Counterpoint

For Praxis 5114

Cantus Firmus

Bottom line of species counterpoint

V

Scale Degree in Bass = ^5

Leads to (I or I6) = Either

V7

Scale Degree in Bass = ^5

Leads to (I or I6) = I

V6

Scale Degree in Bass = ^7

Leads to (I or I6) = I

V6/5

Scale Degree in Bass = ^7

Leads to (I or I6) = I

V4/3

Scale Degree in Bass = ^2

Leads to (I or I6) = Either

• If leading to I6 —> Can have dim5 to P5

• If leading to I6 —> Chordal seventh can resolve up

viio6

Scale Degree in Bass = ^2

Leads to (I or I6) = Either

• If leading to I6 —> Can have dim5 to P5

• ^4 is NOT a chordal seventh

V4/2

Scale Degree in Bass = ^4

Leads to (I or I6) = I6

PAC

• V - I

• ^1 in soprano on I chord

IAC

• V - I

• ^3 or ^5 in soprano on I chord

HC

I - V

Evaded Cadence

PAC that moves to I6 instead of I

Plagal Cadence

IV - I

Deceptive Cadence

V(7) - vi or VI

Phrygian Half Cadence

iv6-V (in minor)

Suspension

Approached —> same note held

Left by —> Down by step

Retardation

Approached —> same note held

Left by —> up by step

Anticipation

Approached —> same note

Left by —> by step/leap

Neighbor Tone

Approached —> by step

Left by —> by step in opposite direction

Approached —> by step

Left by —> by leap (or swap these)

Incomplete Neighbor

Passing Tone

Approached —> by step

Left by —> by step in same direction

Appoggiatura

Approached —> by leap

Left by —> by step in opposite direction

Escape Tone

Approached —> by leap

Left by —> by leap in opposite direction

Pedal Tone

Approached —> same note held

Left by —> same note held

Accented

Embellishing tone on beat

Unaccented

Embellishing tone off-beat

Root position (triad)

5/3 (no figures needed)

First Inversion (traid)

6

Second Inversion (triad)

6/4

Root position (seventh)

7

First inversion (seventh)

6/5

Second inversion (seventh)

4/3

Third inversion (seventh)

4/2

Doubling/Omitting: I

• Root

• Tripling root

  • Usually at the end

  • Usually from V7 - I

  • Must have third of chord if tripled root

Doubling/Omitting: V

Double the root (not third)

Doubling/Omitting: I6

Can double anything

Doubling/Omitting: V6

Can’t double third (because of L.T), anything else

Doubling/Omitting: V7

try not to double anything (omit 5th if absolutely necessary)

Doubling/Omitting: viio7

Can’t double its root (L.T)

Voice Exchange

Two voices swap their voices (A-B-C, the other C-B-A)

4 part Voice Leading Rules

• ^7 must resolve up in outer voices; inner voice can go down to ^5

• CHORDAL SEVENTH RESOLVES DOWN (other than V4/3 to I6, doesn’t have to)

• If harmony changes (ex. V-I), don’t jump → try to keep common tones, move by step

  • If harmony stays the same (V-V7 . . . I-I6), feel free to jump

• Don’t cross voices

• Don’t do parallel 5ths or 8ves

• The simplest solution is often the best

• If the bass moves by step, have upper voices move in opposite direction

• DON’T DOUBLE LEADING TONE

  • Leading tone should go to ^5 in inner voice

Tonic Chords

I, I6, i, i6

Dominant Chords

V, V7, V6, V 6/5, V 4/3, V 4/2, viio6, viio7

Subdominant Chords

IV, ii6, ii (half dim)6/5, iio6, ii6/5, IV6, ii7, IV7

IV

• Usually comes after V —> I

• Subdominant chord

IV6

• Leads to V(7) or V6(6/5)

• Stepwise bass

• Chord that approaches phrygian half cadences

• In major, can double anything

• In minor, don’t double the 3rd (bass) because it can cause a parallel octave or an A2

• When the bass ascends from a raised ^6 through raised ^7 to ^1 in a minor key, use this chord

• Subdominant chord

ii

• Leads to V or V7

• You can double the root

• When leading from I to this chord, upper voices should have contrary motion

• dim. version of this chord should be avoided in minor keys because we don’t use diminished triads in root position

• Subdominant chord

ii7

• Chordal 7th resolves down!

