EPTPart 1: Introduction, and the dominant chord
Let's recapitulate the last blog: It is common to begin a song accompanied by the tonic chord – if the piece is written in the key of C major, that would be a C-major chord – and finish it with an authentic cadence by playing the dominant and then the tonic again.
The dominant is the fifth degree of a major scale. Since some scales can include flats or sharps, the dominant maybe also require accidentals. For simplicity, we continue with examples in C-major because this scale uses only the white-key notes. The dominant for C is G, as it is the fifth note counted from C. C itself acts as tonic which is the first note and point of rest for the entire scale.
How We Count Degrees
There are different ways to explain why we prefer to resolve a G-major triad with C than the other way round. One of them is the property of our brain to prefer a fifth interval – which is stable – over other intervals. The stability of the fifth is the result of the simple tuning ratio: The higher pitch is one-and-a-half as high as the lower pitch.
Once we have established the tonal center, we always count degrees from the tonic, not to the tonic. This is important to remember to avoid confusion. In our blog, we use C-major as example. C is the first degree, D the second and so on. G is the fifth. This remains true even if we play a lower G. Since C is the tonic, we cannot count from G and get G, A, B, C and think of G as fourth degree. In C-major, G is the fifth degree regardless.
With C as tonic, we hear a G-major chord really begging for resolution to C. The G-major triad consists of G-B-D. The note B is very important here.
The Leading Tone
The pitch tuning ratio of the note B is the most complex out of any notes in the C scale. Because a difficult relationship of two notes is hard to recognize, they create an instable interval. We want to have it resolved by going back to stability. Interval tuning ratios are however not the only way to quantify the harmonic distance.
We could also count the number of fifths we need to get from C to. Let us actually do it: From C, we go upwards by fifths and get to G, D, A, E and B. In C-major, none of its notes is farther – by fifths – than B.
Either way, considering fifths or the tuning ratio: The harmonic distance between C and B is big. However, both notes can be played with almost the same pitch, as one needs just a semitone step from B to C. If notes are that close in pitch, we assume a close connection.
So with the tonic C in mind, we perceive both B's harmonic instability towards C, as well as the pitch similarity to C. If we sing the notes of the major scale upwards, we usually don't only sing the first seven degrees, but the octave, too. One of the reason is that the seventh degree, which in C-major is B, leaves us unsatisfied: Regarding the pitch, we are so close to the tonic, but we are also at the most instable point in the scale. We want to resolve this tension with the tonic.
![[image loading]](http://i.imgur.com/laFRZlr.png)
Now It Becomes Clear!
Viewed from C, the G-major triad includes B, the leading tone to C. It does not work the other way round, the C triad does not include the leading tone to G. That would be F♯.
The leading tone ask for resolution to the tonic. However that is only a part of the dominant triad G-B-F – remember, the notes are for C-major. The root note of the dominant is the fifth, G, an extreme consonance to the tonic C and implies a close harmonic relationship. The dominant triad of C-major also includes D. That note is the fifth of G, supporting that G note because of its close harmonic relationship. D also is the secondary dominant – the dominant of the dominant – of our tonic center C.
There is no other triad possible than V – the fifth degree – with a stronger dominant effect. V in this context is a roman numeral, meaning five.
More Leading Tones?
B "leads" to C. That is a semitone upwards, there is no black key between B and C.
You will also find no black key between E and F on a piano, as the notes are only a semitone away from each other anyway.
In a C scale, C is the first scale degree and therefore the tonic, the point of rest. C-E represents a major third, which is a very stable interval. C-F on the other hand constitutes a fourth, which is not stable. Our ears like to hear stable intervals, so if we go from F to E, we achieve just that with a semitone step! Of course all this is only true if C is the tonic, functioning as root of the scale.
Since F does not lead to the tonic, it is not the leading tone. It just has a leading property to the major third of the tonic. It is possible to generalize the concept of leading tones, but we save that for a later blog.
Instability Within A Chord
Chords were developed from of music composed for several voices. A common technique to compose such music is counterpoint. The "point" here is a note. Counterpoint is a system of rules; those rules were developed and sometimes changed over centuries.
From the counterpoint era we already know a method to suspend a note. Today, we use the concept of a suspended chord. A triad in which we replace the third with a fourth is called a suspended, or sus4-chord. Sus4 = using the fourth to hold the third. In C-major, it is C-F-G. After that sus4 chord, we can resolve to the regular major triad C-E-G to get back to stability.
