The Westergaard Rules

This document contains only the rules for simple counterpoint in first, second, third, and fourth species.

Monotriadic Lines

(Note: The S-rules and E-rules correspond to Westergaard’s A-rules and B-rules.)

Rules of Basic Structure

Primary Lines with a basic step motion

• S1. The final pitch in the basic step motion must be a tonic pitch.

• S2. The first pitch in the basic step motion must be a tonic-triad member a third, fifth, or octave above the final pitch.

• S3. These two pitches must be connected by a descending diatonic step motion.

Bass Lines with a basic arpeggiation

• S1. The final pitch of the basic arpeggiation must be a tonic.

• S2. The first pitch of the basic arpeggiation must be a tonic.

• S3. The middle pitch of the basic arpeggiation must lie a fifth above or a fourth below the final pitch of the basic arpeggiation.

Generic Lines

• S1. The final pitch of the basic arpeggiation must be a tonic.

• S2. The first pitch of the basic arpeggiation must be a tonic.

• S3. If different, these two pitches may be connect by a diatonic step motion.

Rules of Elaboration

• E1. Any tonic-triad pitch may be repeated, but not the pitch generated by S1.

• E2. A neighbor note may be inserted between consecutive notes with the same pitch.

• E3. Any tonic-triad pitch may be inserted prior to the first pitch of a basic step motion in primary upper lines or between consecutive notes in any type of line, provided that no dissonant leap or leap larger than an octave occurs. (Note that a perfect fourth is a melodic consonance.) (In bass lines, insertion of scale degree 3 immediately prior to the final tonic should be avoided.)

• E4. Any two consecutive notes forming a leap may be joined by step motion.

Global Rules for Elaborated Lines

• G1. All of the pitches in a line should lie within a single register (i.e., within the span of a tenth or perhaps twelfth).

• G2. The last two notes of a primary upper line must form a step.

• G3. Lines in minor keys should conform to the melodic minor scale in the use of the sixth and seventh scale degrees. The lower neighbor of the tonic pitch is the raised seventh degree.

First Species in Two Parts

Rules for Constructing the Lines

1. Each line must be generated by the rules for constructing species lines.

2. The upper line must be a primary upper line.

3. The lower line must be a bass line.

Rules for Combining Lines

Control of Dissonance

1. Two notes that sound simultaneously must not form a dissonant interval. (Remember that the fourth is a vertical dissonance.)

Forbidden Forms of Motion

1. No parallel unisons, octaves, or fifths between consecutive simultaneities.

2. No non-consecutive parallel unisons or octaves that result from parallel structures in their lines, unless the intervening simultaneity includes a pitch dissonant with the first unison or octave.

3. No similar motion to or from a unison.

4. No similar motion to an octave unless both notes forming the octave are the final tonics in their respective basic structures and the upper note is approached by step.

5. No similar motion to a fifth unless the upper note is approached by step and is either the fifth or second scale degree.

6. No voice crossing, overlapping, or cross relations.

Bass Leaps of a Fourth

1. If the bass leaps a fourth, one of the two notes in the upper line that coincides with the two notes forming the fourth must form a second or a seventh with the contiguous (non-simultaneous) bass note.

Sonority

1. Prefer imperfect consonances.

2. Prefer to use a fifth or octave in the midst of the composition only where the emphasis provided by that interval will help to stress a pitch that belongs to the basic structure.

3. Avoid unisons except in the first and last measures.

4. Avoid intervals larger than a tenth.

Second Species in Two Parts

Rules for Constructing the Half-Note Line

1. The half-note line may begin either on or off the beat, that is, it may begin with a half rest.

2. The last note in the line is a whole note initiated with the last note of the whole-note line.

3. The half-note line must not include any immediate repetitions.

4. Modification of the global rule for final step in a primary upper line. If the half-note line is a primary upper line with basic step motion, at least one note in the penultimate bar of the line must be consonant and must lie a step away from the final tonic. If the step-related note is the first note in the penultimate bar, the second note must not displace it by step.

Rules for Combining Lines

Control of Dissonance

1. On the beat: all intervals must be consonant, as in first species.

2. Off the beat: the interval may be dissonant if the half note is approached and left by step, that is if it is a dissonant passing tone or a dissonant neighbor.

Forbidden Forms of Motion

1. On the beat to off the beat: since all motion is oblique, the only restriction is against the bass crossing the upper voice.

