Canthus Firmus:

Permitted Intervals

Cantus Firmus:

Forbidden Intervals

Cantus Firmus:

Characteristics

1. motion is stepwise
2. few leaps but ones used to relieve stepwise motion
3. ascending motion and leaps create tension
4. descending motion and steps relieve tension
5. no immediately repeated or sustained notes, which create static areas

Cantus Firmus:

Shape and Variety

1. CF begins and ends on the tonic
2. moves to cadence at end in a stepwise fashion
3. line leads immediately to a climax, which is close to the middle or beginning of the line, allowing controlled descent
4. leaps are limited to 2 or three per line, none consecutive
5. interval of a 3rd is neutral with greater intervals followed by a change in direction and stepwise motion

First Species:

Permitted Intervals

First Species:

Stability provided by ____?

First Species:

Permitted types of motion

1. Contrary motion (maximum independence of lines)
2. Oblique motion (the counterpoint holds while the CF moves -- no static areas in the melody)
3. Parallel motion
4. Similar motion

• the CF and Ctpt must both climax but not at the same time
• avoid dissonant intervals with two leaps in the same direction

First Species:

Forbidden Intervals

• parallel 5ths (undermine the forward motion of the CF)
• P1 and P8 (used sparingly at most in the middle and approached either through contrary or oblique motion)

First Species:

Cadences

• supertonic and leading tone in the penultimate bar
• tonic in both CF and Ctpt in final bar

First Species:

Opening Measure

• P5 or P8 with the CF in the upper voice
• P1 or P8 with the CF in the lower voice
• tonic in the lower voice

Second Species:

 Note-against-Note Relationship

• there are two notes against one note now, with the consonant falling on the strong beat (upbeat) of the measure and the dissonant on the weak beat (downbeat) of the measure, creating a distinct rhythm absent in the undifferentiated whole notes of first species
• tones of figuration occur on weaker parts of the beat or measure, called passing tones, involving half notes
• CF is written in whole notes with Ctpt in half notes at longest

Second Species:

Cadences

• supertonic and leading tone occur in the penultimate bar, the latter appearing in the second half note
• in melodic and harmonic minor keys, raised notes must occur in the Ctpt as the cadence is approached
• the final cadence is in whole tones

Second Species:

Opening Measure

• P5 or P8 with the CF in the upper voice
• P1 or P8 with the CF in the lower voice
• tonic in the lower voice
• may begin a whole note in the Ctpt or two half notes
• the Ctpt may begin with a rest with the CF being the first note sounded, thereby emphasizing the half-note rhythm of the second species counterpoint

Second Species:

Permitted Types of Motion

• motion is stepwise, especially in the Ctpt
• dissonances on the weak beat as a passing note, dissipating tension
• all other intervals with the CF must be consonant
• leaps of larger size (5ths, 6ths and octaves) provide new points of departure for the lines from a different register
• unisons can occur but not on the strong beat, rather, i.e., beginning with a fifth and the second half note falling in unison with the CF on the weak beat as the whole note of the CF continues through both beats
• unisons should be approached obliquely, being less intrusive that way, and then a reversal of direction after the unison

Second Species:

Accented 5ths and Octaves

• consecutive parallel 5ths and octaves may occur, unlike in first species, but MUST with the following rules:
  • accented octaves are not permitted, i.e., appearing on consecutive downbeats
  • accented 5ths are permitted if the second 5th arises through stepwise motion after a change in direction
• intervening half notes only partially mitigate consecutive 5ths and octaves

Second Species:

Forbidden Motion

• parallel motion of consecutive 5ths and octaves from the downbeat of one measure to the upbeat of the following measure create the same loss of momentum as in first species and are prohibited
• contrary motion is only permitted with the CF moving obliquely across the bar

Second Species:

Leaps

• large leaps across a bar from weak to strong beat can obscure the passing-note function of the second half-note,  unless, i.e., it is part of an arpeggiated triad which has its own intrinsic motion
• best practice: approach and leave arpeggiations:
  • in a stepwise manner
  • through a change in direction
  • a leap of a 3rd is best onto the strong beat with a stepwise motion and then a change in direction

