What key a particular piece of music is in determines from which notes you build the melodies and harmonies that constitute it. Keys are either major or minor, which means that they are constructed out of the notes provided by the major and minor scale, respectively.
Chords are constructed from scales by playing the scale harmonized with the third and fifth, making seven complete triads. This is a C major scale:
If you construct triads out of all seven notes of the C major scale, you will get the following chords:
These are the seven chords that are native to C major. From left to right, they are:
- Major triad on C.
- Minor triad on D.
- Minor triad on E.
- Major triad on F.
- Major triad on G.
- Minor triad on A.
- Diminished triad on B.
If you use traditional chord symbols, the list looks a lot less unwieldy: C, Dm, Em, F, G, Am and Bm−5.
Every major key has what's known as a relative minor key, whose root is a minor third below (or a major sixth above) the root of the major key. Relative keys are based on the exact same scale and share the exact same notes. The following is an A minor scale; please note that like the preceding C major scale, it consists of natural notes only:
If you likewise construct triads using only the notes from the A minor scale, you will get the seven chords that are native to the key of A minor:
These chords are exactly the same chords as those native to C major: Am, Bm−5, C, Dm, Em, F and G.
As per common music theory practice in English, key names are written like note names: with capital letters, with any accidentals spelled out: D flat major, F sharp minor, etc. It is assumed that the absence of the "major" or "minor" qualifier automatically means the major mode, e.g. Mozart's 39th symphony in E flat [major].
To save space, key names can be abbreviated further, for instance Db or F# minor. Some reference works might use upper- and lower-case letters to signify the major and minor mode: Db versus f#.
The Circle of Fifths
C major and A minor are the only keys that can be written using only natural notes. All other keys use one or more sharp or flat signs to preserve the distinct step pattern of the diatonic scale.
When we list the keys in rising chromatic order, there appears to be a certain pattern to the occurrence of sharps and flats:
There seems to be some mirror image thing going on, centered on F sharp and G flat. These are enharmonically equivalent (F# and Gb both refer to the note between F and G) and coincidentally both use six accidentals.
If we instead list all flat keys together, and all sharp keys together, and sort them in ascending order, we get this:
The circle of fifths is a way to visualize the relationships between keys. When keys are arranged in this fashion—by increasing number of sharps and decreasing number of flats—they find themselves a perfect fifth apart. C is the fifth in F major, G is the fifth in C major, and so on. The system pivots around the enharmonic equivalence of F sharp and G flat, allowing the ride back to C by renotating F sharp into G flat and subtracting one flat per fifth ascended.
The circle of fifths is a handy reference tool for notational purposes, but it also illustrates relations between keys. The more clockwise/counterclockwise steps that separate two keys, the more tenuous the relationship:
- A key is most closely related to the two adjacent keys. (F major, C major, G major.)
- A relative minor key uses the same notes and is found in the same place on the circle.
- A parallel minor key is always found three steps in the counterclockwise direction (C major to C minor).
- Conversely, a parallel major key is always found three steps in the clockwise direction (A minor to A major).
- Keys a half step apart are found five steps apart on the circle of fifths (C major to D flat major).
- Maximum separation is six steps, e.g. C major and F# major, or A major and E flat major.
The Feeling of Key
Once a key is established, there are subtle psychoacoustic phenomena that create a sense of tension and relaxation. This depends on the prevailing harmony, or put more simply, which chord is being played right now, and how that relates to the key center.
In any given key, chords arrange themselves in an order of importance according to their function. Chord functions are used as placeholders to discuss chord relationships without having to state particular chords or a specific key. A 12-bar blues is often described as a I-IV-V progression, for instance.
The most important chord is the tonic chord. The tonic is the triad that is based on the root of the scale. In C major, that chord is a C major triad, in A minor it is an A minor triad. In F major, it is an F major triad, and so on.
The tonic is the starting and ending point of the music, and is the place where the music feels the least tension. When playing the tonic, one feels at home and comfortable.
The second most important chord in a key is the dominant. It can always be found a perfect fifth above the tonic chord. For instance, in C major, the dominant is the G major triad, and in A minor, it is an E minor triad.
If the composer affirmatively establishes the tonic, the dominant will create tension and this tension will only be relieved by going back to the tonic.
It can also be added that any function has a dominant a fifth above it. This kind of relation is termed a secondary dominant, implying a (temporary) tonic.
