The so-called third-species of counterpoint outlined in J. J. Fux’s treatise involves four notes against one. This may also be extended to include three notes and six notes against one.
While instances of true contrapuntal passages in third species may be relatively rare in much guitar-based music, examples can still be found.
Beginning at 1:14 in Air by Jason Becker, is a passage constructed from three against one third-species counterpoint. As with all counterpoint, third-species uses both harmony and non-harmony notes to create the contrapuntal texture.
In the first bar of the following example, beginning at 1:14, the upper part moves in contrary motion with the dotted quarter notes of the lower part, while on the first dotted quarter note beat of the second bar, the lower part uses the eighth note figure from the upper part. The sharing of melodic ideas in this way creates interest and avoids a melody-and-accompaniment style of texture.
Looking at the harmony of these two bars we see that Becker is playing a i – VI – v – V progression in D minor (D minor, B flat major, A minor, A major), the harmony changes on each dotted quarter note beat of the bar, a pattern which is essentially followed throughout this passage. Over the D minor chord the first two eighth notes in the upper part can be heard as the fifth and root (A-D) of tonic harmony, while the final E eighth note is a passing note which leads to the fifth (F) of the B flat major harmony. The F eighth note then moves through an E passing note to the third of the B flat major chord (D) on the final eighth note beat of the first bar.
Bar 2’s harmony is outlined in a similar way: the B flat eighth note on the second eighth note beat of bar two passes between the A and C harmony notes, while over the A major harmony the A leaps to the C sharp then passes by step, through D, to the harmony note at the beginning of bar 3.
Bars 3-6 contain a brief modulation to G minor: the G minor chord on the first dotted quarter note beat of bar 4 acts as the pivot chord which effects this modulation; G minor is chord iv in D minor and chord i in G minor.
As in bars 1-2, through bars 3-6 Becker combines harmony notes (by leap and step) with non-harmony notes (by step) to create the texture. Notable exceptions to this occur on the second dotted quarter note beat of bar 5 and the second dotted quarter note beat of bar 6. On the second dotted quarter note beat of bar 5 the F eighth note can be heard as the ninth of the E flat major harmony on this beat,
the F also continues the ascending line in the lower part of bar 5 and the beginning of bar 6, D – E flat – F – G.
On the second dotted quarter note beat of bar 6, the initial E eighth note is not part of the underlying D minor harmony in the second half of this bar. It also does not pass by step from the preceding G harmony note. Instead, it is an instance of a non-harmony note approached by leap: an appoggiatura. As with this example, an appoggiatura must form a dissonance with the other notes of the harmony with which it sounds. Here, the E does not belong to the D minor harmony, unless we hear it as a ninth (as a means of introducing various types of non-harmony notes, in this instance the D minor harmony is treated as a simple triad). The appoggiatura must proceed by step to either the note above or below; this note must belong to the underlying harmony. In this example the appoggiatura moves to the third of D minor (F). Finally, an appoggiatura must be in a metrically stronger position than the note to which it moves. Here, the E is on the first eighth note beat of the second half of the bar while the F is on the second.
Appoggiaturas create tension which must then resolve to one of the notes of the chord.
The final G eighth note of bar 6 also does not follow the typical rules of movement for non-harmony notes. Here, the G eighth note is not part of the underlying D minor harmony (unless we hear it as an eleventh) and would therefore typically move by step to another harmony note. In this example, however, it leaps to the D harmony note at the beginning of bar 7. This type of movement is called an echappee, or an escape note. An escape note is a non-harmony note which moves by step in the same direction as a preceding harmony note/s but then leaps to another harmony note in the opposite direction to this movement.
Like the appoggiatura, the escape note creates momentary tension which must be resolved. Allowing non-harmony notes to occasionally leap also creates greater interest in the melodic lines as it negates the need for dissonance to always be approached and left by step.
In bars 7-9, instances of non-harmony notes can be summarised by the following example.
The D eighth note on the second dotted quarter note beat of bar 7 and the second dotted quarter note beat of bar 8 must be heard as harmony notes, creating A11 and C9 chords respectively.
A – C sharp – E – G – B – D = A11
C – E – G – B flat – D = C9
As was previously mentioned, examples of true third species contrapuntal textures in guitar-based music is relatively rare, however, many pieces may utilise the techniques common to third species writing.
Much of Tanz Der Washerin (Dance of the Washerwoman) by Hans Neusiedler, while perhaps not being truly contrapuntal, uses four against one, third species contrapuntal techniques. In bar 1, the notes of the underlying D minor harmony are ‘decorated’ by various non-harmony notes. The F-E-G-F eighth note combination in the second half of the bar are changing notes which, like the appoggiatura and escape notes, are non-harmony notes which leap; notice, however, that they do move by step either from or, to harmony notes (F-E and G-F).
On the second eighth note beat of bar two the lower neighbour note is chromatically raised to create a semitone between the harmony note (G) and the neighbour note (F sharp). Composers often raise, or (less commonly) lower neighbour notes to create a semitone where there occurs a tone. Occasionally, as in this example, the chromaticism may be used to preserve a motivic element: the opening F-E-F-D eighth note combination in bar 1 includes a semitone between the F and E lower neighbour note.
On the third eighth note beat of bar 3 the C sharp of the A major harmony in the second half of the bar is sounded before the harmony moves from D minor to A.
This is called an anticipation. Typically, as here, anticipations are on metrically weaker parts of a beat; they anticipate the note on the following strong beat.