Third Species:

Neighbouring Notes

Whereas first species consisted of consonant whole notes and second species introduced the dissonant passing tone on weakbeats with consonants remaining on strong beats, third species introduces neighbouring notes which are directly related adjacent to a stable note as decorations to it as well as double neighbouring notes

Third Species:

Shape and Variety 

• four quarter notes in the the Ctpt for each whole note in the CF, with first note being strong and 3rd note being less strong
• 2nd, 3rd and 4th notes can be consonant or dissonant but the first note must be consonant with the downbeat (first beat of the measure)

Third Species:

Permitted Types of Motion

• as with second species, the dissonant neighbour is approached and left in a stepwise fashion, including double neighbours which may involve a skip naturally of a third to the opposite side of the stable tone (i.e., interval of a 9th to a 7th to octave
  • this is the first example of nonadjacent relationships between notes in strict counterpoint based on stepwise motion

Third Species:

Cadences

(same as first and second species)

• final interval heard in the penultimate bar must contain the supertonic and leading tone
• if the leading tone appears on the first quarter (strong beat), it must recur on the fourth beat (weak beat)

Third Species:

Accented 5ths and Octaves

• because of the presence of three consecutive notes separating downbeats, accented 5ths and octaves (falling on downbeats) is softened but are still forbidden on third beats (less strong) or fourth beats (weak) and subsequent downbeat
• this foreshadows frequent use of them in free composition of prohibited parallels broken up and corrected by intervention of other intervals

Third Species:

Leaps

• triadic apreggiations (two leaps in the same direction) should be used sparingly
• avoid 5-1-3-1 idiom expressions
• arpeggiations can follow the same expansion of a single leap (as in second species) and should b e followed by a stepwise change in direction
• larger leaps can provide variety in Ctpt lines

"Because of the quicker note values, however, liberal use of arpeggiations can make the line sound disjointed."

Third Species:

Balance

• "above all, secure a balance between decorative melodic progressions that ornament a single pitch and directed motions that lead from one place to another."
• while it is easier to avoid incorrect uses of dissonances and forbidden parallels, it is more difficult with greater number of notes to create a coherent and purposeful moving line
• avoid hovering, leaping, hovering again, and then leaping again

Fourth Species:

Rhythmic Factors

• in second and third species ctpt passing and neighbouring notes (respectively) represent two treatments of dissonances which fall on weak beats
• in fourth species rhythmic factors are a third type of treatment of dissonance:
  • suspensions, rhythmic displacements and syncopation: notes which are tied across a bar, can form dissonances with the bass on the downbeats, i.e., K.457 III, which resolve on the 2nd quarter (of three) to a consonance in a stepwise manner -- meaning the main note (consonance) falls on the second beat (weaker) rather than the downbeat (rhythmically strongest) 

Fourth Species:

Note against Note relationships

• two half notes in the Ctpt occur against a whole note in the CF
• the first half note (save at the beginning) occurs from a suspension from the previous measure; second half note is tied over into the following measure and is always consonant; the suspension on the downbeat may be consonant and can move stepwise or by leap to the next consonant (upbeat) but if it is dissonant, it must resolve down stepwise.
• because of melodic constraints of half note to whole note, it is permissible to occasionally break the species by abandoning tied suspensions, temporarily introducing second species (passing notes for dissonances)

Fourth Species:

Dissonant Upper Voice Suspensions

Dissonant Lower Voice Suspensions

9-8, 7-6, 4-3

2-3, 9-10, occasionally 4-5

Three components:

1. preparation: this is the second half note and must be consonant
2. suspension: the tied half note
3. resolution: the second half note which is consonant, resolved in a downward stepwise motion (resolution then can become preparation)

Fourth Species:

Consonant Suspensions

• as a consonant, no resolution is required
• because dissonances resolve in stepwise motion but consonants can lead to leaps, consonant suspensions allow for an upward motion in the melodic line

Fourth Species:

Unisons

• unison preparation and suspension: because of the oblique motion between lines (indicative of suspensions by definition), unisons may appear on either the first or second half note (away from unison with unison as prep; toward unison as suspension)

Fourth Species:

Cadences

The best cadence is one in  which the leading tone appears in the fourth species line on the second half note after a dissonant suspension.  This is most easily achieved if the CF ends with the descending motion 3-2-1.

