II. Counterpoint and Galant Schemas

Introduction to Species Counterpoint

Kris Shaffer and Mark Gotham

Key Takeaways

 is a step-by-step way of learning to write melodies and to combine them. While the ‘rules’ involved are somewhat linked to music in the sixteenth century, the idea really is to train basic skills, independent of a specific repertoire or style. This chapter recaps some key concepts we met in the fundamentals section and introduces some basic ‘rules’ that will be relevant for each of the following chapters.

While there are many variants on this approach, the chapters here are closely based on Johann Joseph Fux’s Gradus ad Parnassum (Steps to Parnassus, 1725). Many composers from the eighteenth to the twenty-first centuries have used this method, or some variation on it. Specifically, the following 5 chapters will go through the first part of Gradus ad Parnassum in which Fux works though five “species” for combining two-voices. The “Gradus ad Parnassum” Exercises chapter provides all of the exercises from Gradus ad Parnassum in an editable format so you can try this yourself.

Before getting into those 5 species, we begin in this chapter with a digest of some of the most common-invoked principles that apply to writing lines in all species. Before even that, let’s start with a review of some key considerations and definitions we have met before in the fundamentals section.

Review

Consonance and Dissonance

We distinguish in species counterpoint between:

  • ‘Perfect’ Consonances (perfect unisons, fifths, and octave)
  • ‘Imperfect’ Consonances (major and minor thirds and sixths)
  • Dissonances (all seconds, sevenths, diminished and augmented intervals)
Consonant and dissonant intervals

The Elusive Perfect 4th

The perfect 4th has a special status in species counterpoint (as indeed for many theories of tonal music). This is because it depends on where it appears in the texture. Basically the interval of a Perfect 4th:

  • is dissonant when it involves the lowest voice in the texture;
  • is consonant otherwise, when it appears between upper parts neither of which is the lowest.

This survey of species counterpoint will only cover combination of the cantus firmus with one additional line. As such all fourths between those two parts will involve the lowest part in the texture and be classed as dissonant. We’ll come to ‘resolution’ of the ‘dissonant’ fourth later on, and there’s more on this topic in the chapters on cadences in the Harmony part of the textbook.

Types of motion

  • Contrary: the two parts move in opposite directions (one up, the other down)
  • Similar: the two parts move in the same direction (both up or both down)
  • Parallel: the two parts move in the same direction (both up or both down) by the same ‘amount’ such that the starting and ending interval is of the same type (e.g. parallel thirds).
  • Oblique: One part moves, the other stays on the same pitch

Exercises in strict voice-leading, or species counterpoint, begin with a single, well formed musical line called the (fixed voice, or fixed melody; pl. cantus firmi. Cantus firmus composition gives us the opportunity to engage the following fundamental musical traits:

  • smoothness
  • independence and integrity of melodic lines
  • variety
  • motion (towards a goal)

Here are the cantus firmi which Fux uses throughout Gradus at Parnassum: one for each mode, presented here in the upper and lower of two parts. Apart from using this to review the type of cantus firmi Fux composed, you can use this to practice any of the species, on any of the modes, and in both the upper and lower part.


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Notice how in each case the general musical characteristics of smoothness, melodic integrity, variety, and motion towards a goal are worked out in specific characteristics. The following characteristics are typical of all well formed cantus firmi:

  • length of about 8–16 notes;
  • arhythmic (all whole notes; no long or short notes);
  • begin and end on do;
  • approach final tonic by step (usually re–do, sometimes ti–do);
  • all note-to-note progressions are melodic consonances;
  • range (interval between lowest and highest notes) of no more than a tenth, usually less than an octave;
  • a single climax (high point) that usually appears only once in the melody;
  • clear logical connection and smooth shape from beginning to climax to ending;
  • mostly stepwise motion, but with some leaps (mostly small leaps);
  • no repetition of “motives” or “licks”;
  • any large leaps (fourth or larger) are followed by step in opposite direction;
  • no more than two leaps in a row and no consecutive leaps in the same direction (the F-mode cantus firmus is an exception, where the back-to-back descending leaps outline a consonant triad.);
  • the leading tone progresses to the tonic;
  • leading notes in all cases, including in ‘minor’-type modes for which that 7th degree needs to be raised.

