Compendium of Progressions Help

In the Classical era of music, one finds a fairly consistent set of harmonic progressions used. This course presents a rich set of progressions. It isn't exhaustive, but it is fairly comprehensive, and makes for an easy approach to composing in the style of a late 18th century composer. These progressions are catalogued as Basic or Sequential. Common chord inversions as well as approaches to chord substitution and insertion within the basic progressions are offered. Once one is familiar with the strategies for substitution and insertion, then one gains a healthy amount of freedom in crafting harmonic progressions that should stay fairly stylistically accurate. Details on all of this are given in the weekly videos.

Basic ProgressionsI-V-I

I-IV-I (Plagal Progression)

I-IV-V-I

I-VI-II-V-I

Basic Progressions with InversionsI-V6-I

I-V65-IOne can also used 7th chords in inversions. Unless otherwise noted, dominant 7th chords can be used were dominant triads are illustrated.

Passing Six-Four Chords: I-V64-I6, I-V43-I6, or IV6-I64-IV

The pedal six-four chord: I-IV64-I, also possible with V-I64-V

The cadential six-four chord: I64-V (This one usually goes to a root position dominant triad rather than a 7th chord.)

The IV6-V progression as well as the V42-I6 progression. Note you can't do a V42-I6 with a dominant triad. You need to 7th in order to do it.

Sequential Progressions

Circle of Fifths

Descending 5-6

Parallel Sixths

Passacaglia Progression (Original and a Chromatic Variant as examples)

Diatonic SubstitutionsDominant Substitutions

As seen in the chord chart presented at the beginning of the course, substitutions are possible between the V or and viio chords. It is also possible to substitution V7 with viio7 chords. Both of these chords can have a dominant function, that is, they function to bring the progression back to the tonic chord.

Subdominant Substitutions

The substitution of a ii chord for a IV chord is very common. In fact, the ii6 chord is so much more common that the IV chord in classical era music, that the substitution probably should be thought of in reverse: the IV chord occasionally substituting for the ii6. Using the ii6 instead of the IV lends greater authenticity to 18th century style writing.

Tonic Substitutions

As seen with the dominant and subdominant substitutions, the nature of substitution is the founded on swapping out one chord for another with which it has a mediant relationship, that is, they are a diatonic third apart. One can also do this with the I and VI chords, but only when preceded by a V chord. For instance, I-IV-V-I cannot be altered into a VI-IV-V-I. Although this is an acceptable progression, in general, the sense of substitution does not exist. However, I-IV-V-VI is also possible, and the sense of substitution is very clear. This progressions from V-VI has a distinctive character in classical music, and it is given the name deceptive progression. The name is apt: one feels that they have been cheated of a return to the tonic and are surprised to see the VI chord presented as its substitution. At least, this is what one "should" feel when hearing this progression in the context of 18th century European music making.

Chromatic Substitutions

Neapolitan 6

Augmented 6

Borrowed Chords

Insertion (Progressions within Progressions)

It is possible to place dominant-tonic progressions within a larger harmonic progression. When this is done, the inserted dominant is called a secondary dominant. For instance, in a I-IV-V-I progression, one could do something like the following: I-IV-V/V-V-I. Here there is a dominant-tonic progression on the dominant. The V chords acts as both a tonic and a dominant. The insertion is seen in the example below. In this example, the V/V is a 7th chord placed in first inversion. This smooths out the voice leading. This example should serve as an approach to adding a secondary dominant for any progression that is a 2nd apart - for instance, the V-vi progression.

Below are further examples of common secondary dominants. They have been listed by the interval (and direction) separating the 2 chords in the original progression.

Finally, it should be noted that the leading tone chord as well as the fully diminished 7th chord can be used as a substitution for the secondary dominant. These chords are called secondary leading tone chords.

Function in Tonal Harmony

The concept of a harmonic function is very important in classical music. There are really only 3 functions - pre-dominant, dominant, and tonic. The tonic (the I chord) functions as both the start and end of any progression. It is a goal to be achieved. At a minimum, it needs to return by the end of a work. But frequently, we see it returning at the end of a phrase. The dominant function (usually presented by the V chords, but also the viio chords) serves to bring the progression back to the tonic. It is generally the case that the return of a tonic chord is preceded by a chord with a dominant function. Finally, there are pre-dominant chords. These are largely presented by the subdominant collection of chords - IV chords, ii chords, and their various substitutes.