• beginnings: the same for other species, tonic appear in the lower voice
• initiation: a half rest followed by a suspended half note is best for establishing independence of fourth species line
• supertonic and leading note: appear in penultimate bar but because the rhythm is displaced, then the leading note is shifted to the second beat
• syncopation ceases with final bar containing only whole notes in both voices

Fourth Species:

Identical Suspensions

• Best patterns are 7-6 7-6 in the upper Ctpt and 2-3, 2-3 in the lower, avoiding more than three consecutive suspensions of the same type (rule of three).  These can be ways of approaching the cadence
• accented 5ths and octaves: cannot be mitigated by dissonances on the downbeat

Four Species:

9-8  and 4-5 Suspensions

Fourth Species:

5-6, 5-6 and 6-5, 6-5 Progressions

The consonant interval (6th) softens the effect of the successive perfect intervals (5ths).  Rule of Three applies: avoid three consecutive consonant suspensions in a row.

Fourth Species:

2-3 and 9-10 Suspensions

These are the best suspensions for the lower voices.

Fifth Species:

Overview

• combines the rhythmic and dissonance patterns of second to fourth species
• introduces:
  • decorative suspensions
  • pairs of eighth notes on weak beats (2 and 4)
• goal: to create fluid forward momentum without        sharp stops or starts, achieved by:
  • not allowing a given rhythm to continue too long such that any change would seem abrupt
  • longer note values (unless suspended) coincide with strong beats (1 and 3)

Fifth Species:

Shape and Variety

• open the exercise with a rest:
  • half rest and half note
  • quarter rest and three quarter notes
• open with slower notes and progress to quicker notes to intensify and give direction to the line
• climax occurs as:
  • half note on beat 1
  • suspended half note in the preceding measure
• end with a dissonant suspension resolving into the (now possibly decorated) leading tone

Fifth Species:

Note Values in Measures

• unique to fifth species, combinations of half and quarter notes can occur within a measure but:
  • half notes should fall on beat 1, or
  • suspended half notes on beat 3, allowing tie into the beat 1 of the successive measure and a continuation of forward momentum
  • half notes should not fall:
    • on weak beats (not coinciding with metrical accents)
    • on beat 3 unsuspended

Fifth Species:

General Rules

1. no whole notes except in the final measure (otherwise, interrupts forward momentum)
2. note values follow their species rules:
   1. half note for second species
   2. quarter note for third species
   3. suspended half notes
3. eighth notes are:
   1. decorative
   2. always stepwise
   3. occur in beats 2 and 4 (weak)
   4. never occur more than 2 at a time
   5. either may be dissonant
4. no single note should dominate the exercises, which would impair fluid motion by creating static spaces:
   1. no two successive measures should be unvaried (i.e., halves, quarters or syncopated notes with suspensions)
5. longer notes should be kept at the beginning of a measure (metrical accent with the strongest beat)
6. quicker notes, later in the measure on weaker beats and driving the momentum to strong beat of successive measure, when that occurs

Fifth Species:

Decorative Idioms

1. UN: upper neighbour to the suspension
2. LN: lower neighbour to the resolution note
3. ant.: tone of anticipation (repeat of the resolution)
4. CS: consonant leaps (followed by a change in direction)
   1. for 1,2 and 4 the nonadjacent, stepwise resolution of the dissonant suspension is postponed to the third beat
   2. the suspended note on the beat 1 of the next measure is reduced to a quarter note with the other quarter note being the decoration (3/4/1, 2 3/4, or if followed by a second suspension 2 3/4/1)
   3. alternatively to quarters, the second beat can be subdivided into eighth notes for a quicker, stepwise motion, driving towards the cadence
5. P: passing tone (do not fall on the downbeat (beat 1 but can in freer textures can appear on stronger portions of a beat)