The subdominant appears a fourth above the tonic. In C major, it is an F major triad; in A minor, it is a D minor triad.
The subdominant is a temporary resting place in a key, and is often used to prepare the dominant in order to get back to the tonic.
Since the subdominant is a perfect fourth above the tonic, it can also be inverted to a perfect fifth below. This means that the tonic is a potential dominant to its own subdominant:
Generally, movement towards the subdominant tends to decrease tension, wheras towards the dominant, it increases tension.
In English-language music theory, each scale step (and its chord) is equally important; i.e. there are seven primary chords in a key. The tonic, dominant and subdominant are often abbreviated by the Roman numerals I, V and IV since those are the scale steps where they can be found.
The other chords, II, III, VI and VII, are termed supertonic, mediant, submediant and leading-note chord, respectively. The first three are relatives of the tonic, subdominant and dominant, which concept we discussed in the article on chord theory.
In German- and Swedish-language music theory, there are two levels of chords. The tonic, dominant and subdominant are the primary functions. However, their relative chords are analyzed as subsets of the tonic, dominant and subdominant and are termed secondary functions.
The tonic-dominant relationship depends on something that is called the leading-note relationship. If the seventh note of the scale is a major seventh, i.e. a semitone from the octave/root, it is called a leading note.
The psychology of the leading note doesn't actually need to be explained. You can easily experience it yourself. Try playing a major scale, C to B, without playing the final high C. Let the final B hang for a while and I'll bet in a minute some neighbor is going to pound on the wall, screaming for the resolution provided by that final C!
This leading-note-to-root movement is the key to the strong relationship between a tonic and its dominant. The leading note of the key is part of the dominant chord. In C major, the note B appears in the G major triad. This B strives towards the resolution provided by playing that C, highlighted in the following example by a red line:
This tension is often compounded by adding dissonant notes to a dominant chord: most common is the dominant seventh, which can be extended into a dominant ninth:
The dominant seventh chord receives much of its character because of its built-in dissonance. The minor seventh is a dissonant interval in and of itself. There is also a dissonant diminished fifth between the third and the seventh (the notes B and F in the example above).
Dissonant intervals want to resolve into consonant intervals by each note making a stepwise motion. Diminished intervals resolve by shrinking, augmented intervals by growing. In the following example, the augmented fourth F-B grows into the minor sixth E-C. Next, the diminished fifth B-F shrinks into the major third C-E:
When the dominant seventh chord resolves to the tonic, its third moves by a semitone to the root of the tonic (red line in the illustration below). Its seventh moves to the third of the tonic (green line below):
You can also regard this as a double leading note relationship: the B-C and F-E (or F-E flat) gravitation in the very same chord.
A dominant ninth chord adds another level of dissonance and tension to the dominant seventh chord. The ninth is also a dissonant interval. Furthermore, the chord has a second tritone relationship—between the fifth and the ninth. Therefore, the ninth of this chord resolves by step to the fifth of the tonic, illustrated in blue. The seventh still resolves to the third of the tonic:
The one limitation of the diatonic scale and the major-minor tonal system is that it lacks a naturally occurring leading note in the minor mode:
The seventh note, G, is a minor seventh from the root and a whole step up to the octave A, or what is otherwise known as a subtonic as opposed to a leading note.
As already mentioned, the chord on the fifth note of the A minor scale is an E minor triad.
What does this mean? First of all, try it yourself: play a minor scale from A, but stop at G instead of the top A. Do you feel the same gravitation towards the top A? No, the scale might just as well drop back from G via F to E.
What about playing a sequence of notes over an A minor chord, and then going to the dominant E minor? You don't get the same sense of tension. True, there is tension because you've veered away from the tonic, but there is nothing in the minor dominant chord that desperately screams, "give me A minor, give me A minor!"
However, try to raise the seventh scale degree to a major seventh (in this case G sharp):
Now, the scale suddenly has a leading note. There is a semitone between G sharp and A, just as there is between B and C (the leading-note relationship in C major). This modified A minor scale will not sound relaxed when paused on that G sharp, it wants to be resolved by going that extra half step up to A.
What follows naturally from this is that you now have a major dominant chord (E major), that has the very same strong gravitational effect towards the tonic.
This modified minor scale is called the harmonic minor scale simply because it has more harmonic possibilities.
However, the raising of the seventh degree creates a non-diatonic and comparatively large interval between the sixth and the seventh. This interval, an augmented second, can make for rather awkward voice leading.
