Bonus+Units+Continued


 * **Third Species Counterpoint** ||
 * In Third Species counterpoint one part moves in rhythmic values that in a duple meter are one fourth the value of the [|cantus firmus] notes (in a triple meter third species runs six accompaniment notes to each one of the cantus firmus). If there are more than two voices, one voice has the shorter note values while the others move together as in [|First Species] : ||


 * **How to Write in Third Species** ||
 * Third Species offers more chances for dissonance: the faster voice has four notes to one of the cantus firmus in duple time (6 in ternary), and every other note can be dissonant so long as it is approached and left by step. Third Species also introduces the possibility of an exception to the rule about leaving dissonance by step: the [|//Cambiata//] or "changing tone" is an accepted figure in which a dissonance is left by a downward leap of a third but quickly returns upward to what would have been the note of resolution. With regard to rhythm, Fux's Third Species examples all begin together with the cantus firmus, but Counterpointer will allow you to begin with a quarter note rest so long as that first note is acceptable in other ways. You can substitute a rest for one or two of the first notes in other measures, too, but don't do it more than 2 or 3 times at the most.

__Melodic movement__:

//(Modified from [|first species] )// No voice should make a leap larger than a fifth, except for the octave. Motion is too quick in Third Species to allow the minor sixth leap.

(As in first species) Avoid making successive same-direction leaps in the same voice unless they outline a triad. If they can't be avoided they should at least total less than an octave.

(As in first species) Leaps greater than a fifth should be compensated by stepwise movement in the opposite direction.

(As in first species) No voice should move by a chromatic interval (any augmented or diminished interval).

(As in first species) Avoid repeating a pitch in the lowest voice. In upper parts you can repeat a pitch as many as three times successively if necessary.

(As in first species) Keep each voice confined to a singable range for the part, preferably not exceeding a 10th from its highest to its lowest pitch.

(As in [|second species] ) Avoid writing the same melodic interval twice on the same pitches.

//(New)// You should take care not to outline a tritone in melody. A tritone is outlined if the melodic line changes direction at the notes that form it:



__Rhythm__:

//(New)// One voice has four notes to each note of the [|cantus firmus], or in ternary meter it has six. If there are additional voices, they move with the cantus firmus as in first species.

(As in [|second species] ) In both binary and ternary meter you may occasionally substitute a rest for the first note of each group (that is, the one that coincides with the cantus firmus).

(As in second species) The faster voice should begin after the cantus firmus, following a rest. The parts will still end together and can use the same note value for the final sonority. In three or more parts only one voice will be moving faster than the others; the others can still enter together.

__Independence of voices__:

(As in [|first species] ) Avoid writing parallel fifths or octaves (moving two voices in the same direction from one fifth or octave to another).

//(New)// Some authorities believe you should avoid parallel perfect intervals between prominent notes of each measure, particularly between the first notes of successive measures. Fux's examples do include at least two instances of such parallels, but since the opinion of other writers ( [|Lytle] says "all authorities" p. 54) is united against this practice we should observe the rule. Avoid parallel perfect intervals between prominent notes of each measure, as displayed in this example from Fux:



(As in first species) Avoid writing direct fifths or octaves (moving two voices in the same direction to a fifth or an octave). There are exceptions: these may be acceptable at a cadence, or if one voice is inner and the exposed voice moves stepwise. Direct 5ths in the outer voices will be accepted if the upper voice moves by step.

(As in first species) Do not let two voices leap to a perfect interval unless one of them is an inner part.

(As in first species) One perfect interval can follow another in the same voices only if one of the voices moves stepwise.

(As in first species) Avoid parallel fourths unless the lower tone of the fourth is not the bass and the pitch class a third below that note is present (that is, parallel 1st-inversion triads are OK). Fourths can also be allowed if one of the tones is [|nonessential].

(As in first species) Upper voices can sometimes cross if necessary, but avoid "overlapping" (in an overlap voices do not cross, but one moves to a position that is at or beyond the previous pitch of another voice).

(As in first species) Avoid writing more than three of the same interval in a row in any two parts (e.g. four consecutive thirds or four consecutive sixths).

