These rules apply for major and minor first inversion triads.

(1) Double the root or the fifth, preferably, of a first inversion triad. Only double the third if it provides the best possible voice leading.

(2) Don’t double the bass of a V6 chord, ever. The bass of V6 is the LT. Leading tones in the bass are always resolved.

(3) A change of position from V to V6 requires that the LT in the upper voice for the root position V change to a new chord tone. This change avoids doubling the LT. The upper voice change is usually from scale degree 7 to 2, so that the original LT can still resolve to 1. You want to resolve the original LT, as well as the new LT in the bass.

(4) When moving from root position to first inversion, or vice versa, the best voice leading is a voice exchange. (The bass and the soprano swap chord tones.)

(5) When a voice exchange is not possible, one voice must remain static.

(6) To avoid parallel octaves between root position and first inversion chords of different harmonies, approach and leave the doubled chord tone by oblique or contrary motion.

(7) Chordal figuration (chordal skips or changes of position) can be used to avoid parallel fifths and octaves.

Scale Degree Tendencies in the Dominant Harmony

It is important to think about the scale degrees present in any harmony. For the dominant triad you have scale degrees 5, 7, and 2. The leading tone (7) strongly wants to resolve to tonic (1). The supertonic (2) also wants to resolve to either tonic (1) or the mediant (3).

I – V – I, and Principles of Prolongation

Harmonies can group together to extend, or prolong, the function of a chord class. I – V – I happens a lot at the beginnings of phrases to prolong the opening tonic. In this way, the dominant harmony serves in an auxiliary way to the tonic harmony, embellishing it. We can think of this embellishment in terms that draw on our past species counterpoint experience as we refer to the outer voice movement – in this case, the soprano movement. In tonic prolongations we can refer to the soprano movement as consisting of specific non-chord tone (NCT) movements. (In minor, scale degree 7 is always raised to form the leading tone.)

• Lower Neighbor Note Progression (LN): Soprano moves 1 – 7 – 1.
• Passing Tone Progression (PT): 3 – 2 – 1.
• Upper Neighbor Note Progression (UN): 1 – 2 – 1.
• Incomplete Neighbor Progression (IN): 3 – 7 – 1.

Voice Leading Issues

The lower neighbor and incomplete neighbor progressions move according to the principles we have been studying. The roots area fifth apart, so there will be one common tone between chords. Keep the common tone in the same voice throughout the three-chord progression, and move the other voices as smoothly as possible to the nearest chord tones. All chords will have doubled roots, and will be complete triads.

Both the passing tone and upper neighbor progressions have slight issues to deal with. To move from V to I with complete triads, scale degree 2 in the dominant needs to move to scale degree 3 in the tonic resolution. Since both progressions have soprano lines that move 2 to 1, you can not use our standard voice leading techniques. In both of these cases, resolving the leading tone leads to a tripled root. This is ok. If the common tone remains in the same voice from V – I, then you will not have a third in the tonic triad. This is not ok. Drop the upper-voice 5 in the dominant down to 3 in the tonic.

All of these examples are in the book on p. 161.

Frustrating the Leading Tone

It is possible in some cases to not resolve the leading tone to tonic, resulting in a frustrated leading tone. The book, like most, is wishy on this. For now, I’d like to maintain some rigor and offer only one possibility for this. The leading tone can be frustrated if an adjacent upper voice (the voice above it) moves to the tonic resolution at pitch (not in another octave). On p. 161, see example 2.2F. Example 2.2E shows a frustrated leading tone without same pitch resolution. AVOID THIS FOR NOW.

If the leading tone is frustrated, it drops down a major third to scale degree 5 in the tonic harmony. It can not go anywhere else!

Voice leading refers to the way you move from one chord to another in four-part writing.

My outline will basically cover two lists from the textbook – on pp. 142 – 145, and p. 147.

The textbook refers to the first list as the “nine basic rules of voice leading,” but the first is really a guideline. However, it is a really important guideline, so I’m going to say it more than once:

Keep common tones in the same voice, and move other voices to the nearest chord tones.

Part writing will go so much more smoothly if you follow this basic principle than if you ignore it.

The Nine Eight Basic Rules of Voice Leading

1. General Principle: keep common tones in the same voice, and move other voices to the nearest chord tones, as long as this does not create other voice leading errors. For example, moving from a C major triad (C – E – G) to an F major triad (F – A – C) involves one common tone between the two triads — C. If the C major triad is in root position, then there will be two C’s in the first triad (one in the bass, and one in some other voice). The bass will probably move to the root of the F major triad, but the other C can remain in its voice and repeat itself in the F major triad. The most common errors that could result are objectionable perfect parallel intervals, but you could also end up with doubling issues or missing chord tones. Remember that this is a guideline, not a rule, but that it is a great way to start the process.
   
2. Leaps: stepwise motion is preferred. Avoid large leaps (greater than a P4 or P5) in upper voices, which is like our counterpoint rules. The bass can leap often by 4/5 or even 8, as it has to move more to support the changing harmonies.
3. Augmented and diminished intervals: avoid augmented intervals. Diminished intervals usually descend, and usually occur in the bass.
4. Contrapuntal motion: motion types are the same as two voice counterpoint. Avoid having all the voices move in similar motion.
5. Forbidden parallels (P5/8): forbidden in the same way as in species counterpoint. Consecutive perfect intervals by contrary motion are also not allowed. Consecutive  perfect intervals can only happen if they are unequal (one diminished) and not in outer voices.
6. Direct/Hidden 5ths/8ves: occur when voices move in similar motion, with a leap in the soprano. This is also similar to species counterpoint.
7. Leading Tone: resolve the LT up by step to tonic, especially in outer voices. Sometimes the leading tone can be frustrated if voice above LT moves to tonic. A frustrated LT drops to the dominant scale degree.
8. Voice overlap and crossing: forbidden the same ways as in species counterpoint.
   1. The unison rule is really a subset of overlapping and crossing. You can have a unison between two voices as long as it is approached and left by contrary motion. Otherwise, you’ll have voice crossings or overlaps.