One needs to understand that not all V chords carry a dominant function. For instance, the V64 chord can serve as a passing chord between a I and I6 chord. (See Basic Progressions with Inversions above.) In such a case, that chord has no dominant function. Instead, dominant function is expressed most clearly when the dominant doesn't just bring us back to I, but when it serves to also helps to establish the key of the passage.

Using this CompendiumWith the progressions and strategies presented above, let us look at an example of using them to create something elaborate out of something very simple. We start with a I-IV-V-I progression from the list of basic progressions.

We know that we can use an inversion here, so we add it: I-IV6-V-I

We also know that there is a passing progression often seen with the IV6 chord, so we insert it: I-IV6-[I64-IV]-V-I

We also know that the V chord can be expanded to include a cadential six-four chord, so we add that: I-IV6-[I64-IV]-[I64]-V-I

We also know that we could add a progression within a progression between I and IV chords (a 5th apart) as well as the IV and V chords (a 2nd part). So, we add those in and use nice inversions to smooth out the bass line: I-[V42/IV]-IV6-[I64-IV]-[V65/V-I64]-V-I.

Now, we have something quite elaborate.

Voice Leading Principles Help

VoicingPrior to addressing voice leading, one should consider voicing strategies in 4-part writing.

In terms of note distribution and doubling, follow these guidelines:

With root position triads: double the root.With first inversion triads: double the root or 5th, in general. If one needs to double the 3rd, that is acceptable, but avoid doubling the leading tone*.With second inversion triads: double the fifth.With seventh chords: there is one voice for each note, so distribute as fits. If one must omit a note from the chord, then omit the 5th.

The main concerns of composers writing homorhythmic, homophonic music were both unity and independence. This seems contradictory at first. However, unity is a vertical dimension concern (the chords), while independence is a horizontal concern (the lines). Each of these concerns is addressed in principles of voice spacing.

To achieve sonorous (unified) chords, one wants to do the following:

1. never have more than an octave between adjacent voices in the upper three voices (SAT),2. never have more than a 12th between the bass and tenor.

To achieve independence of lines through spacing, one wants to mainly avoid voice crossing. For example, the alto shouldn't go below the tenor or above the soprano in a chord, tenor should never go below bass, etc. The other strategies to reenforce independence are found in the voice leading strategies below.

There are two approaches to voicing a chord with 4 voices: open structure and close structure. With open structure, the interval between the upper three voices (SAT) is greater than an octave. With close structure, the upper three voices fit within an octave or less. One way to think about close structure is that it places the upper three voices next to each other on adjacent chord tones. This doesn't always happen, but it is frequently the case.

Keyboard Voicing

The above principles for voice spacing of SATB more or less apply to keyboard voicing. There are some differences worth noting though. The most obvious is that, with keyboard voicing, one places 3 notes on treble staff and 1 note in the bass. Also, close structure is most frequently encountered because the 3 notes on the treble staff are to be played by a single hand, and hands don't generally stretch much more than an octave or tenth without some form of assistance (like a medieval torture device).

* Doubling of the leading tone is bad practice in general when trying to emulate this style of music. It isn't seen much. The reason for this? Some say composers avoided it so that the leading tone wouldn't be overemphasized. On a more practical level, since the leading tone tends to resolve to the tonic, two leadings tones would both resolve to the tonic at the same time, forcing parallel octaves (see below as to why that's to be avoided).

Principles of Voice Leading

The principles of voice leading can be summarize as follows:

1. Keep common tones,2. Move voices by step, if possible,3. If you can't move by step, move by smallest possible interval,4. Use contrary motion, if possible.

There are, however, more specific rules used in late 18th century music, particularly with a homorhythmic, homophonic texture like SATB chorale writing. These include:

1. Avoid parallel fifths and octaves, as well as fifths and octaves by contrary motion;2. Avoid doubling the leading tone;3. Avoid hidden (or direct) fifths and octaves;4. Avoid using the +2 interval melodically.

Below are some illustrations of these "sins".

Luckily, at least with root position chords, there is a set of algorithms that can be used to create stylistically accurate voice leading. These really only work with root position chords in SATB writing. Once inversions are introduced, there are too many possibilities and considerations. The algorithms for root position chords are given below along with musical illustrations.

For chords a fourth or fifth apart, there are two approaches: a common tone approach and a non-common tone approach.