(As in first species) In all species of counterpoint, use contrary motion frequently to emphasize the independence of voices.

//(New)// Unlike First and Second Species, unisons are now permitted within the composition (not just at the beginning and end), except on the first note of a measure.

__Dissonance handling__:

//(Modified from [|second species] )// The first note in each group must be consonant. Fux ( [|Mann], p.50) allows the third note to be dissonant if the 2nd and 4th notes are consonant, and we will follow Fux for this exercise. You should be aware, however, that [|Jeppeson] (p. 143) says with his considerable authority that a dissonant third note in a group of four is entirely inappropriate in the [|style of Palestrina]. If you would like to observe that more strict rule in personal study just turn on the "no accented dissonances" option.

Dissonances must be approached and left by step, with the exception of the figure known as the [|Cambiata] (or "changing tone"). If you were observing [|Palestrina's stricter style], as per Jeppeson's above note, the Cambiata would need to be one in which only the second note was dissonant.



__Harmony__:

(As in [|first species] ) If in two parts the music must begin with perfect consonances (octaves, fifths, or unisons) and end with octaves or unisons. In three or more parts you can begin and end with full triads, but the ending must be either a major triad or a perfect consonance. Fux advises that if the mode does not contain a major third over the tonic, then it is best to leave the third out of the final chord rather than to raise it to a major third.

(As in first species) The cantus firmus will always begin and end with the tonic. If the cantus firmus is in an upper voice be sure not to harmonize it with a fifth below at the beginning. That would give the impression of a different mode.

(As in first species) Avoid doubling a seventh.

(As in first species) Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered form in a different voice (i.e. cross relation).

(As in first species) In two-part writing, avoid adjacent use in different voices of two pitches that form the tritone (tritone cross relation).

(As in first species) In general keep to the pitch classes of the mode expressed by the cantus firmus. Unless you transpose a cantus firmus this will in practice mean the "white key" notes in Counterpointer's species exercises. Nonmodal tones may be introduced, however, if they accord with [|conventional principles for altered tones]. ||


 * **Fourth Species Counterpoint** ||
 * Fourth Species deals with syncopation. In duple meter one voice has two notes to each one of the other parts, and the second of each pair is tied forward. The second of each pair is the offbeat note, so each measure begins with a note held from before. The accented note that begins each measure can be either dissonant or consonant, but if dissonant it must resolve by step to a consonance. The second note of each measure must always be consonant. At the final cadence, however, or on rare occasions within the composition, you can revert to [|Second Species] (we'll allow one such pre-cadence reversion for every 8 notes of the [|cantus firmus] ):



In a triple meter, the active voice will have three notes to each one of the other parts, and the third note of each group will be tied forward. In triple meter the second note of each group can be a dissonant passing or neighbor tone, though again the third note of each group must be consonant. ||


 * **How to Write in Fourth Species** ||
 * Fourth Species is all about practice in writing suspensions, one of the most effective contrapuntal devices you'll encounter. It seems we never tire of hearing well-crafted suspensions presented at important moments; they have an emotional impact. Doing these Second Species exercises will not only add to your general skill in note-handling but will also help you to quickly recognize an opportunity for a good suspension when one comes along. In these exercises it's particularly desireable to begin the fast voice with a rest. You will also be allowed occasionally to revert to Second Species by not tying a note over the barline.

__Melodic movement__:

(As in [|first species] ) No voice should make a leap larger than a fifth, except for the octave and minor sixth.

(As in first species) Avoid making successive same-direction leaps in the same voice unless they outline a triad. If they can't be avoided they should at least total less than an octave.

(As in first species) Leaps greater than a fifth should be compensated by stepwise movement in the opposite direction.

(As in first species) No voice should move by a chromatic interval (any augmented or diminished interval).

(As in first species) Avoid repeating a pitch in the lowest voice. In upper parts you can repeat a pitch as many as three times successively if necessary.

(As in first species) Keep each voice confined to a singable range for the part, preferably not exceeding a 10th from its highest to its lowest pitch.