2. Off the beat to on the beat: as in first species, except that cross relations are permitted if the half notes form steps.

3. On the beat to on the beat

   • No parallel unisons or octaves.

   • No parallel motion to a perfect fifth except where the half note forming the second fifth is approached and left by a step motion in the opposite direction from the parallel fifths.

4. Off the beat to off the beat

   • No parallel unisons.

   • Parallel octaves related by seconds may occur, but only if the two off-the-beat half notes are approached from opposite directions.

   • Parallel octaves related by any other interval may occur if either

     1. the two off-the-beat half notes are approached from opposite directions, or

     2. the first off-the-beat half note is left by step.

5. No noncontiguous cross relations between an on-the-beat half note and the whole note in the next measure unless the half note moves by step.

Bass Leaps of a Fourth

1. When the half-note line occurs in the bass:

   • A leap of a fourth may not occur within a measure.

   • A leap of a fourth may occur off the beat to on the beat if either

     1. one of the half notes in the fourth forms a second or seventh with the contiguous whole note, or

     2. the pitch of the preceding on-the-beat half note lies a step away from the pitch of the second note of the fourth.

2. When the whole-note line occurs in the bass:

   • A fourth is permitted in the bass if there is a half-note in the upper line that

     1. sounds during and is consonant with one of the notes forming the fourth,

     2. forms a second or seventh with the other, and

     3. either

        • falls on the beat,

        • is approached by leap, or

        • is contiguous with the note it forms a second or seventh with.

Sonority

1. On the beat: as in first species.

2. Off the beat: any interval is permitted, but dissonant intervals are preferred.

Third Species: Two Lines

Constructing Lines in Third Species

1. The species line may begin on any part of the first measure.

2. The last note in the species line is a whole note initiated with the last note of the whole-note line.

3. Localized rule E1 (L1). In this line (but not the whole-note line) any consonant pitch may be repeated within a measure.

4. No immediate repetitions may remain in the completed line. If rule E1 is applied, then some other rule must be applied subsequently to insert a note between the pitch and its repetition.

5. Localized rule E2 (L2).A neighbor may be inserted between a locally consonant pitch and its repetition. In minor, the lower neighbor to the diatonic or raised seventh degree, is the raised sixth degree; and the upper neighbor to the diatonic or raised sixth degree is the lowered seventh degree.

6. Localized rule E3 (L3). [1] A non–tonic-triad pitch may be inserted within a measure if

   • the inserted pitch is consonant with the whole note,

   • another note in the measure is consonant with the whole note and generated by the global rules,

   • the inserted pitch is linearly consonant with this globally generated note and with every other locally consonant pitch that is approached or left by leap, and

   • the inserted pitch is eventually displaced (scale-wise) by a tonic-triad pitch.

7. Localized rule E4 (L4). Two locally consonant pitches may be may be joined by a step motion.

Rules for Combining Lines

Control of Dissonance

1. On the beat: as in second species.

2. Off the beat:

   • Any interval may be dissonant as long as it is approached and left by step.

   • If two consecutive intervals are dissonant, they must be approached and left in the same direction.

Forbidden Forms of Motion

1. On the beat to immediately following off the beat, or off the beat to immediately following off the beat:

   • The bass may not cross the upper voice.

2. Off the beat to immediately following beat (across the barline):

   • As in first and second species.

3. On the beat to on the beat:

   • No parallel unisons.

   • No parallel octaves or fifths except where either the half or quarter note forming the second octave or fifth is approached and left by a step motion moving in the opposite direction to the parallel motion, or the pitch of the second octave or fifth appears as a consonance in the preceding measure.

4. Off the beat to next (but not immediately following) on the beat (in the next measure):

   • No parallel unisons.

   • No parallel octaves except where either the note forming the second octave is approached and left by a step motion moving in the opposite direction to the parallel motion, or the pitch of the second octave appears as a consonance in the preceding measure.

Bass Leaps of a Fourth

1. When the triplet-half- or quarter-note line occurs in the bass:

   • A leap or a fourth may not occur within a measure unless the same measure includes a lower pitch that is consonant with both pitches forming the fourth.

   • A leap of a fourth may occur off the beat to on the beat if either

     1. one of the notes in the fourth forms a second or seventh with the contiguous whole note, or

     2. the pitch of either the immediately preceding off-the-beat note or the preceding on-the-beat note lies a step away from the pitch of the second note of the fourth.

