Species Counterpoint: Notes by Harold Powers and Paul Reale

 

Some Basic Questions:

 

1. What is species counterpoint?

 

It is a systematized approach which gives training in the manipulation of materials in which the linear aspect (melody) with the independence of lines is emphasized. Since the tonal orientation is based on the Church modes, complex considerations of tonality, like modulations and temporary tonicizations are set aside. The music is a streamlined version of the 16th Century vocal style of Palestrina, Lassus, Tallis, Byrd and the like. While each composer's style is truly unique, the approach of species counterpoint gives a generalized analysis. Considering that the original approach to this style in the 16th Century was to emulate the flowing style of Plainchant, species counterpoint is consistent in concept.

 

2. What are the species?

 

The student writes exercises using a cantus firmus (CF), or pre-existing Gregorian melody (Lutheran hymns will work also). A new melodic line is written either above or below this CF, and it is called the contrapunctus (CP). The various species treat note-against-note, 2 notes CP against one note of CF , three notes, syncopation, etc. until in species V all are combined.

 

3. What are the benefits of this study?

 

Given the overt simplicity of the approach, the power of the various elements of melody (ambitus, repeated notes, decoration, non chord tones, etc.) can be assimilated. Since these elements are present in all historical musical styles, the student can extrapolate on the concepts learned here. Since, originally the music is merely two-part, the elements of harmonic dissonance and cadence can be addressed in the same way.

Tonal Materia1

The tones used are those of the medieva1 diatonic system (A,B,C,D,E,F,,

and G, plus Bb, the "transposed" diatonic system (D,E,F,G,A, Bb

C plus Eb) and the chromatically altered lower leading-tones G#,C#, and F#

(C#,F#, and B in the "transposed" system). The two systems, untransposed

and transposed, have almost all of their material and treatments in common. Special

properties associated only with the "transposed" system are discussed in I.E. below.

Species I: Note against note

A. Melodic line.

l. Range .

a. The total range for all parts will lie between E and a".

b. The range for any single part in a whole setting will be between one

and two octaves. For a single phrase in Spocies I and IV one octave

or less is the norm; in other species, an octave and a sixth is the

extreme for a single phrase.

The spread been two parts runs between unison or less (see I.C.4.b-

and two octaves and a third.

2. The following intervals relay be used melodically:

whole and half steps

major and minor thirds

perfect fourths and perfect fifths

minor Sixths (ascending only)

octaves (ascending only) .

Note: Two tones, an augmented fourth ("tritone") or diminished fifth

("false fifth") apart, or a major or minor seventh apart may not

be used in immediate succession.

3. Melodic gravity.

Two tones separated by half-step or whole-step are melodic "steps"; all

other melodic intervals are "skips".

a. No more than two skips in the same direction in succession.

b. No more than three skips in succession in any direction.

c. Tho sum of successive motions in the same direction must not outline

or suggest an augmented fourth, a diminished fifth, or a major seventh.

d. The larger the interval between two successive tones, the more necessary

it becomes eventually to turn back in the opposite direction,

filling in the interval of the skip with Stepwise motion or smaller

skips (which in turn may be handled the same way). In the case of

sixths and octaves, it is obligatory to return by stepwise motion in

the opposite direction.

e. In any succession of four or more tones in one direction which includes

a skip, the skip should not be in the middle of the line.

f. In any CP phrase there will be more steps than skips.

 

 

4. Repetitions

a. No tone may occur more than twice in succession (same note repeated) in any

one phrase of the contrapunctus (CP). No more than three such pairs of tone repetitions in the setting of the whole cantus firmus (CF). Most importantly,, repeated tones may not be used where the CF has repeated tones. This repetition would stop the flow of the melody and force attention to the vertical, rather than horizontal aspects of the setting.

 

b. Avoid excessive recurrences of any one tone in a single phrase, especially of the highest or lowest tone. Recurrences emphasize one particular tone, and the highest and lowest tones are already emphasized by being at the extremes of the melodic curve.

 

c. Do not repeat in immediate succession any sequences: these are successions of the same or like intervals. As a rule (above three notes), sequences of even numbered tones are more prominent, especially in Species III, where for example a sequence of four tones will be highlighted by the simultaneous change of the whole-note pitch of the CF. The most obtrusive examples follow:

g-e f-d or c-g f-c as two-tone offenses.

a-g-e g-f-d or d-g-a e-a-b as three-tone offenses

a-g-f-a g-f-e-g or c-d-f-e f-g-b-a as four-tone offenses (notice that the replacement of the minor third with a major third does not eliminate the sense of sequence).