(As in [|second species] ) Avoid writing the same melodic interval twice on the same pitches.

__Rhythm__:

//(New)// As in Second Species, one voice has two notes to each note of the [|cantus firmus], or in triple time it has three. The difference is that the last of each group is tied to the first of the next. If there are additional voices, they move with the cantus firmus as in first species.

//(New)// You may occasionally revert to Second Species if the situation demands it, simply by not tying the last note of the group over to the downbeat. But if you do, the downbeat note must be consonant as it is in Second Species.

(As in [|second species] ) The faster voice should begin after the cantus firmus, following a rest. The parts will still end together and can use the same note value for the final sonority. In three or more parts only one voice will be moving faster than the others; the others can still enter together.

__Independence of voices__:

(As in [|first species] ) Avoid writing parallel fifths or octaves (moving two voices in the same direction from one fifth or octave to another).

(As in [|third species] ) Avoid parallel fifths or octaves between the downbeat (accented) notes of two successive measures, unless the faster voice leaps by more than a third from the first perfect interval, or if the intervening note is consonant.

(As in first species) Avoid writing direct fifths or octaves (moving two voices in the same direction to a fifth or an octave). There are exceptions: these may be acceptable at a cadence, or if one voice is inner and the exposed voice moves stepwise. Direct 5ths in the outer voices will be accepted if the upper voice moves by step.

(As in first species) Do not let two voices leap to a perfect interval unless one of them is an inner part.

(As in first species) Avoid parallel fourths unless the lower tone of the fourth is not the bass and the pitch class a third below that note is present (that is, parallel 1st-inversion triads are OK). Fourths can also be allowed if one of the tones is [|nonessential].

(As in first species) One perfect interval can follow another in the same voices only if one of the voices moves stepwise.

(As in first species) Upper voices can sometimes cross if necessary, but avoid "overlapping" (in an overlap voices do not cross, but one moves to a position that is at or beyond the previous pitch of another voice). Overlap is allowed between upper voices in three or more parts.

(As in first species) Avoid writing more than three of the same interval in a row in any two parts (e.g. four consecutive thirds or four consecutive sixths).

(As in first species) In all species of counterpoint, use contrary motion frequently to emphasize the independence of voices.

//(Modified from third species)// The unison is acceptable on the second of a pair of accompaniment notes if it is preparing a properly resolved dissonance:



__Dissonance Handling__:

//(New)// The note tied forward must be consonant (the suspension is prepared by a consonance). Fux (see [|Mann], p.98) allows for an exception to this, saying that if the untied note is repeating a pitch then the preparation can be dissonant. Maybe this derives from [|Palestrina's] use of the fourth as its own preparation (see [|Kitson], p.117) - that can only be accomplished if the longer tone is continuing the same pitch. For the present exercises we'll require a consonant preparation except for the fourth, which can serve as its own preparation if its bass is continuing.

//(New)// The downbeat note tied from before can now be either consonant or dissonant, but if dissonant it must be left by downward step. There can be no upward resolution of dissonance in Fourth Species.

//(New)// Accented dissonances (the only kind in Fourth Species) are best resolved to an inperfect consonance (a third or a sixth) but there are exceptions: the ninth can resolve to an octave, the second to a unison, and the fourth to a fifth.

//(New)// At the moment of dissonance the pitch class of the resolution should not be already present somewhere else in the sonority. In the following example the note of resolution is C, already present in the middle voice.



__Harmony__:

(As in [|first species] ) If in two parts the music must begin with perfect consonances (octaves, fifths, or unisons) and end with octaves or unisons. In three or more parts you can begin and end with full triads, but the ending must be either a major triad or a perfect consonance. Fux advises that if the mode does not contain a major third over the tonic, then it is best to leave the third out of the final chord rather than to raise it to a major third.

(As in first species) The cantus firmus will always begin and end with the tonic. If the cantus firmus is in an upper voice be sure not to harmonize it with a fifth below at the beginning. That would give the impression of a different mode.

(As in first species) Avoid doubling a seventh.

