CHAPTER I

PRIMARY TRIADS

PROGRESSIONS USING THE PRIMARY TRIADS

A succession of chords is called a progression. The creation of these progressions is the subject of our harmony studies. The simplest but very important progressions are called cadences.

CADENCES

The primary triads are: I (tonic), IV (subdominant), and V (dominant). A strong and satisfactory cadence can be constructed by the use of these chords. Every phrase ends with some kind of a cadence.

A cadence is an ending that defines the tonality or key. The primary triads contain all the notes of the scale, therefore, they do not leave us any doubt about the tonality. If you want to create a strong and non-ambivalent ending you should include all the three types of functions (Tonic, Dominant, Subdominant) since two only do not determine the key completely. For example, the C-E-G and G-B-D chords can be found not only in C major but G major as well; but if you add F-A-C the only key possible is C major - therefore the tonality is absolutely clear. See the following example:

You can add either F or F# to complete this scale but the resulting key will be C major or G major, respectively!

C major is the only possible key since these three triads contain all notes of the C major scale!

For ease of understanding I will give all examples in the key of C major and a minor. It will be easier to compare the examples and to remember the most important points. However, in your exercises you should use all keys. Keeping everything in C major and a minor might place some of the examples in a less comfortable vocal range. This is a sacrifice we have to make in order to keep things simple. You should understand that for this reason the range of some of the exercises would not conform to the normal voice range of a choir.

Examples taken from classical musical works will, of course, retain the original key.

When you write in choral style you should keep in mind the natural range of choir voices. The normal voice ranges are shown below (approximately):

Soprano: C4 - A5

Alto: G3 - E5

Tenor: C3 - A4

Bass: F2 - D4

[C4 = middle C on the piano]

When you write for keyboard, these ranges do not have to be observed strictly.

NOTE:

It is important to know that in many choral music publications the Tenor is written in treble clef and an octave higher than it actually sounds. Sometimes you can see a little number 8 below the treble clef, at other times you are just expected to know this. Do not get confused about this and always take it into consideration when writing or analyzing harmonies written this way. You can see this in a section below from my Kardtánc (Sword Dance) written for mixed choir and piano:

The actual pitch of the Tenor line of the above selection can be seen below:

THE MOST IMPORTANT TYPES OF CADENCES

AUTHENTIC (perfect) (e.g. I-IV-V-I or simply V-I)

PLAGAL ( e.g. I-V-IV-I or more commonly IV-I)

IMPERFECT (e.g. I-V)

DECEPTIVE (e.g. V-VI)

Let us look at examples of these in the three different starting positions. For the sake of simplicity we will use C major and a minor in these cadences.

1. AUTHENTIC (PERFECT) CADENCE

EXERCISES:

ü Play these examples in all keys (major and minor) and in all three starting positions.

ü Write these examples in the choral form (Soprano and Alto in the treble clef, Tenor and Bass in bass clef).

The following examples show similar cadences written in the chorale style. Note the direction of the stems and that the voices are further apart (i.e. in the open position).

Take a look at a few examples of the authentic cadence from various compositions.

Below is a section of a choral composition by Gastoldi for five voices (SSATB):

Another example in minor key:

Although a complete cadence includes a subdominant chord before the dominant and closing tonic often we see endings where only the V – I appears. This also creates a satisfactory ending in most cases, especially when the tonality is not in question.

During your harmonic analysis you will find that in most cases (especially in piano music) the cadences do not appear in their simplest form. First of all, the number of voices may be more or less than the customary four you have seen in chorale harmonizations. Secondly, often the chords are broken up in various patterns or rhythmically altered some way. Finally, “alien” notes decorate the chords. You will have to be able to recognize the harmonies despite these complications.

Let us look at a few examples:

(The V7 chord will be explained later)

Often we find pieces written for two voices only. After studying this book you will be able to determine the harmonies even under these circumstances. Later you will see that in four-part harmony the fifth of a chord may be missing occasionally. The root and the third is a good indication of the harmony in most cases. Take a look at the next example:

2. IMPERFECT CADENCE (sometimes called Half Cadence)

In the broad sense any cadence that does not end with a tonic chord can be considered imperfect. In everyday terminology we call imperfect only those cadences that end on V.

These cadences are the most common in the classical melody construction of two phrases; one like a Question and the other like an Answer. The first phrase ends with an imperfect cadence while the answer is perfect. We will explain this in depth later in Part IV, Musical Forms – The Period chapter.

EXERCISES:

ü Play these examples in all keys (major and minor) and in all three starting positions.

ü Write these examples in the choral form (Soprano an Alto in the treble clef, Tenor and Bass in bass clef).

Study the following examples of the imperfect cadence from various compositions:

Next you can see a complete composition by Gastoldi for a five-voice choir (part of it was previously shown). The chord symbols appear at the cadences. You can find both perfect and imperfect cadences in this example. Label them appropriately!