 

d. In moving from an internal cadence (not the last cadence) to the next phrase, the previous cadential sonority may be repeated. However, the previous cadential interval cannot be repeated at the different pitch level (see forbidden parallels under harmonic sonorities).

5. Half-steps: linear motion involving a half-step often has special properties in which a tone is

particularly brought out by being approached by half-step. In tonality, the half step increases the

tendency of the first pitch to go to the second.

 

a. There are two exceptions to the earlier stated rule that the sum of successive motions in one direction must not outline certain dissonant internals: a descending line outlining a diminished fifth is possible if, following the lowest tone, the tone a half-step higher occurs. The result is that the tendency is to hear the ambitus of the line to that tone with the previous one as an auxiliary. Similarly, a line outlining a minor seventh is possible if it turns inward by half-step.

The perception is that the section of melody has the ambitus of a sixth.

 

b. The tone, Bb, in the "untransposed" system (no Bb in the signature) may be used occasionally to evade the tritone F-B and the Bb is always followed by A.

 

c. The tone Eb would operate in exactly the same way in the "transposed" system (i.e. Bb in the signature).

 

d. At the penultimate (next-to-cadence) tone of a phrase, certain altered tones may be required in the CP (use F#, C#, G#). These are always followed by G, D, A. G# may be immediately preceded by F#.

 

e. No altered tone may be preceded or followed by the unaltered variant of the

same scale-degree. The reason is that in the diatonic modes, each pitch exists in one form of itself (Gb, G, G# are all forms of G). The order of the intervals in the scale degrees of the mode

determines that mode's identity.

B. Harmonic (simultaneously sounding) sonorities.

1. For the simultaneously sounding interval betweenn CF and CP, only con-

sonances may be used. The consonances are as follows:

Perfect: unison, perfcct fifth, octave

Imperfect:major and minor sixth

major and minor third

(extensions to other octaves - tenths, twefth, double

octave, etc. - are considered equivalent).

All other intervals are defined as dissonance. (one exception for

special use of diminished fifth).

 

NOTE: Intervals are called perfect because they exist in only one form, and any change in the interval eliminates its unique sound quality. A perfect fifth has a certain open sound which is

eliminated if it is increased or decreased a half-step.

2. The normal spread between two parts runs between a unison or less (voices cross,

subject to certain restrictions and two octaves.

N.B. Remember that the replacement of a tone by its chromatic alteration (Bb for B, or C# for C) changes the harmonic interval that tone forms with other tones in the CF.

C. Combined motion.

1. Four types of combined motion may be distinguishod:

a. Contrary motion, in which the voices move in opposite directions.

b. Parallel motion, in which the voices move in the same direction in

intervals of the same order (e.g., al1 thirds and sixths, without distinction

as to major or minor).

c. Similar motion, in which the voices move in the same direction in

intervals of different orders.

d. Oblique motion, in which one voice remains at the same pitch while

the other voice moves.

2. Motion towards and away from perfect consonances.

a. Perfect consonances may be approached by contrary or oblique motion

only.

b. Perfect consonances may be left by similar motion, as well as by contrary

or oblique motion.

c. Pcrfect consonances must never be either approached or left by paralle1

.

motion.

NOTE: Pcrfect consonances, approached by similar motion are called

"direct" e.g., "direct octaves", "direct fifths", etc.

They are, or course, prohibited.

d. When perfect consonances (fifth and octave) are used in mid phrase,

at Ieast one element must be approached in stepwise (or oblique)

motion, at least one element left in stepwise (or oblique) motion.

 

 

Perfect consonances should be used sparingly in mid-phrasc, to prepare

or mediate between imperfect consonances.