(As in first species) Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered form in a different voice (i.e. cross relation).

(As in first species) In two-part writing, avoid adjacent use in different voices of two pitches that form the tritone (tritone cross relation).

(As in first species) In general keep to the pitch classes of the mode expressed by the cantus firmus. Unless you transpose a cantus firmus this will in practice mean the "white key" notes in Counterpointer's species exercises. Nonmodal tones may be introduced, however, if they accord with [|conventional principles for altered tones]. ||


 * **Fifth Species Counterpoint** ||
 * Fifth species is also known as florid counterpoint. It is a combination of the first four species. This is not the same thing as free counterpoint, since the florid part is still confined to just one accompaniment voice. All additional parts remain in first species: ||


 * **How to write in Fifth Species** ||
 * In Fifth Species one of the voices can use any of the patterns from Second, Third, and Fourth Species, which means you can employ whole, half, and quarter notes plus half and quarter rests. Counterpointer will allow you to employ eighth notes too, but only in pairs, and these can occur in common time only on the second and fourth beats - you are not permitted to begin a measure or the second half of a measure with eighth notes. You may find that working within these limits actually frees your imagination. The "rules" ensure that your results will sound plausible, and with luck could even be beautiful. In Fifth Species you'll want to begin with a rest, but it can be either a half or a quarter rest. Try to have as much variety as possible within the limits of the first four species.

__Melodic movement__:

//(Modified from [|first species] )// No voice should make a leap larger than a fifth, except for the octave and ascending minor sixth. But large leaps are not allowed between notes less than half the value of the c.f.'s notes. Very quick notes (eighth notes in our examples: notes 1/4 the value of the beat) must be stepwise.

(As in first species) Avoid making successive same-direction leaps in the same voice unless they outline a triad. If they can't be avoided they should at least total less than an octave.

(As in first species) Leaps greater than a fifth should be compensated by stepwise movement in the opposite direction.

(As in first species) No voice should move by a chromatic interval (any augmented or diminished interval).

//(New)//You should take care not to outline a tritone in melody. A tritone is outlined if the melodic line changes direction at the notes that form it:



(As in first species) Avoid repeating a pitch in the lowest voice. In upper parts you can repeat a pitch as many as three times successively if necessary.

(As in first species) Keep each voice confined to a singable range for the part, preferably not exceeding a 10th from its highest to its lowest pitch.

(As in [|second species] ) Avoid writing the same melodic interval twice on the same pitches.

__Rhythm__:

//(New)// One voice of your accompaniment may freely mix elements of Species 1-4, and you can add pairs of eighth notes as well (see below). Dotted notes will not be used. Additional voices remain in First Species.

//(New)// Avoid beginning a passage with rapid notes, unless the first note is offbeat.

(As in [|second species] ) The faster voice should begin after the [|cantus firmus], following a rest. The parts will still end together and can use the same note value for the final sonority. In three or more parts only one voice will be moving faster than the others; the others can still enter together.

//(New)// Avoid beginning a measure with the rhythm known as Anapest (short-short-long) unless the long note is tied forward.

//(New)// When you tie a note forward in the [|Fourth Species] style, you should make the second note half the value of the first except at a final cadence. In Fourth Species both notes would have the same value, but in Fifth Species this pattern is modified.

//(New)// Assuming that the cantus firmus moves in whole notes, you should avoid using more than two eighth notes in any measure, and they should always appear in pairs and only in metrically weak positions (the 2nd or 4th beats of a 4/4 measure, for example).

__Independence of voices__:

(As in [|first species] ) Avoid writing parallel fifths or octaves (moving two voices in the same direction from one fifth or octave to another).

(As in [|third species] ) Avoid parallel fifths or octaves between the downbeat (accented) notes of two successive measures, unless the faster voice leaps by more than a third from the first perfect interval, or if an intervening note are consonant.

(As in first species) Avoid writing direct fifths or octaves (moving two voices in the same direction to a fifth or an octave). There are exceptions: these may be acceptable at a cadence, or if one voice is inner and the exposed voice moves stepwise. Direct fifths in the outer voices will be accepted if the upper voice moves by step.

