Triads and Chords
Harmony2 in Western music3 is based on triads. Triads are simple three-note chords4 built of thirds (p. 11).
The chords in Figure 3.1 (Triads in Root Position) are written in root position, which is the most basic way to write a triad. In root position, the root, which is the note that names the chord, is the lowest note. The third of the chord is written a third (Figure 1.15: Simple Intervals) higher than the root, and the fifth of the chord is written a fifth (Figure 1.15: Simple Intervals) higher than the root (which is also a third higher than the third of the chord). So the simplest way to write a triad is as a stack of thirds, in root position.
NOTE: The type of interval or chord - major, minor, diminished, etc., is not important when you are determining the position of the chord. To simplify things, all notes in the examples and exercises below are natural, but it would not change their position at all if some notes were sharp or at. It would, however, change the name of the triad - see Naming Triads (Section 3.2).
Exercise 3.1.1
(Solution on p. 79.)
Write a triad in root position using each root given. If you need some staff paper for exercises you can print this PDF le5.
Any other chord that has the same-named notes as a root position chord is considered to be essentially the same chord in a different position. In other words, all chords that have only D naturals, F sharps, and A naturals, are considered D major chords.
NOTE: But if you change the pitch6 or spelling7 of any note in the triad, you have changed the chord (see Naming Triads (Section 3.2)). For example, if the F sharps are written as G flats, or if the A's are sharp instead of natural, you have a different chord, not an inversion of the same chord. If you add notes, you have also changed the name of the chord (see Beyond Triads (Section 3.6)). You cannot call one chord the inversion of another if either one of them has a note that does not share a name (for example "F sharp" or "B natural") with a note in the other chord.
If the third of the chord is the lowest note, the chord is in first inversion. If the fifth of the chord is the lowest note, the chord is in second inversion. A chord in second inversion may also be called a six-four chord, because the intervals (Section 1.3) in it are a sixth and a fourth.
It does not matter how far the higher notes are from the lowest note, or how many of each note there are (at different octaves or on different instruments); all that matters is which note is lowest. (In fact, one of the notes may not even be written, only implied by the context of the chord in a piece of music. A practiced ear will tell you what the missing note is; we won't worry about that here.) To decide what position a chord is in, move the notes to make a stack of thirds and identify the root.
Example 3.1
Example 3.2
Exercise 3.1.2
(Solution on p. 79.)
Rewrite each chord in root position, and name the original position of the chord.
The position (Section 3.1) that a chord is in does make a difference in how it sounds, but it is a fairly small difference. Listen9 to a G major chord in three different positions.
A much bigger difference in the chord's sound comes from the intervals (Section 1.3) between the root position notes of the chord. For example, if the B in one of the chords above was changed to a B at, you would still have a G triad (Section 3.1), but the chord would now sound very different. So chords are named according to the intervals between the notes when the chord is in root position (Section 3.1). Listen10 to four different G chords.
The most commonly used triads (Section 3.1) form major (Section 2.1) chords and minor (Section 2.2) chords. All major chords and minor chords have an interval (Section 1.3) of a perfect fifth (p. 14) between the root and the fifth of the chord (Section 3.1). A perfect fifth (7 half-steps) can be divided into a major third (Major and Minor Intervals, p. 14) (4 half-steps) plus a minor third (Major and Minor Intervals, p. 14) (3 half-steps). If the interval between the root and the third of the chord is the major third (with the minor third between the third and the fifth of the chord), the triad is a major chord. If the interval between the root and the third of the chord is the minor third (and the major third is between the third and fifth of the chord), then the triad is a minor chord. Listen closely to a major triad11 and a minor triad12.
Example 3.3
Example 3.4
Exercise 3.2.1
(Solution on p. 79.)
Write the major chord for each root given.
Exercise 3.2.2
(Solution on p. 79.)
Write the minor chord for each root given.
Because they don't contain a perfect fifth, augmented and diminished chords have an unsettled feeling and are normally used sparingly. An augmented chord is built from two major thirds, which adds up to an augmented fifth. A diminished chord is built from two minor thirds, which add up to a diminished fifth. Listen closely to an augmented triad13 and a diminished triad14.
Example 3.5
Exercise 3.2.3
(Solution on p. 80.)
Write the augmented triad for each root given.
Exercise 3.2.4
(Solution on p. 80.)
Write the diminished triad for each root given.