2. When the whole-note line occurs in the bass:

   • A fourth is permitted in the bass if there is a note in the upper line that either

     1. sounds during and is consonant with the first of the notes forming the fourth, forms a second or seventh with the second of the notes forming the fourth, and either

        • comes at the beginning of the measure or end of the measure, or

        • is not followed in that measure by a note a step away that is consonant;

     2. or sounds during and is consonant with the second of the notes forming the fourth, forms a second or seventh with the first of the notes forming the fourth, and either

        • comes at the beginning of the measure, or

        • is not preceded in that measure by a note a step away that is consonant.

Sonority

1. On the beat: as in first species.

2. Off the beat: any interval is permitted, but dissonant intervals are preferred, especially for the final off-the-beat note.

Fourth Species: Two Lines

Rules for Constructing the Syncopated Line

1. The syncopated line must begin off the beat, following a half rest.

2. The last note in the line is a breve initiated with the last note of the whole-note line.

3. The syncopated line must not include any immediate repetitions.

4. The syncopated line may switch to second species once in the middle of the composition, but the line must begin with at least three syncopes and must immediately return to fourth species. [2]

Rules for Combining Lines

Control of Dissonance

1. Off the beat: all notes must be consonant.

2. On the beat: a note may be consonant or dissonant. If it forms a dissonance, it must move down by step to form one of the following successions of intervals against the whole note:

   • 7–6, 9–8, and 4–3 for suspensions in the upper line, and

   • 2–3, augmented 4–5 (but not perfect 4–5), and augmented or diminished 5–6 for suspensions in the lower line.

Forbidden Forms of Motion

1. End of the piece: as in second species.

2. Off the beat to the next off the beat: no parallel unisons; parallel octaves may occur only if the intervening interval is consonant.

3. On the beat to the next on the beat: no parallel unisons.

Bass Leaps of a Fourth

1. Leaps of a fourth in the bass:

   • If the whole note line is in the bass, a leap of a fourth is permitted if either

     1. the first note of the fourth is dissonant with the second note in the next measure, or

     2. the second note of the fourth is dissonant with the syncopated note.

   • If the species line is in the bass, a leap of a fourth may occur only at the end.

Sonority

1. The full sonority of seconds and sevenths is preferred — suspended — on the beat.

First Species: Three Lines

Construction of Lines

1. The lowest line must have the structure of a bass line.

2. One upper line, not necessarily the highest, must have a basic step motion.

3. The other upper line may have the structure of either a generic or primary upper line.

Rules for Combining Lines

Control of Dissonance

1. No dissonance may be formed between simultaneous notes. (Though the fourth is a harmonic dissonance when formed between an upper voice and the bass, fourths between upper voices are considered consonant.) Exception: An augmented fourth or diminished fifth is allowed between the upper voices if the bass forms a sixth with one upper voice and a third with the other.

Forbidden Forms of Motion

1. No parallel unisons, octaves or fifths between consecutive notes in any pair of lines.

2. No non-consecutive parallel unisons or octaves unless the intervening simultaneity includes either (a) a pitch forming a second or seventh with the first unison or octave or (b) a member of the same pitch class as the pitches of the second unison or octave.

3. No similar motion to or from a unison.

4. No similar motion to an octave unless the upper note is approached by step and both notes forming the octave are the final tonics in their respective basic structures.

5. No similar motion to a fifth unless the upper note is approached by step and either the upper note is the fifth or second scale degree or the fifth is in the upper two voices and the bass note is a member of a different pitch class.

6. No voice crossing or overlapping between the bass and either upper line. The upper voices may cross or overlap so long as the structure of each line is clear.

7. No cross relations unless the third line moves by step at the same time that the second note of the cross relation occurs.

Bass Leaps of a Fourth

1. There must be a note in one of the upper lines that sounds simultaneously with one of the notes forming the fourth and creates a second or seventh with the other note forming the fourth.

Sonority

1. A sonority of three different pitch classes in each measure is most satisfactory. Where impossible or undesirable, use the next fullest sonority (two notes of one pitch class and a third forming an imperfect consonance with the other two).

2. Avoid simultaneities that form only perfect intervals except at the beginning and end.

3. The upper two voices should rarely be further than an octave apart.

Endnotes

[1]

Permitting local insertions is an extension of the rules not found in Westergaard.

[2]

Permitting a break in the syncopations is an extension of the rules not found in Westergaard.