 

3. Motion involving imperfect consonances.

a. Imperfect consonances may he approachcd and left by any kind of motion.

b. Parallel thirds or sixths in stepwise motion are good; however,

four in parallel stepwise succession is the maximum permissible.

c. Parallel sixths moving by skip are prohibited. Parallel thirds may

move by skip of a third or (perfect) fourth, with certain restrictions:

If they move by third, one third must be major, the other minor (in

either order), if they Move by perfect fourth, both thirds must be

major (e.g. F*A to C*E, C*E to G*B or Bb*d to F*A or F*A to C-*E [x*y means a hamonic rather than a melodic interval]). Once again, this restriction causes blurring of the aural identity of the mode.

d. Parallel stepwise major thirds or minor sixths are permitted, but

only under certain limiting restrictions. They may be used in this

way only if one element of the first one is approached by half-step

and the other element of the second is left by half-step. (The most

common application of this genera1 rule is the occurrence of successive

parallel major thirds or minor sixths in a series of four parallel

imperfect consonances. )

4. Additional notes on combined motion.

a. Contrary motion is preferred, wherever consistent with melodic requirements.

b. Voices may cross; but the last sonorities in each phrase should find

the voice in the respective positions relative to one another in

which they begin. It is better if they do not cross.

c. Two voices should not skip at the same time in the same direction. To break this rule would compromise the linear independence of the two voices.

D. Cadences (phrase endings) and beginnings (marked by frematas in the given CF's

Settings must end with an octave or a unison and begin with an octave, unison,

of fifth. Unisons may be used only at beginnings and ends of phrases. Phrases

other than the first may occasionally begin with a third. Phrases other than

the last may, under certain circumstances, end with a fifth or a major third.

In moving from a phrase-final sonority into the next phrase, the cadential

sonority may repeat, and the lines may be considered as starting fresh.

Paralle1 octaves and fifths, however, must not occur in this conjunction. (For

cadences in the "transposed" system, See I.E. below).

1. Cadences to octave or unison.

a. Any phrase may end with an octave or a unison. In such cases the

motion to the final interval must be by stepwise contrary motion, in

which one voice moves by whole step and the other by half-step. In

other words, each phrase-final octave must be preceded by a major

sixth or a minor tenth, and each phrase-final unison must be pre-

ceded by a minor third.

b. In order to produce the required half-step motion in one part,

chromatic alteration of the penultimate tone of the CP is often

accessory (C.F. may not be altered). Any pcnultimate tone so altered

is called the leading tone with respect to the tone which must follow it;

and unaltered tones functioning in the same way are also called

leading-tones. A leading-tone is always present in the penultimate

sonority at a cadence.

c. The leading-tones belonging to the various tones in the "untransposed

system are listed below:

Leading-tone Resolution (Whole-step in other voice)

C [upper) B A - B

B C D - C

C# D E - D

F (upper) E D - E

E F G - F

F# G A - G

G# A B - A

Bb (upper) A G - A

In the "transposed" system G#-A drops out, and the following is

possible :

Leading-tone Resolution (Whole-step in other voice)

Eb D C - D

d. F#, C#, and G# are used only at cadences, as above. For occasional

mid-phrase uses of Bb ant Eb see above I.A.5.b. and below I.E.4.

Note: The interval F-G# (also Bb-C#) is called an "augmented second",

and is not used melodically in this style. In later tonal music, it has

strong harmonic implications. If necessary, F may be altered to

F# before penultimate G#. Similarly, Bb in the "transposed"

system may be altered to B-natural before a penultimate C#.

2. Cadences to a perfect fifth.

In the "untransposed" system, simultaneous fifths E*B or A *E may

end any phrase other than the final one. They must also be made by step-wise

contrary motion from the penultimate sonority, which must be a major

third, with the upper leading tone in the lower voice. In short, they

must be preceded by (simultaneous) F*A or Bb*D, respectively. The reason for this cadence is that the root of a perfect fifth is the lower note, and the half-step in the cadence must support that pitch. If Bb*D cadences to A*E, the Bb-A half-step supports that note as the root of the interval.

3. Cadences to a major third.

For variety from cadence to cadence, it is sometimes useful to be able

to come to rest on a major third (or tenth, (C*E, F*A, G*B). (This cadence

may not be done in the last phrase). The tonal cadential properties

which are retained in major third cadences are: Stepwise motion in both

voices, half-step motion in at least one voice. The "exceptional"

properties are as follows:

a. Where half-step motion in one voice versus whole-step motion in the

other voice is retained, contrary motion is sacrificed. In other

words, the final major third is approached from its neighboring minor

third, in parallel motion e.g.: B*D to C*E, or D*F to C*E.