Notice that you can't avoid double sharps or double flats by writing the note on a different space or line. If you change the spelling15 of a chord's notes, you have also changed the chord's name. For example, if, in an augmented G sharp major chord, you rewrite the D double sharp as an E natural, the triad becomes an E augmented chord.
You can put the chord in a different position (Section 3.1) or add more of the same-named notes at other octaves without changing the name of the chord. But changing the note names or adding different-named notes, will change the name of the chord. Here is a summary of the intervals in triads in root position.
Exercise 3.2.5
(Solution on p. 80.)
Now see if you can identify these chords that are not necessarily in root position. Rewrite them in root position first if that helps.
It sounds like a very technical idea, but basic harmonic analysis just means understanding how a chord is related to the key and to the other chords in a piece of music. This can be such useful information that you will find many musicians who have not studied much music theory, and even some who don't read music, but who can tell you what the I ("one") or the V ("ve") chord are in a certain key.
Why is it useful to know how chords are related?
Any chord might show up in any key, but some chords are much more likely than others. The most likely chords to show up in a key are the chords that use only the notes in that key (no accidentals21). So these chords have both names and numbers that tell how they t into the key. (We'll just discuss basic triads (Section 3.1) for the moment, not seventh chords (p. 73) or other added-note (Section 3.6.4: Added Notes, Suspensions, and Extensions) or altered (p. 77) chords.) The chords are numbered using Roman numerals from I to vii.
Exercise 3.3.1
(Solution on p. 81.)
Write and name the chords in G major and in B at major. (Hint: Determine the key signature22 first. Make certain that each chord begins on a note in the major scale (Section 2.1) and contains only notes in the key signature.) If you need some staff paper, you can print this PDF file23
You can find all the basic triads that are possible in a key by building one triad, in the key, on each note of the scale (each scale degree). One easy way to name all these chords is just to number them: the chord that starts on the first note of the scale is "I", the chord that starts on the next scale degree is "ii", and so on. Roman numerals are used to number the chords. Capital Roman numerals are used for major chords (Section 3.2.1: Major and Minor Chords) and small Roman numerals for minor chords (Section 3.2.1: Major and Minor Chords). The diminished chord (Section 3.2.2: Augmented and Diminished Chords) is in small Roman numerals followed by a small circle. Because major scales always follow the same pattern, the pattern of major and minor chords is also the same in any major key. The chords built on the first, fourth, and fifth degrees of the scale are always major chords (I, IV, and V). The chords built on the second, third, and sixth degrees of the scale are always minor chords (ii, iii, and vi). The chord built on the seventh degree of the scale is a diminished chord.
NOTE: Notice that IV in the key of B at is an E at major chord, not an E major chord, and vii in the key of G is F sharp diminished, not F diminished. If you can't name the scale notes in a key, you may find it difficult to predict whether a chord should be based on a sharp, at, or natural note. This is only one reason (out of many) why it is a good idea to memorize all the scales. ( See Major Keys and Scales (Section 2.1).) However, if you don't plan on memorizing all the scales at this time, you'll find it useful to memorize at least the most important chords (start with I, IV, and V) in your favorite keys.
Even among the chords that naturally occur in a key signature, some are much more likely to be used than others. In most music, the most common chord is I. In Western music24, I is the tonal center (Section 2.1) of the music, the chord that feels like the "home base" of the music. As the other two major chords in the key, IV and V are also likely to be very common. In fact, the most common added-note chord in most types of Western music is a V chord (the dominant chord (Section 3.3.4: Naming Chords Within a Key)) with a minor seventh (Major and Minor Intervals, p. 14) added (V7). It is so common that this particular flavor of seventh (Section 3.6.3: Seventh Chords) (a major chord with a minor seventh added) is often called a dominant seventh, regardless of whether the chord is being used as the V (the dominant) of the key. Whereas the I chord feels most strongly "at home", V7 gives the strongest feeling of "time to head home now". This is very useful for giving music a satisfying ending. Although it is much less common than the V7, the diminished vii chord (often with a diminished seventh (Section 3.2.2: Augmented and Diminished Chords) added), is considered to be a harmonically unstable chord that strongly wants to resolve to I. Listen to these very short progressions and see how strongly each suggests that you must be in the key of C: C (major) chord(I)25; F chord to C chord (IV - I)26; G chord to C chord (V - I)27; G seventh chord to C chord (V7 - I)28; B diminished seventh chord to C chord (viidim7 - I)29 (Please see Cadence (Section 3.4) for more on this subject.)
Many folk songs and other simple tunes can be accompanied using only the I, IV and V (or V7) chords of a key, a fact greatly appreciated by many beginning guitar players. Look at some chord progressions from real music.