Melodic tendencies

The characteristics listed above are fairly detailed, and some of them are specific to strict species counterpoint. However, taken together, they express in detail some general tendencies of melodies in a variety of styles.

David Huron identifies five general properties of melodies in Western music that connect to the basic principles of perception and cognition listed above, but play out in slightly different specific ways in musical styles. They are:

  • Pitch proximity. The tendency for melodies to progress by steps more than leaps and by small leaps more than large leaps. An expression of smoothness and melodic integrity.
  • Step declination. The tendency for melodies to move by descending step more than ascending. Possibly an expression of goal-oriented motion, as we tend to perceive a move down as a decrease in energy (movement towards a state of rest).
  • Step inertia. The tendency for melodies to change direction less frequently than they continue in the same direction. (I.e., the majority of melodic progressions are in the same direction as the previous one.) An expression of smoothness and, at times, goal-oriented motion.
  • Melodic regression. The tendency for melodic notes in extreme registers to progress back towards the middle. An expression of motion towards a position of rest (with non-extreme notes representing “rest”). Also an expression simply of the statistical distribution of notes in a melody: the higher a note is, the more notes there are below it for a composer to choose from, and the less notes there are above it.
  • Melodic arch. The tendency for melodies to ascend in the first half of a phrase, reach a climax, and descend in the second half. An expression of goal-orientation and the rest–motion–rest pattern. Also, a combination of the above rules in the context of a musical phrase.

‘Rules’

Species counterpoint will see us both write these melodic lines and also combine them. Here, as promised, is that set of ‘rules’ invoked in all the species, separating the melodic matters discussed already with some ‘harmonic’ considerations that we will focus on in the following chapters.

Melodic writing (‘horizontal’ intervals)

Approach the final pitches of each exercise by step.

Limit the number of:

  • contiguously repeated notes: the same pitch more than once in a row;
  • non-contiguously repeated notes: the same pitch more than once across the whole exercise;
  • contiguous leaps: intervals of a third of greater (separate them with step-wise motion);
  • non-contiguous leaps: the total number within a short span, even if they’re not successive;
  • contiguously repeated ‘generic’ intervals: the same interval type (e.g. ‘3rd’) even if not the same specific interval (minor third).

Control the melodic ‘climax’ (highest note)

  • Aim for exactly one, unique climax in each melodic part;
  • Avoid ending on that climax;
  • Preferably leap to that climax;
  • Avoid the two parts reaching their respective climax pitches at the same time.

Avoid melodic leaps of:

  • an augmented interval;
  • a diminished interval;
  • any seventh;
  • any sixth, except perhaps the ascending minor sixth;
  • any interval larger than an octave;

Also avoid ‘outlining’:

  • an augmented interval;
  • a diminished interval;
  • any seventh.
Melodic outlinings

‘Harmonic’ writing (‘vertical’ intervals and the combination of parts)

Make sure to avoid:

  • : two parts start an octave apart and both move in the same direction by the same interval to also end an octave apart;
  • : two parts start an perfect fifth apart and both move in the same direction by the same interval to also end a perfect fifth apart;

Also try to avoid:

  • : two parts begin any interval apart and move in the same direction to a perfect fifth or octave.
  • unisons within the exercise (i.e. excluding the first and last).

Further restrict vertical intervals (between parts) in the special contexts of the:

  • first interval: use a perfect unison, fifth, or octave for two-part writing;
  • last interval: use a perfect unison or octave (not fifth) for two-part writing.

Restrict the gap between parts to a 12th (compound 5th) maximum, and to an octave for the most part.

Avoiding ‘overlapping’ part (where the nominally ‘upper’ part goes below the ‘lower’ one).

Assignments
  1. Cantus firmus A (.pdf, .mscx). Asks students to critique one cantus firmus and write their own.
  2. Cantus firmus B (.pdf, .mscx). Asks students to critique one cantus firmus and write their own.
  3. For the complete set of Fux exercises, see the Gradus ad Parnassum chapter.

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OPEN MUSIC THEORY by Kris Shaffer and Mark Gotham is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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