One common workaround is to also raise the sixth degree of the minor scale. With the raised sixth and seventh degrees, only one note separates the minor scale from the major, namely the characteristic third. This development of the minor scale is known as the melodic minor scale:
Variable 6 and 7
The melodic minor scale is written like above because music theory reference books always state categorically that the melodic minor scale needs the 6th and 7th degrees only when ascending. When descending, the leading-note is not necessary and thus the augmented 2nd between those two steps is not an issue.
In real, actual music, however, it gets a bit more complex than that. It all depends on the situation, the harmony and the direction of the melody. But at the same time it's simple, since we revert to the basic rule of music, namely that what sounds good to you wins out in the end.
Another mistake is to regard the three minor scales as three separate musical realities. It is considerably more flexible to consider the 6th and 7th degrees as adaptable. They can be minor or major depending on the context.
Among the seven chords that occur in major and minor keys, six can be explained. The three primary functions tonic, subdominant and dominant always occur on the first, fourth and fifth notes of the scale. The three secondary functions are the relative chords of the primary functions.
The Diminished Triad
There is also a seventh chord that is often passed over: the diminished triad on the seventh degree of the major scale and second degree of the minor scale.
A diminished triad is inherently unstable since it is dissonant, but not even if we alter the fifth so that the chord becomes a regular minor triad does it solve the issue. On the surface, a B minor triad serves no obvious function in C major. Neither does a D minor triad in C minor.
If, on the other hand, you regard the chord as something else entirely, it suddenly falls into place. This seventh chord is actually an incomplete chord, more specifically an incomplete dominant seventh chord. It consists of the three upper notes of the full dominant seventh chord, the only missing note is the root.
In this context, the Dm−5 chord in C minor is actually a Bb7 chord. Since Bb7 is dominant to E flat—the mediant, or tonic relative—Dm−5 can be regarded as an incomplete secondary dominant.
The Diminished Seventh Chord
A diminished triad can be extended by adding a diminished seventh, thereby creating the diminished seventh chord. Since the diminished triad is an incomplete dominant seventh, what does that make of the diminished seventh chord?
Let's continue the example of Bm−5, the chord found on the seventh degree of C major. It consists of the notes B (root), D (minor third) and F (diminished fifth). In order to extend this into a diminished seventh chord, we must add the note A flat.
Now, add the "missing" root G. This makes a five-note chord containing the notes G-B-D-F-A flat. The interval between G and (high) A flat is a minor ninth. Hence, the diminished seventh chord is a dominant ninth chord that is missing its root.
Since the diminished seventh chord is perfectly symmetrical, it is infinitely inversible. Any of the chord members can be regarded as the root. This also means that with a bit of enharmonic substitution, you can regard any one dim7 chord as either of four incomplete dominant ninth chords.
All you have to do is imagine the missing root notes: a major third below any of the chord members. A dominant ninth on G can be reshuffled into one on B flat, D flat or E as well. This means that one diminished seventh chord is the potential dominant of no less than eight tonic chords. Because of this, composers have used diminished seventh chord for centuries as modulating tools.
The preceding paragraphs might encourage the thought that the concept of key is rigid and strict. It is so, but only in the strictest sense, on paper.
In actual, sounding music, it is quite the opposite. That a piece music is written in a certain key does determine the starting point, the ending point, and any possible resting points (i.e. the tonic chord). However, this shouldn't discourage notes and/or chords that are foreign to the key.
Just as in real life, or in literature or in the movies, it is simply no fun if everyone gets along perfectly all the time. Music is also a kind of drama, but instead of dissenting opinions and/or random events, musical drama is created by short- and long-term tension.
Much music, especially classical music, was written expressly to steer away from the calm and relaxation of the tonic chord. A melody might have a restless note that is alien to the key and threatens to destabilize the harmonic foundation. A theme might not come to its conclusion in the home key, but modulate to the dominant, or the relative minor (or major), or some other key. The more you delay the return to the tonic, the more tension is created—and the more satisfying the resolution when the tonic does return. A multi-movement work might even have entire movements that are not even in the home key.
Therefore, that a piece of music is "in C major" does not mean that the composer sat down and thought: "Okay, so now I have seven notes to play with, plus whatever chords I can put together using those notes." It means that a C major chord is (usually) the starting- and stopping-point, but anything can happen in-between. Including a long section in F sharp major, an atonal 12-note fugue and an important secondary theme in A flat minor.