In the analogous aporoachcs to the other major thirds, the motions

Bb*A or F#*G may be required in one of the voices. In these

cadences, it is the penultimate minor third (or tenth) which must be

approached by contrary (or oblique) motion.

b. Where contrary motion is retained, the penultimate interval will be

a diminished fifth (or twelfth) (B*F. E*Bb, or F#*C), With

both voices resolving inward by half-step. This penultimate diminished

fifth must also be approached in contrary or oblique motion. It

may be used in this way to approach major thirds in any position in

the phrase, but the main use will be for cadences.

c. For approaches to major thirds in the "transposed" system, see I.E.5

below.

E. The "transposed" diatonic system.

If the tone Bb Cadences on a primary function in a particular CF (and accompanying

CP) such that B-natural functions only as a leading tone to C, this occurrence

has the effect of producing amongst the tones D,E,F,G,A, Bb, and C

the same complex of relationships that exists among the tones A,B,C,D,E,F,G,

in the "medieval" diatonic system. For convenience, the tone Bb

is written as a signature, right after the clef sign, and one may speak of

a transposition of the whole diatonic system down a perfect fifth (or up a fourth).

Most of the tones of the "transposed" and the "untransposed" systems coincide

in designation and function, but there are five important differences.

1. The tone Bb becomes a freely usable tone in the system.

2. The tone B may be used only as a lower leading-tone with respect

to the tone C.

3. The lower leading-tone G# disappears from the system.

4. The tone Eb enters the system, as a possible upper leading-tone with

respect to the tone D. (analogous to the relationship between Bb

and A in the "untransposed" system, see I.A.5.b above). Note that Eb

forms a tritone or diminished fifth with A, and must be treated accord-

ingly: likewise, it can lead to an augmented second with respect to F#,

which must be avoided in melodic lines.

5. The major third Bb*D becomes available as the final sonority at a

cadence and the major third G*B is no longer available. Likewise

the perfect fifth D*A becomes available as the final sonority at a

cadence, while the perfect fifth E*B is no longer available.

F. Contrapunta1 inversion: the complement of any interval with respect to

another interval is called its inversion. The usual intervals with respect

to which complementary intervals are considered are the octave, the twelfth,

and the tenth. In other words, in invertible counterpoint at the octave, the lower note is moved up an octave with respect to the upper note, at the tenth, a tenth, etc. (at octave C*E becomes E*C).

 

NOTE: the term, "inversion" is also used with respect to the spacial configuration of a melody. For example: a melody which goes C-F-G could be melodically inverted to C-G-F. These two concepts must not be confused.

1. Inversion at the octave.

This is the most common kind of inversion. Two complementary intervals

adding up to an octave, such as a major third and minor sixth, or perfect

fifth and perfect fourth, will of course have the same pair of letter-names,

eg., C and E, or D and A. A table of complementary diatonic

intervals at the octave follows:

unison, octave octave, unison

m 2 M 7

M 2 m 7

m 3 M 6

M 3 m 6

pf 4 pf 5

aug 4 dim 5

pf5 pf4

 

 

 

 

2. Inversion at the twelfth.

 

 

unison, octave pf5 12th

m2 tritone

M2 pf4

m3 M3

M3 m3

pf4 M2

aug4 (tritone) m2

pf5 unison

 

3. Inversion at the tenth

unison, octave M3, M10

m2 m3

M2 M2

m3 m2

M3 unison

pf4 M7

tritone m7

pf5 M6

 

In actual practice, invertible counterpoint at the octave is used most frequently; however, in the music itself, both voices may be transposed so that although the pitches are different, the complementary intervals would be the same.

 

 

Some terms to remember:

 

1. "Transposed" system: Bb in the signature, as opposed to "untransposed" system with no signature.

2. Mode: a system of ordered half and whole steps. Each mode has a unique ordering.

3. Leading tone: the tone that forms a half-step when going to the cadence at the end of a phrase.

4. CP: contrapunctus, the line written by the student.

5. CF: the cantus firmus or preexisting melody.

6. Invertible counterpoint: a method of reordering the spacial position of voices relative to one another for the purpose of development and variety.

7. "Direct" fifths or octaves: intervals approach by similar motion and forbidden in the style.

8. Perfect intervals: intervals like the octave or fifth which exist in only one form with similar sound.

9. Imperfect intervals: intervals like the third or second which retain the same quality with semitone alteration.