Fourth species counterpoint is the syncopated species of strict counterpoint. One voice moves in two minims (half notes) against each semibreve (whole note) of the cantus firmus — a 2:1 texture — and the second minim is tied across the beat/barline to the following downbeat, producing syncopation. In the terminology of the species, the first minim falls on the arsis (weak beat) and must be consonant; the second falls on the thesis (strong beat) and may be consonant or dissonant. A dissonant thesis is a structural suspension: it is prepared by the consonant arsis, struck on the strong beat, and must resolve downward by step into the nearest consonance on the following weak beat. The characteristic sound is a chain of suspensions — most typically 7–6, and in other positions 4–3, 9–10, 2–1. Fux describes tied notes as “bound in chains”: they delay the following note and then seem to emerge into freedom; removing the delay reveals the underlying consonances. The source document is a complete fourth-species exercise from Fux's Gradus ad Parnassum (Fig. 73), in the Dorian mode on D with the cantus firmus in the lower voice.
Key Points
Texture: two half notes/minims in the syncopating voice per whole note/semibreve of the cantus firmus (2:1), with the second minim tied over the beat/barline into the next downbeat.
Ligature / syncopation: the tied minims stay at one pitch and delay the following note; the first minim is the arsis and must be consonant, while the second is the thesis and may be consonant or dissonant.
Consonant vs. dissonant ligature: a consonant ligature has both minims consonant; a dissonant ligature has a consonant arsis and a dissonant thesis.
The syncopation is the point: the tied note sounds on the strong beat, so the ear hears the “wrong” note stressed; the following weak-beat note supplies the resolution.
Dissonance treatment: dissonance is not incidental or produced by diminution; it stands substantially on the thesis and must resolve downward by step to the nearest consonance.
Resolution depends on cantus-firmus position: the allowed dissonances and their resolutions differ according to whether the cantus firmus lies below or above (see Details).
Consonant syncopations (3rd, 5th, 6th, octave on the downbeat) are permitted; Fux mixes them with the dissonant suspensions rather than using dissonance in every bar.
Forbidden ligature progressions: some ligatures are rejected because, once the delay is removed, they produce consecutive unisons or octaves — for example, unison to second, or octave to ninth. By contrast, third to second and tenth to ninth are acceptable because they remain valid when the ligature is removed.
Ligature placement: each measure should receive a ligature where possible; if not, untied minims fill the measure until a ligature can be made. Fux also accepts omitting a possible ligature to avoid irritating repetition, allowing for melodic line and graceful progression.
Melodic shape of the syncopating voice: the resolutions form descending stepwise chains, interrupted by upward leaps (3rd or 4th) that reposition the voice for the next chain.
Opening: the exercise begins with a rest in the syncopating voice on the first downbeat so that its first note can be struck on the weak beat and tied over — the species's defining gesture is established immediately.
Close: the penultimate measure follows prescribed formulas according to cantus-firmus position. In the current exercise the penultimate note is raised by musica ficta (C♯) to make a semitone approach to the final, which arrives on the octave over the cantus firmus.
Ascent: Joseph asks whether a dissonant ligature may also occur in ascent; Aloysius treats this as a difficult question to be resolved elsewhere. For the present, the rule remains that all dissonances must resolve by descending to the nearest consonance.
Variations: ligatures may be varied or broken in customary ways for melodic grace and swifter motion. In the following species, two fusae may be mixed in, but only in the second and fourth parts of the measure — never in the first and third.
Concepts
Species counterpoint — Fux's graded teaching method (first through fifth species) built on a given cantus firmus.
Cantus firmus — the slow, given line (here whole notes, in the lower voice).
Ligature / ligatura — tied minims that delay the following note; the basis of the species' syncopation.
Syncopation — the rhythmic character produced by the tied minims displacing the metric accent.
Arsis and thesis — the first and second minim positions within the species unit; the arsis is the weak-beat preparation, the thesis the strong-beat syncopation.
Consonant and dissonant ligature — ligatures whose thesis is consonant or dissonant.
Resolution — the downward step from a dissonant thesis into the nearest consonance.
Cantus firmus position — whether the cantus firmus lies below or above the counterpointing line, which determines allowed dissonances and resolutions.
Consonance and dissonance — intervals classified as perfect (1, 5, 8) or imperfect (3, 6) consonances vs. dissonances (2, 4, 7, 9).
Musica ficta — editorial accidentals (marked X in the encoding) such as B♭ to avoid the tritone and C♯ as a raised leading tone.
Dorian mode — the modal final is D; the key signature is empty, so B♭ must be added as ficta.
Fusae — passing eighth-note-like figures that may be mixed into the following species under strict placement rules.
Details
Mechanism of the species
Rendering diagram…
In fourth species, the syncopating voice's second minim is tied to the first minim of the next measure. That tied note coincides with the new cantus firmus note and therefore determines the harmonic interval on the downbeat. If it is dissonant, the following weak beat must resolve it by step, normally downward. Because every measure repeats this figure, the voice articulates a continuous chain of suspensions rather than a melody of independent consonances.