded this as "an extraordinary feat of virtuosity."^[14] However, Donald Tovey noted that, unlike classical counterpoint, these themes do not inherently combine into a complete or euphonious harmony, suggesting a different aesthetic intent.^[15]>

2️⃣ Second Species: Two Against One

Second species counterpoint introduces rhythmic variety, with two notes in the added part sounding against each longer note in the given part. An upbeat start with a half-rest in the added voice is permissible. The accented beat must be consonant (perfect or imperfect), while the unaccented beat may feature dissonance through melodic embellishments such as passing notes (stepwise movement between consonances), neighbor notes (a step away from and back to a consonance), or escape tones (a step to a dissonance followed by a leap in the opposite direction to a consonance). Accented dissonance is also allowed if the following unaccented beat is consonant. Unisons are generally avoided except at the beginning or end, or on unaccented beats. Caution is advised with successive accented perfect fifths or octaves, especially in sequential patterns.

3️⃣ Third Species: Four Against One

In third species counterpoint, four (or more) notes in the added part move against each longer note in the given part. This species introduces specific melodic figures that allow for more complex dissonances and embellishments. These include the nota cambiata, double neighbor tones, and double passing tones. Double neighbor tones prolong a figure over four beats, allowing special dissonances prepared on beat 1 and resolved on beat 4, with the subsequent note moving stepwise in the same direction. Double passing tones permit two consecutive dissonant passing tones within a four-note stepwise figure, where the dissonant interval of a fourth might proceed into a diminished fifth, resolving to a sixth.^[18]>

4️⃣ Fourth Species: Suspensions

Fourth species counterpoint is characterized by the use of sustained or suspended notes in an added part. These suspensions create a dissonance on the beat, which then resolves to a consonance as the suspended note changes and "catches up" with the note in the given part. This technique inherently creates syncopation. A dissonant interval is permitted on beat 1 due to the syncopated nature of the suspension. While starting with a half note is acceptable, beginning with a half rest is also common. When the added-part notes vary in length, it is referred to as expanded fourth species.

5️⃣ Fifth Species: Florid Counterpoint

Fifth species, also known as florid counterpoint, represents the culmination of species study. In this species, elements from all the preceding four species are combined within the added parts. The key characteristic of florid counterpoint is that no single species should dominate the composition; instead, there is a fluid interplay of different rhythmic and melodic densities. For example, a passage might begin with second species, transition to third species, incorporate elements of embellished fourth species, and conclude with first species, demonstrating a comprehensive command of contrapuntal techniques.

evol Evolution of Practice

From the Baroque period onward, the majority of contrapuntal compositions shifted towards a style known as free counterpoint. This evolution reflected a change in compositional focus: less emphasis was placed on how individual melodies related to a strict cantus firmus, and more on the intricate relationships between the melodies themselves. While formal instruction in "strict" counterpoint persisted well into the late nineteenth century, as noted by Kent Kennan,^[23] composers like Mozart, Beethoven, and Schumann, though educated in traditional methods, actively sought to expand upon these concepts in their practical compositions.

🔓 Liberated Composition

The main features distinguishing free counterpoint from its stricter predecessors include:

• Expanded Harmonic Vocabulary: Previously "forbidden" chords, such as second-inversion, seventh, and ninth chords, can be used more freely, provided they resolve appropriately to a consonant triad.
• Chromaticism: The use of chromatic notes and harmonies is permitted, adding greater expressive potential.
• Flexible Dissonance Treatment: Restrictions on the rhythmic placement of dissonance are relaxed, allowing for passing tones on accented beats.
• Appoggiatura: Dissonant tones can be approached by leaps, offering more dramatic melodic possibilities.

🔄 Rules Reversed

Dissonant counterpoint was initially conceptualized by Charles Seeger as a "purely a school-room discipline." This radical approach involved reversing all the traditional rules of species counterpoint. For instance, first species counterpoint, instead of being entirely consonant, was mandated to be composed entirely of dissonances, thereby establishing "dissonance, rather than consonance, as the rule." Furthermore, consonances were "resolved" through a skip, rather than the traditional step. Seeger posited that the "effect of this discipline" was one of "purification," and the same principle could be applied to "dissonate" other aspects of composition, such as rhythm.^[27]>

avant-garde Influential Practitioners

While Charles Seeger was the first to theorize and actively promote dissonant counterpoint, he was not the sole practitioner. A number of other significant composers have employed dissonant counterpoint, though perhaps not always in the exact manner prescribed by Seeger. These include figures such as Johanna Beyer, John Cage, Ruth Crawford-Seeger, Vivian Fine, Carl Ruggles, Henry Cowell, Carlos Chávez, John J. Becker, Henry Brant, Lou Harrison, Wallingford Riegger, and Frank Wigglesworth.^[28] Their work demonstrates the diverse applications and interpretations of this innovative contrapuntal philosophy.

📜 References