With the common tone approach you:

1. move the bass to the root of the next chord,2. carry over the common tone from the previous chord,3. move the remaining voices by step or smallest possible interval,4. try to incorporate contrary motion.

With the non-common tone approach you:

1. move the bass to the root of the next chord,2. move all of the remaining voices to the nearest chord tone of the next chord,3. try to incorporate contrary motion.

For chords a third or sixth apart:

1. move the bass to the root of the next chord,2. carry over the two common tones from the previous chord,3. move the remaining voice by step to complete the chord.

For chords that are a second apart:

1. move the bass to the root of the next chord,2. in contrary motion to the bass, move the remaining voices to the nearest chord tone of the

next chord.

Created Wed 25 Sep 2013 6:38 PM PDT

Applying Patterns Help

Making an AccompanimentIf one is familiar and comfortable with creating 4-voice keyboard homorhythmic homophony, then creating an accompaniment pattern is fairly easy. One can simply choose a rhythmic pattern to apply to the left hand and a rhythmic pattern to apply to the right hand. The right hand is usually much more active since it holds the chord. The bass pattern is generally significantly simpler.

Nonetheless, patterns do not need to be elaborate. In fact, very elaborate patterns are often not stylistic of Classical era music. Below are some examples. Note that none uses NCTs, but it is possible to incorporate NCTs.

Alberti BassPerhaps one of the most characteristic accompaniment patterns in Classical era music is the Alberti bass. Typically, the Alberti bass takes 3 chord tones and projects them in the following pattern: lowest-highest-middle-highest. The pattern is repeated for the duration of the harmonic rhythm. But this particular pattern isn't the only kind of Alberti bass one will find. Within reason, one can be creative with the pattern. But certain things should be kept in mind:

1. the lowest note should always be first,2. the pattern should only include chord tones,3. the rhythm should be even but fast enough to allow for all 3 chord tones to sound within

the space allowed by the harmonic rhythm.

Patterns and Sequential ProgressionsSequential harmonic progressions like the circle of fifths also rely on patterns for their melodic and rhythm elaboration. Below are some examples of the 3 sequential progressions we look at in this course. Unlike the simpler elaborations above, these include NCTs and a "translation" from 4-voice SATB homophony to 3-voice polyphony. There is even a version given where the upper 3 voices have been merged into a single voice. This kind of writing would be typical in solo, unaccompanied music, particularly from the Baroque era. Bach's violin partitas and cello suites provide expert examples.

Circle of Fifths

Circle of Fifths (single line)

Descending 5-6

Parallel 6ths

Created Wed 25 Sep 2013 6:39 PM PDT

Non-Chord Tones Help

Non-chord tones can be classified by how one arrives at them and how one departs them. It is important to note that in most cases NCTs in classical music are preceded and followed by chord tones, that is, they are used in fairly strict ways to decorate melodies built off of chord tones.

Passing Tones

One steps into a passing tone and steps out of it in the same direction. Sometimes you will see a pair of passing tones next to each other. This is inevitable: otherwise, one couldn't compose melodies with scales, where it is frequently the case that two adjacent notes are both NCTs of a sounding harmony.

Neighbor Notes

Like the passing tone, one steps into and out of neighbor tones. However, one steps out in the opposite direction as one stepped in. There are both upper and lower neighbor tones and combinations of these, sometimes called cambiata or changing tones.

Escape Tone

One needn't just step into and out of NCTs. If one steps in and skips out, then the NCT is called an escape tone. Direction doesn't matter: both can go up, both can go down, they can go in opposite directions. However, there is a very characteristic use of escape tones in Baroque and Classical era music involving a step up and a skip down of a third, as seen in the example below.

Appoggiatura

Appoggiatura could be described as the opposite of the escape tone in that one leaps into it and steps out of it. Like with the escape tone, direction doesn't matter.

Anticipation

The next several NCTs involve a certain degree of either eagerness or laziness. An anticipation is an eager beaver. It moves by step or skip into a NCT, but that NCT turns out to be a chord tone when the following chord sounds. The name is a fitting description of its sound.