Typically, folk, blues, rock, marches, and Classical-era30 music is based on relatively straightforward chord progressions, but of course there are plenty of exceptions. Jazz and some pop styles tend to include many chords with added (Section 3.6.4: Added Notes, Suspensions, and Extensions) or altered (p. 77) notes. Romantic-era31 music also tends to use more complex chords in greater variety, and is very likely to use chords that are not in the key.
Extensive study and practice are needed to be able to identify and understand these more complex progressions. It is not uncommon to find college-level music theory courses that are largely devoted to harmonic analysis and its relationship to musical forms. This course will go no further than to encourage you to develop a basic understanding of what harmonic analysis is about.
So far we have concentrated on identifying chord relationships by number, because this system is commonly used by musicians to talk about every kind of music from classical to jazz to blues. There is another set of names that is commonly used, particularly in classical music, to talk about harmonic relationships. Because numbers are used in music to identify everything from beats to intervals to harmonics to what fingering to use, this naming system is sometimes less confusing.
Exercise 3.3.2
(Solution on p. 81.)
Name the chord.
1. Dominant in C major
2. Subdominant in E major
3. Tonic in G sharp major
4. Mediant in F major
5. Supertonic in D major
6. Submediant in C major
7. Dominant seventh in A major
Exercise 3.3.3
(Solution on p. 82.)
The following chord progression is in the key of G major. Identify the relationship of each chord to the key by both name and number. Which chord is not in the key? Which chord in the key has been left out of the progression?
Since minor scales (Section 2.2) follow a different pattern of intervals (Section 1.3) than major scales, they will produce chord progressions with important differences from major key chord progressions.
Exercise 3.3.4
(Solution on p. 82.)
Write (triad) chords that occur in the keys of A minor, E minor, and D minor. Remember to begin each triad on a note of the natural minor (Section 2.2.3: Relative Minor and Major Keys) scale and to include only notes in the scale in each chord. Which chord relationships are major? Which minor? Which diminished? If you need staff paper, print this PDF file32
Notice that the actual chords created using the major scale and its relative minor (Section 2.2.3: Relative Minor and Major Keys) scale are the same. For example, compare the chords in A minor (Figure 3.48) to the chords in C major (Figure 3.19 (Chords in the keys of C major and D major)). The difference is in how the chords are used. As explained above (p. 59), if the key is C major, the chord progression33 will likely make it clear that C is the tonal center (p. 30) of the piece, for example by featuring the bright-sounding (major) tonic, dominant, and subdominant chords (C major, G major or G7, and F major), particularly in strong cadences (Section 3.4) that end on a C chord.
If the piece is in A minor, on the other hand, it will be more likely to feature (particularly in cadences) the tonic, dominant, and subdominant of A minor (the A minor, D minor, and E minor chords). These chords are also available in the key of C major, of course, but they typically are not given such a prominent place.
As mentioned above (p. 59), the "flavor" of sound that is created by a major chord with a minor seventh added, gives a particularly dominant (wanting-to-go-to-the-home-chord) sound, which in turn gives a more strong feeling of tonality to a piece of music. Because of this, many minor pieces change the dominant chord so that it is a dominant seventh (a major chord with a minor seventh), even though that requires using a note that is not in the key.
Exercise 3.3.5
(Solution on p. 82.)
Look at the chords in Figure 3.48. What note of each scale would have to be changed in order to make v major? Which other chords would be affected by this change? What would they become, and are these altered chords also likely to be used in the minor key?
The point of the harmonic minor (Section 2.2.3: Relative Minor and Major Keys) scale is to familiarize the musician with this common feature of harmony, so that the expected chords become easy to play in every minor key. There are also changes that can be made to the melodic34 lines of a minor-key piece that also make it more strongly tonal. This involves raising (by one half step (Section 1.2)) both the sixth and seventh scale notes, but only when the melody is ascending. So the musician who wants to become familiar with melodic patterns in every minor key will practice melodic minor (Section 2.2.3: Relative Minor and Major Keys) scales, which use different notes for the ascending and descending scale.
You can begin practicing harmonic analysis by practicing identifying whether a piece is in the major key or in its relative minor. Pick any piece of music for which you have the written music, and use the following steps to determine whether the piece is major or minor:
Is it Major or Minor?
