In second species, the counterpoint voice moves in half notes while the cantus firmus moves in whole notes. This 2:1 ratio introduces passing tones — the first permitted dissonances — and the concept of metric placement.
The 2:1 Ratio
Second species counterpoint introduces rhythm: the counterpoint voice now moves in half notes while the cantus firmus moves in whole notes. For every one cantus firmus note, the counterpoint voice provides two notes. This ratio creates a metric distinction between downbeats (the first half note in each measure, coinciding with the cantus firmus note) and upbeats (the second half note, falling between cantus firmus notes). The introduction of metric hierarchy — strong beat versus weak beat — is the most important conceptual advance of second species.
This distinction is crucial: the rules for downbeat intervals are stricter than for upbeat intervals. On the downbeat, only consonances are permitted — just as in first species. But on the upbeat, dissonance is permitted under specific conditions: the dissonant note must be a passing tone, approached by step and left by step in the same direction. A passing tone fills in the gap between two consonances by stepwise motion: C (downbeat consonance) to D (upbeat passing tone) to E (next downbeat consonance). The D may be dissonant — a second or a seventh against the cantus firmus — because it is approached and left by step, making its function clear and its dissonance controlled.
The Passing Tone: The Fundamental Dissonance
The passing tone is the foundational dissonance of tonal music. It appears in every style, every era, and every genre. Understanding it in the context of species counterpoint reveals why: the passing tone is dissonant but controlled — its motion (stepwise, in one direction, approached from and resolved to consonance) makes it musically comprehensible even as it creates tension. The ear forgives a dissonance it can predict and explain; it rejects a dissonance that arrives without preparation and leaves without resolution.
The passing tone appears in expanding contexts as species counterpoint progresses:
- In second species, passing tones appear on the upbeat between two consonant downbeats.
- In third species (four notes against one), passing tones can appear on any of the three inner beats, sometimes in chains of two or three consecutive passing tones.
- In fifth species (florid counterpoint), passing tones are so common that they are the predominant dissonance.
- In tonal harmony, passing tones appear in every texture, as ornamental tones between structural chord tones, as the basis of chord inversion (the first inversion of a chord is often the result of a passing tone in the bass), and as the source of the V7 chord's characteristic voice leading (the seventh of V7 is a passing tone that was "retained" and harmonised).
Cambiata and Nota Cambiante
Fux introduces the cambiata (changing note figure) in third species, and it is discussed here because it grows out of the passing-tone logic of second species: a four-note pattern that steps down — down by step, down by third, up by step (for example C-B-G-A). The third leap is permitted in this context because of the specific voice-leading pattern, even though the B may be dissonant. Jeppesen documents this figure extensively in Palestrina's music, where it appears as a characteristic melodic gesture and represents one of the most frequent dissonance treatments in Renaissance vocal style.
The term nota cambiante (changing note) is used for the same figure, in which the second note may be an unprepared dissonance that is left by leap. Fux permits it with caution; Jeppesen restricts it to specific rhythmic positions. Both writers recognise it as a feature of Palestrina's practice but warn the student against overusing it. The general principle is that any departure from the strict passing-tone or neighbour-tone treatment of dissonance must be justified by a specific, documented melodic formula.
Parallel Perfect Consonances Across the Bar
A subtle but critical rule in second species: parallel fifths or octaves between successive downbeats are still prohibited, even if a passing tone intervenes on the upbeat between them. A downbeat fifth followed by another downbeat fifth in the next measure counts as parallel fifths in the structural voice leading, because the metrically strong beats define the harmonic skeleton. This is often called the "fifth-by-leap" prohibition: the intervening upbeat does not "save" the parallel fifths if the listener perceives the downbeats as the controlling sonorities.
Conversely, parallel thirds and sixths on successive downbeats are perfectly acceptable, since these are imperfect consonances. The general principle: imperfect consonances move freely in parallel; perfect consonances must alternate with different intervals.
Melodic Considerations in Second Species
The doubled rate of motion in second species places new demands on the melodic line. With twice as many notes, the line must avoid both excessive stepwise motion (which becomes dull) and excessive leaping (which becomes disjointed). Good second species counterpoint typically alternates: a leap from the downbeat to the upbeat may be followed by stepwise descent into the next downbeat; or stepwise ascent from downbeat to upbeat may be answered by a downward leap. The overall arch shape of the line must still be present, with a single climax note identifiable across the whole exercise.
The opening of a second species exercise is typically marked by a half rest, with the counterpoint entering on the second half of the first measure. This allows the cantus firmus to establish itself before the counterpoint joins, and gives the opening a sense of conversation rather than simultaneous declaration.
Practical Exercise for Second Species
Take the same cantus firmus used in the first species exercise (C-D-F-E-G-F-D-C). Now write two notes for each cantus firmus note, beginning with consonances on the downbeats. On the upbeats, try passing tones where possible. Avoid consecutive perfect consonances even when they are rhythmically offset (two consecutive downbeat perfect fifths count as prohibited parallel fifths, even if a passing tone intervenes on the upbeat). Verify by singing or playing.
Then write a second version with the counterpoint below the cantus firmus. Note how the choices change: a third above the cantus firmus becomes a sixth below; a fifth above becomes a fourth below (and therefore is now a dissonance, since the fourth above the bass is dissonant). The inverted relationships expose how the rules of consonance depend on which voice is the bass.
Sources and Further Reading
- Fux/Mann. The Study of Counterpoint. Norton. Part II, Chapter 3.
- Jeppesen. Counterpoint. Prentice-Hall. Chapter 5.
- Open Music Theory — Species Counterpoint (openmusictheory.net, CC BY-SA 4.0).
- Gauldin. A Practical Approach to 18th-Century Counterpoint. Waveland Press.
- Aldwell and Schachter. Harmony and Voice Leading. Schirmer/Cengage. Chapter 9: Voice Leading.