• The quality of this chord in a major key is minor

  • Half diminished in minor

• 5th of this chord may be omitted if the root is doubled

  • But not in minor keys

• Subdominant chord

IV7

•  In major keys, this chord is major

  • In minor key, this chord is minor

• The most common positions for this chord are root position and first inversion (6/5)

• The 3rd of this chord can be raised in minor keys because we want to avoid A2’s

• Subdominant Chord

Cadential 6/4

• Dominant Harmony (no I6/4 for now)

• Followed by root position V (or V7) 

• Bass stays the same

  • Rhythmic options for bass:

    • Sustain

    • Repeat

    • Jumping down an octave

• Can follow tonic or subdominant harmonies

• Can’t follow dominant harmonies (because it is dominant)

• Double the bass (^5)/ the root of the chord

• Resolving:

  • 4 - 3 (down by step)

  • 6 usually down to 5, but it can go somewhere else

• Can occur on strong beats (1 and 3)

• d5 can always go to P5

Pedal 6/4

• Functions as embellishing rather than cadential

• Embellishing tone we ignore

• Upper voices —> neighbor tone

• Bass —> drone

  • V6/4 also needs neighbor tone

• Passing 6/4

• Functions as embellishing rather than cadential

• P.T in melody instead of bass

• Usually double bass

• ^5 commonly occurs

Arpeggiated 6/4

• Functions as embellishing rather than cadential

• Linear 

• Bass arpeggiates, chord sustains in upper voice

Cadenza Doppia

• Double Cadence

• 2 embellishing (I6/4 and 4/3 sus)

• Delay getting to I

• Don’t add another tenor

• Double bass in 6/4

Types of sequences

Down 3 up 4, 5-6, romanesca, descending 2nds, descending 5ths, ascending 5ths, and parallel 6/3 chords

viio7

• Dominant function that wants to resolve to a tonic

• Needs to have the 7th lowered to make it fully diminished in major keys

  • Don’t have to change anything in minor key except the root (raise it up)

• Chordal 7th needs to resolve down in this chord

• Leading tone needs to resolve up in this chord

  • Might need to double the third if d5 → P5

• I, I6, V7 typically follow this chord

• 4/2 inversion of this chord usually goes to V7,V5/3,V 6/4-5/3

iii

• This chord in major keys resembles . . .

  • I6 + i6 in a minor key (tonic)

• This chord uses ^7 differently than its major variant in dominant harmonies because it doesn’t have to resolve up

• Don’t use this chord or its inversions in simple four-part exercises

• This chord in a major key is dominant

  • In minor key is also dominant

vi/VI

• Submediant Harmony

• When it comes after V(7), it is called a deceptive cadence

• When this chord leads to subdominant harmonies, the voice leading should descend by 3rds (in the bass) and contrary motion

• When V(7) leads to this chord (minor), the voice leading should double the third (yes, really)

• When leading V(7) to this chord (major) in a minor key, watch for A2’s (leading tone should be raised and resolved up) and still double the third

• Only double the third for deceptive cadences though

Sequence

• Repetition of musical idea @ a higher or lower pitch

  • Model first, then copy follows

• 2 types → melodic and harmonic

  • Melodic → single line

  • Harmonic → down a 3rd, up a 4th (for example)

• Voice leading:

  • Keep things the same

  • Chordal 7th still resolves down

  • No parallel 8ves

  • Leading tone within inner voice in a minor key doesn’t really matter (outer voices still do though)

Down 3, Up 4

Sequence that goes down 3 then up 4

5 - 6

• Type of sequence

• Moving from 5/3 triad to 6 triad

Romanesca

• Sequence that goes down 4, up 2

• Can look like a scale in the bass

Descending 2nds

Type of sequence that has the roots descend by 2nds

Descending 5ths

• Type of sequence that has the roots descend by 5ths

• Keep voice leading when copying

• Normally alternates with inversions

Ascending 5ths

Type of sequence that has the roots ascend by 5ths

Parallel 6/3 chords

• Type of sequence

• Normally parallel 4ths in soprano

Tonal Sequence

Intervals of first phrase are NOT reproduced exactly

Real Sequence

Exact transposition of each note in a sequence

Tonization

• Temporary key change unlike modulation which is permanent 

• Major → raise 3 (^4)

• Minor → raise 3 and 5 (^4 and ^5)

• Treat 3rd like leading tone

Similar Motion

Same direction, different intervals

Parallel motion

Same direction, same intervals

Oblique motion

1 voice moves, other doesn’t

Contrary motion

1 moves up, 1 moves down