Sometimes a piece of music temporarily moves into a new key. This is called modulation. It is very common in traditional classical music; long symphony and concerto movements almost always spend at least some time in a different key (usually a closely related key (Section 2.3) such as the dominant (Section 3.3.4: Naming Chords Within a Key) or subdominant (Section 3.3.4: Naming Chords Within a Key), or the relative minor or relative major (Section 2.2.3: Relative Minor and Major Keys)), in order to keep things interesting. Shorter works, even in classical style, are less likely to have complete modulations. Abrupt changes of key can seem unpleasant and jarring. In most styles of music, modulation is accomplished gradually, using a progression of chords that seems to move naturally towards the new key. But implied modulations, in which the tonal center seems to suddenly shift for a short time, can be very common in some shorter works (jazz standards, for example). As in longer works, modulation, with its new set of chords, is a good way to keep a piece interesting. If you find that the chord progression in a piece of music suddenly contains many chords that you would not expect in that key, it may be that the piece has modulated. Lots of accidentals, or even an actual change of key signature40, are other clues that the music has modulated.
A new key signature41 may help you to identify the modulation key. If there is not a change of key signature, remember that the new key is likely to contain whatever accidentals42 are showing up. It is also likely that many of the chords in the progression will be chords that are common in the new key. Look particularly for tonic chords and dominant sevenths. The new key is likely to be closely related (Section 2.3) to the original key, but another favorite trick in popular music is to simply move the key up one whole step (Section 1.2), for example from C major to D major. Modulations can make harmonic analysis much more challenging, so try to become comfortable analyzing easier pieces before tackling pieces with modulations.
Although the concept of harmonic analysis is pretty basic, actually analyzing complex pieces can be a major challenge. This is one of the main fields of study for those who are interested in studying music theory at a more advanced level. One next step for those interested in the subject is to become familiar with all the ways notes may be added to basic triads. (Please see Beyond Triads (Section 3.6) for an introduction to that subject.) At that point, you may want to spend some time practicing analyzing some simple, familiar pieces. Depending on your interests, you may also want to spend time creating pleasing chord progressions by choosing chords from the correct key that will complement a melody that you know. As of this writing, the site Music Theory for Songwriters43 featured "chord maps" that help the student predict likely chord progressions.
For more advanced practice, look for music theory books that focus entirely on harmony or that spend plenty of time analyzing harmonies in real music. (Some music history textbooks are in this category.) You will progress more quickly if you can find books that focus on the music genre that you are most interested in (there are books specifically about jazz harmony, for example).
A cadence is any place in a piece of music that has the feel of an ending point. This can be either a strong, definite stopping point - the end of the piece, for example, or the end of a movement or a verse - but it also refers to the "temporary-resting-place" pauses that round off the ends of musical ideas within each larger section.
A musical phrase45, like a sentence, usually contains an understandable idea, and then pauses before the next idea starts. Some of these musical pauses are simply take-a-breath-type pauses, and don't really give an "ending" feeling. In fact, like questions that need answers, many phrases leave the listener with a strong expectation of hearing the next, "answering", phrase. Other phrases, though, end with a more definite "we've arrived where we were going" feeling. The composer's expert control over such feelings of expectation and arrival are one of the main sources of the listener's enjoyment of the music.
Like a story, a piece of music can come to an end by simply stopping, but most listeners will react to such abruptness with dissatisfaction: the story or music simply "stopped" instead of "ending" properly. A more satisfying ending, in both stories and music, is usually provided by giving clues that an end is coming, and then ending in a commonly-accepted way. Stories are also divided into paragraphs, chapters, stanzas, scenes, or episodes, each with their own endings, to help us keep track of things and understand what is going on. Music also groups phrases and motifs46 into verses, choruses, sections, and movements, marked off by strong cadences to help us keep track of them. In good stories, there are clues in the plot and the pacing - in the Western47 tradition, the chase gets more exciting, characters good and bad get what they deserve, the inevitable tragedy occurs, or misunderstandings get resolved - that signal that the end of the story is nearing. Similarly, in music there are clues that signal to the listener that the end is coming up. These clues may be in the form48; in the development of the musical ideas; in the music's tempo49, texture50, or rhythmic51 complexity; in the chord progression52; even in the number and length of the phrases53 (Western listeners are fond of powers of two54). Like the ending of a story, an ending in music is more satisfying if it follows certain customs that the listener expects to hear. If you have grown up listening to a particular musical tradition, you will automatically have these expectations for a piece of music, even if you are not aware of having them. And like the customs for storytelling, these expectations can be different in different musical traditions.
Some things that produce a feeling of cadence