Suspension

The suspension is a bit lazy. It gets into the NCT by doing nothing. It just stays the same. Then, it resolves downward by step to a chord tone. Note: it must resolve by step. There are a number of different types of suspensions. They are labeled based on their interval from the

bass note. For instance, a 4-3 suspension starts a 4th above the bass and resolved downward by step to the 3rd above the bass. Note that a "3rd" could be a 10th or a 17th, that is, there could be an octave or two between the bass and the suspended note. The 3 main types of suspensions are the 4-3, 7-6, and 9-8.

Sometimes we will see suspensions that resolve upward. This is particularly characteristic at the end of works or sections in Classical era music. These upward-resolving suspensions are called retardations. For our purposes, let's use them only at the end of a work. The example below includes both a 4-3 suspension and a 7-8 retardation.

Pedal Tone

This last NCT is truly the laziest of all NCTs we will see. It does nothing. How to get into it? Stay the same. How to get out of it? Stay the same. Take a holiday, cause some dissonance, let the other notes solve the problem. It's all okay. It's like the boss' son of non-chord tones.

Cadence Types Help

Overview

Cadences define the end of phrases. An important thing to note is that the term phrase here has a specifically harmonic meaning. Often, the term phrase is used to mean a gesture, a group of notes placed together within a single slur, a melody that is joined by a single breath or bow stroke. But when talking about cadences, a phrase is defined harmonically, rather than melodically.

There are a variety of cadence types, but they can be categorized as either inconclusive or conclusive, that is, whether or not a work could end with the cadence. Conclusive cadences are used to mark closures of sections or movements. Inconclusive cadences are used to delineate phrases and allow subsequent phrases to be grouped with it. They are usually not used to delineate sections or end of movements.

Half Cadence (H.C.) and Phrygian Half Cadence

The half cadence is an inconclusive cadence that usually ends on a V chord. It is usually preceded by a tonic chord or a subdominant chord of some type.

A variant of the HC is the phrygian half cadence. This is distinguished by a bass movement from the lowered 6th scale degree to the 5th scale degree. One might see, for instance, the progression iv6-V (or the substitute of +6-V) to achieve this bass movement. The name derives from the Phrygian mode, which is unique in that there is a semitone rather than a whole tone between the 1st and 2nd scale degrees. (All other church modes - excluding the 19th century addition of Locrian - have a whole step between the 1st and 2nd scale degrees.)

Perfect Authentic Cadence (P.A.C.) and Imperfect Authentic Cadences (I.A.C.)

The perfect authentic cadence is a conclusive cadence. It is often used at the ends of groups

of phrases, sections, and movements to articulate a sense of closure. A perfect authentic cadence must have the following things:

1. A V-I (or V7-I) harmonic progression wherein both the V and I chords are in root position;

2. The tonic note in the melody when the I chord arrives.

It is frequently the case that V-I progressions occur at cadences but one or both of the chords are in inversion, or that the melody note on the I chord is the 3rd or 5th scale degree, or that a viio chord is used in substitution for the V chord. In any of these instances, the cadence is not deemed a perfect authentic cadence, but instead an imperfect authentic cadence. Whereas the PAC is a conclusive cadence, the IAC is not. For example, it would be uncommon to see a movement finished with an IAC.

Deceptive Cadence

The deceptive cadence occurs when a deceptive progression of V-vi (or V-VI in minor) is placed at a cadence. This is a very inconclusive cadence. In fact, it usually requires immediate action to get the harmonic progression back on track. The deceptive cadence is often found within a phrase rather than just at the end because its instability causes an extension that terminates in a cadence with more conclusive qualities, like an IAC or PAC to be added to the phrase.

Plagal Cadence

Plagal cadences are uncommonly seen in Classical era music. They are often placed in a phrase extension following a more conclusive cadence. They are often used as a reference to a religious context, since the plagal progression of IV-I is commonly used in hymns to sing "Amen."

Strategies for 2-voice Counterpoint Help

This course aims to introduce counterpoint. As a subject, counterpoint is extensive. So, we should be satisfied in getting our feet wet and staying in until the water feels warm. To put it in perspective, a trained composer like Bach could be given a theme and improvise an entire fugue (or several) from it. We will be happy to just write 2 melody notes against 1 bass note.

Let's use a procedure for this as well.

1. Choose a harmonic progression,2. Write out the bass line of this progression in quarter

notes,3. Craft a 1:1 counterpoint against the bass in the melody,4. Add either 1 NCT or chord tone to each of the notes in

the melody.

The first 2 points of the procedure won't be covered it. It's assumed that you can do this on your own already.