3. PLAGAL CADENCE

While the most common ending that we can find in the classical period of music is the Authentic or (Perfect) cadence; quite often you will find that the primary triads follow each other in a different order. If the final tonic chord (I) is preceded by a subdominant chord (IV), the resulting progression will have a very different feeling and is called a Plagal cadence. It is unusual to have all three functions present as shown below – more often the V does not precede the subdominant IV.

NOTE: The concept of authentic and plagal steps will be explained in Chapter XVII, GENERAL CONSIDERATIONS.

Minor key

NOTE: V-IV progressions are very seldom found, although you can see one in the previous madrigal by Gastoldi. I include them in this example to show how different they sound from the authentic cadences.

The marked V – IV sounds unusual because of the augmented fourth (tritone) step between the outer voices. This kind of step is well tolerated in the inner voices but less acceptable in the outer voices (Soprano and Bass).

EXERCISES:

ü Play these examples in all keys (major and minor) and in all three starting positions.

ü Write these examples in the choral style starting in open position (Soprano and Alto in the treble clef, Tenor and Bass in the bass clef)

Now let us look at a few examples of the plagal cadence from various compositions.

The next is the ending of a well-known madrigal by a 16^th century composer:

EXERCISES:

ü Find plagal cadences in your own music material!

4. DECEPTIVE CADENCE

I want to mention here briefly the deceptive cadence as well (some books call it interrupted cadence). We will work more thoroughly with this in the next chapter when we examine the other triads (connecting the V with a VI requires doubling the third of VI instead of the root).

The deceptive cadence got its name because it is substituting the real tonic chord with another – VI – that has a similar function but still does not constitute a satisfactory ending in the home key. It “deceives” the listener. The deceptive cadence has a nice, surprising effect (if not used too often) and requires further continuation of the progression – thus it can be used as a means to extend the composition by another phrase.

Third doubled

Look at the next few examples of deceptive cadences. The first one taken from Bach’s Invention in d minor is the simplest form it can take. Although there are only two voices the harmonies V and VI are still clearly recognizable.

The next excerpt from Mozart’s Marriage of Figaro is another example how the deceptive cadence could be used to extend the composition:

Pamina’s g minor aria from The Magic Flute by Mozart is a simple V7-VI progression, which is the most typical. Although we did not discuss the V7 chord as yet (it contains one extra note – a seventh from the bass) the effect is the same.

NOTE: Other chords - not just the VI - can also be used in a deceptive cadence. The following example is taken from the same aria, just a few bars later:

The final secondary dominant chord that follows the V creates a “surprise ending” just like the VI in the previous example. Although the chord is entirely different the feeling it creates is very similar. (Secondary dominant chords will be explained later.)

The next example shows a similar situation except a diminished seventh on the raised third degree is used (these chords will be explained later).

Deceptive cadence in a broad sense means that the dominant chord does not resolve cadentially (perfect fourth up/perfect fifth down) to the tonic. In the narrow sense, deceptive cadence means a V – VI progression.

CLASSIFICATION OF CADENCES

The cadences create endings that are not equally satisfying. I already mentioned that the imperfect and deceptive cadences are less satisfactory to finish a piece. There must be some criteria to compare them in order to arrange them in a hierarchical order. We can divide these criteria into three categories:

Harmonic (observe the closing chord)

Melodic (observe the last melody note)

Rhythmic (observe if it ends on a strong, medium strong or weak beat)

The most complete/satisfactory cadence

q Ends on the I (Tonic) chord (of the original or home key)

q Ends the melody on the tonic note

q Ends on a strong beat

CONCLUSION

In this chapter we have examined the primary triads and learned about:

q Arranging chords in four part harmony

q Styles of harmony writing

q Connection of chords in a progression

q Types of cadences

It is important to know that the rules we have learned so far are valid in a situation when no melody line is given. This kind of playing is used e.g. by a harpsichordist playing the Continuo line (figured bass) in a baroque ensemble. You will hear more about this in the Figured Bass Chapter. When we have to harmonize a given melody line there will be special considerations. I will explain this in the HARMONIZING MELODIES chapter.

In the next chapter we will examine the remaining – secondary – triads of both major and minor keys.

EXERCISES:

ü Find, analyze and compare cadences according to the above classification in your own piano (or other) repertoire!

ü Arrange the following cadences in a hierarchical order (from strongest to weakest)

Order of cadences: …… …….. …….. …… ……..

Write the chord symbols for the next excerpt:

C:

Write complete authentic cadences in the space provided below. Use the keys indicated. You can choose your starting position and style. Make sure that you follow the basic voice leading principles and fill the bars properly from the rhythmic point of view. Mark the chords with the proper symbols.

Use half notes (or multiples of it) since it saves quite a bit of time. Having to fill in the notes (quarters) is an extra burden that we can avoid by using mostly half notes in our exercises. You also should note that I use capital letters to indicate major and lower case letters to show minor keys.

Write imperfect cadences in the space provided. Do not forget to write the proper key signatures.