Changes of Voicing or Position

A repeated chord can its voicing change between chords. If the bass remains the same you can move either two or three of the upper voices.

If a chord changes position (from root to first inversion, for example), then one of the upper voices must remain static.

Some How-To Guidelines for Basic Types of Progression

Root movement by fifth: The smoothest voice leading occurs when the common tone remains in the same voice, and the other two upper voices move by step to the closest chord tones.(I – IV, I – V, V – I, vi – ii, ii – V, etc.)

Root movement by third: Triads with roots a third apart will have two common tones between them. Keep both common tones in the same voice, with the remaining voice moving by step. (I – vi, vi – IV, etc.)

Root movement by second: Chords a second apart will not have any common tones. These types of progression are the most susceptible to illegal parallel intervals, since the nearest chord tones are all the same distance away in the same direction. The safest voice leading involves moving all the upper voices in contrary motion to the bass.

We use four-part writing (SATB), or part-writing, to aid in our study of harmony – specifically, the horizontal movement between harmonies. The four parts are Soprano (S), Alto (A), Tenor (T), and Bass (B). The range for each voice for part-writing purposes is smaller than what a trained vocalist could easily sing. Simplifying from the book, the ranges are:

• Soprano: G5 – C4
• Alto: C5 – G3
• Tenor: G4 – C3
• Bass: C4 – E2.

Voicing

Chord voicing describes the way in which chord tones are distributed among the four voices, including the spacing between voices, and the doubling of chord tones if necessary. In practice, doublings and spacing will often be controlled by the motion between chords. For triads, at least one note will need to be doubled. The root and third of a triad must always be present.

Doublings

This information is slightly different from the sheet. Below are the guidelines that I use for chord-tone doublings.

For root position major and minor triads:

• Usually double the root. It is the most prominent chord tone, and most consonant with the bass.
• The second choice is to double the chordal fifth. The P5 is the next most stable interval harmonically.
• Double the chordal third as a last choice. While OK, it does not provide the most stable sounding chord.

Major and minor triads in first inversion:

• Often double the chord tone in the soprano voice, down an octave in the tenor voice.
• Otherwise, double the root or chordal fifth.
• Never double the third of a V chord. This doubles the leading tone, which has such a strong tendency to resolve to tonic that it appear that you have parallel octaves even if you don’t move both leading tones to tonic.

Diminished triads:

• Always appear in first inversion to avoid having a diminished fifth above the bass.
• Always double the chordal third, which is the only note that doesn’t form a dissonant interval with another note.

Spacing

The soprano, alto, and tenor parts (SAT) are considered the upper voices. Adjacent upper voices (soprano to alto, and alto to tenor) must remain within an octave of each other all the time. The spacing from soprano to tenor can be larger than an octave. There are no restrictions on the spacing from tenor to bass.

Open-spaced chords usually have more than an octave between the soprano and tenor. To achieve this spacing you will need to skip at least one chord tone between each upper voice. (Skipping one and only one chord tone of a triad between the upper voices will insure that you have a complete triad in the upper voices. Try it!)

Close-spaced chords have less than an octave between the soprano and tenor. To achieve close spacing you must not skip any chord tones between adjacent upper voices. (Even skipping one chord tone will result in an octave between soprano and tenor.)

Many first inversion triads are in what is called open-octave spacing, with the tenor doubling the soprano chord tone down an octave.

Second species counterpoint uses two notes in the counterpoint line for every one note in the cantus firmus. When writing second species counterpoint you need to make sure that the counterpoint line maintains shape and direction, rather than continually circling around the same few notes.

The meter for second species is cut time (2/2), with the first beat metrically stressed and the second beat metrically unstressed.

Unless otherwise contradicted by a second species rule, all first species rules still apply.

Rules

• The stressed half note must be consonant.
• The unstressed half note can be either consonant or dissonant.
• The only dissonance allowed (for the unstressed half) is the passing tone (PT). A passing tone fills in the gap of a melodic third.
• A PT may be consonant or dissonant. A consonant PT involves either the intervals 5 – 6, or 6 – 5.
• Neighbor notes (NN) for the unstressed half note must be consonant, involving the same intervals as the consonant PT.
• If the unstressed half note is consonant then it must remain within the same triad implied by the first half note.
• Avoid parallel 5ths and 8ves between successive strong beats. Consecutive parallel 5ths and 8ves are already not allowed, but this rule pertains to the intervals on the beginnings of measures.
• Unisons can only happen on weak beats.
• Do not repeat notes in the half note (counterpoint) line.
• The counterpoint can begin with a half rest.
• The last note in the counterpoint must be a whole note. The cadence in the counterpoint can both be whole notes.
• Climaxes can happen in the same measure if the climax of the counterpoint happens on the unstressed beat.

Note that a lot of the rules pertain to how dissonances must be handled, and how the second note fits with the first.

Writing Strategies

For beginners I think that it is much easier to start by writing a first species counterpoint line. From there you can add the second note for each measure while thinking about second species rules. With the given rules it is natural that your second species counterpoint line will have more leaps than a first species line. However, your second species line should still be mostly stepwise. You will also find that second species lines will have more changes of direction, since you have almost twice as many notes than the cantus firmus.

With practice it becomes easier to conceive a second species line from the start, skipping the first species framework.