Tips for 1:1 Counterpoint

1. Use only chord tones. NCTs can be added in the 2:1 counterpoint (step 4).

2. Try starting on either the root or 3rd of the first chord, and try ending on the root of the last chord.

3. Move mostly by step, but don't move exclusively by step. Make sure your leaps are an octave or less. The larger the leap, the less you should use it. Leaps of a 3rd or 4th are quite common. Sixths and octaves are less common.

4. Try to get a nice shape to your melody. One should be able to follow a line when hearing the melody.

5. Make sure that the harmonic progression can be heard by just two voices.

6. Imagine you are doing voice leading of just soprano and bass. To this extent, you need to be conscious of parallel fifths and octaves, direct fifths and octave, double leading tones, +2 melodic intervals, etc.

7. Try to get a single highest note, or less commonly a single lowest note if the direction of the melody generally move downward.

8. Keep things in perspective. Getting a smooth line with clear direction that only uses chord tones via a mixture

of stepwise motion and skips is very difficult. In 2:1 counterpoint, the smoothness and clarity of direction can be more easily addressed.

Below is an example of a fairly good 1:1 counterpoint. It's fine, but I would criticize the "turbulence" (see below) at in the last 3 measures, and think it might be nice if a skip could be incorporated earlier than the 4th measure. These aren't big issues, and they can be addressed when moving to 2:1 counterpoint.

Tips for 2:1 Counterpoint

1. Use NCTs where possible. This will be a chance to add or further define shape in your 1:1 counterpoint.

2. Use chord tones as well, particularly when the 1:1 counterpoint hasn't provided a clear articulation of the harmony or you are looking for an opportunity for a larger leap, like a 4th, 6th, or octave. Why use a larger leap? There are both practical and expressive reasons. Sometimes a large leap is like pressing a reset button; it changes the register and gives you more options. On the other hand, since large leaps like sixths and octaves are infrequently encountered, they are experienced as expression gestures and capture attention.

3. It is okay to shift the note in the 1:1 melody over to the upbeat if that helps get the right shape. Put another way, the note you add can be on the downbeat or the upbeat. It will generally be on the upbeat, but it doesn't always make sense to do that.

4. Forget your 1:1 counterpoint when it isn't translating well. Sometimes moving from 1:1 to 2:1 counterpoint opens up opportunities that shouldn't be ignored. Don't feel bad if you ignore your 1:1 counterpoint contour for a few beats to take advantage of something that wasn't foreseeable in a 1:1 setting.

Below is a 2:1 setting of the previous 1:1 counterpoint. Take a moment to compare them. Notice that #2 is used in measure 1, beat 2 to help make the dominant function more clearly hear. Note that #2 is used in the second to last bar. The contour is completely changed there, and a much clearer shape is used. This helps address the turbulence issue that I criticized in the 1:1 setting.

Consistency vs. Variety

The secret of counterpoint is balancing consistency with variety. Very clear shapes can be very boring. While step-wise movement lends consistency and clarity to a melodic line, well, too much of a good thing can be a bad thing. Leaps should, therefore, be incorporated to add interest.

In general, if you leap a third in one direction you can continue in that direction. If you leap more than a 3rd, then you should move in the opposite direction, generally by step. In effect, you are "filling in the gap" you made.

If you aren't continually sensitive to the shape of the melodic line, you could end up with what I describe as turbulence. Your line goes up and down but never very far and never for any reason, that is, the movement of the line doesn't translate into direction, but instead just simple activity. Just like too much consistency, having too much turbulence is a bad thing for a contrapuntal melodic line.

NCTs by Interval

There are only so many ways to move between two intervals with a single additional note. Below is a list of examples of NCTs that are possible between smaller intervals. You can use it as a kind of cheat sheet for moving from 1:1 into 2:1 counterpoint. For larger intervals, you would probably fill in with a chord tone or perhaps an appoggiatura.

NCTS that aren't NCTs

Be careful when adding NCTs. They might be NCTs to the harmony that you are trying to project, but are chord tones in related chords. In the example below, one thinks that they are innocently adding an appoggiatura, but actually, the G chord (IV) simple gets changed into a e chord (ii6). These chords substitution nicely for each other, so this isn't a problem. But it is very easy for something similar to happen with the I and iii chords, and these do not substitute for each other. The harmony and its progression are damaged.