(As in first species) Do not let two voices leap to a perfect interval unless one of them is an inner part.

(As in first species) One perfect interval can follow another in the same voices only if one of the voices moves stepwise.

(As in first species) Avoid parallel fourths unless the lower tone of the fourth is not the bass and the pitch class a third below that note is present (i.e. parallel first-inversion triads are OK). Fourths can also be allowed if one of the tones is [|nonessential].

(As in first species) Upper voices can sometimes cross if necessary, but avoid "overlapping" (in an overlap voices do not cross, but one moves to a position that is at or beyond the previous pitch of another voice).

(As in first species) Avoid writing more than three of the same interval in a row in any two parts (e.g. four consecutive thirds or four consecutive sixths).

(As in first species) In all species of counterpoint, use contrary motion frequently to emphasize the independence of voices.

//(Modified from [|fourth species] )// The unison is acceptable at the beginning or end of the composition, and in passing within it if not accented.

__Dissonance Handling__:

(As in [|fourth species] ) With the exception of the [|Cambiata] figure in [|Third Species] passages, dissonances are resolved stepwise.

(As in fourth species) Any dissonant downbeat note must have been approached by [|suspension] as in Fourth Species, and must be left by downward step.

(As in fourth species) When resolving a suspension dissonance it is best if the note of resolution is not already present in the sonority at the time of the dissonance.

//(New)// In Fifth Species you'll be allowed to delay by one note the resolution of a suspension, as in the following example from Fux. The intervening note must be a concord.



__Harmony__:

(As in [|first species] ) If in two parts the music must begin with perfect consonances (octaves, fifths, or unisons) and end with octaves or unisons. In three or more parts you can begin and end with full triads, but the ending must be either a major triad or a perfect consonance. Fux advises that if the mode does not contain a major third over the tonic, then it is best to leave the third out of the final chord rather than to raise it to a major third.

(As in first species) The cantus firmus will always begin and end with the tonic. If the cantus firmus is in an upper voice be sure not to harmonize it with a fifth below at the beginning. That would give the impression of a different mode.

(As in first species) Avoid doubling a seventh.

(As in first species) Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered form in a different voice (i.e. cross relation).

(As in first species) In two-part writing, avoid adjacent use in different voices of two pitches that form the tritone (tritone cross relation).

(As in first species) In general keep to the pitch classes of the mode expressed by the cantus firmus. Unless you transpose a cantus firmus this will in practice mean the "white key" notes in Counterpointer's species exercises. Nonmodal tones may be introduced, however, if they accord with [|conventional principles for altered tones]. ||

__**COMPLEX CHORDS:**__

The Neapolitan
 * Neapolitan chord** (or simply a "**Neapolitan**") is a major chord built on the lowered second (supertonic) scale degree. It most commonly occurs in first inversion so that it is notated either as <span class="music-symbol" style="font-family: 'Arial Unicode MS','Lucida Sans Unicode';">♭ II 6 or N 6 and normally referred to as a **Neapolitan sixth chord**. In C, a Neapolitan sixth chord in first inversion contains an interval of a sixth between F and D<span class="music-symbol" style="font-family: 'Arial Unicode MS','Lucida Sans Unicode';">♭.

=<span style="font-size: 1.4em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**Augmented Sixth Chords** =

==<span style="font-size: 1.3em; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**There are three types of augmented sixths: the Italian sixth, the French sixth, and the German sixth. Those chords are generally used to reach the dominant or tonic chord in second inversion when performing a cadence in major and minor keys.** ==


 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">An altered tone is always present.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The chord represents an chromatic modification of the the IV6 in the so-called "Phrygian" cadence.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The chord functions invariably as dominant preparation. In the most common instance, the ^6 is in the bass (natural ^6 in minor, lowered ^6 in major) and the raised ^4 is in the top voice.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The augmented-6th chord is enharmonically equivalent to the interval of a minor seventh, and likewise, it has an obligatory (but very different) resolution! Both voices of the characteristic interval (the ^6 and the raised ^4) move by semitone to ^5.