Because this type of suspension is the most used, though other types exist, it is also the sus chord. While regular triads are stable, suspended ones are not and require a resolution. That means, not only the chord degree is important, but also how we modify the chord on that degree. In this case, we have a tonic degree, also called I as roman numeral for "one" which requires resolution. This I can be played as sus4 and creates a resolution-seeking effect as we clearly recognize that the suspended chord just teases us until a standard triad – with a third – is played.
It is also possible to play the dominant, the V, as sus4 chord and then resolve it with its default form and then finally play the tonic triad.
Old Scales Did Not Have This Problems
Both F and B are funny: Counted from our tonic C, B is extremely far when we go through the fifths. F is close, but a fifth counted in the "wrong" direction, downwards instead of upwards.
What happens when we remove both F and B these from our C-major scale?
Down from seven notes to five, we have a pentatonic scale now. To be more precise, an actually very commonly used pentatonic scale in the history of music. Common pentatonic scales do not include leading tones, because they do not include semitone steps.
Seven-Note-Scales Are Useful
The irony is that we do need some notes which are instable towards to the tonic to point to it by creating tension. If we begin with a pentatonic scale, three approaches are available to get semitone steps: Either we continue to add two fifths, resulting in the Lydian scale. Or we add two fifth below the tonic, resulting in the Mixolydian scale. Or we add a note below the tonic and as well an additional fifth at the end of the scale. This gets us natural major.
This short discussion of scales is needed for chords as well. We soon will see, why.
Another Dominant Degree
While the fourth interval is very instable, especially when we compare it with the extremely stable fifth interval, the fourth does inherit a dominant effect from the fifth. This has several reasons, let us look on just two: The fourth is the next harmonic interval after the fifth, just one step narrower. As major and minor thirds are both thirds, even though with different characteristics, they share the property of bringing color and content into a chord. Fifth and fourth can also be viewed as twins, creating an empty sound (unlike the thirds) but having a dominant effect.
The fourth is also the octave complement of a fifth. Complement intervals inherit properties from the original interval. This is logical as the octave an interval so extremely harmonic that it doesn't even create a new note. So if we have an interval and determine its effect, it should not matter too much if we shift one of their notes by an octave. We still use the same notes!
We should therefore expect to get another dominant chord if we play a triad on the fourth degree. In C-major, that would be F.
Introducing The Subdominant
Let us do a note-by-note analysis of F-A-C, the F-major chord. F is the fourth of C, an instable interval. The note A is the first degree of the relative minor key to C-major. C is the tonic itself, but now functioning as the fifth to F and therefore making clear that F is indeed the chord root.
This chord of the fourth scale degree, the IV chord, creates some instability as we can expect from the fourth degree. A connection to C is still there, as any note has a meaning in the context created by the C tonic. IV has a weaker dominant force than V and therefore is not as good to be used for the final cadence of a piece. But it has good use within the piece. The IV chord is labeled the subdominant.
The IV triad creates a very relaxed sound. This effect is used – overused – in popular music.
The Subdominant – How Does It Work?
As the subdominant degree, the fourth, is the octave complement and therefore an inversion of the fifth, it does keep some properties of the original fifth interval. The fourth has a close relationship to the fifth and inherits a dominant effect, even though the dominant force to the tonic is not as strong.
It is possible to use this IV-I chord progession as the final cadence, this was done by some composers for church music. The church modes using the "hypo" modifier were created just for this so-called plagal cadence. In Greek, "plagios" means oblique, used as opposite to authentic, because the plagal cadence is not the direct one but an indirect one. If a chant ends with "Amen", the syllables A-men are often represented by IV-I.
A Standard Cadence
Almost all pieces begin with the tonic chord. This gives us a lead to interpret the next chords. Assume we are now in the middle of a score.
For a standard cadence, we play the subdominant first. That IV chord creates instability and a bit of tension. Then we play the dominant, which is the V. That chord creates much tension. Then we resolve with the tonic chord.
The IV-V-I progression has additional properties. Both the IV and the V chords can be viewed as being a fifth away from the tonic. The IV is a fifth below the tonic, the V a fight above it. So we have a kind of a harmonic pendulum with the tonic in the center, and the last chord confirms the center by playing the tonic.
If we play the IV-V-I progression in C-major, we play F-A-C first, G-B-D next and resolve with C-E-G. The tonic and the fifth appear twice, but every other note of the C-major scale also appears in one the chords. That means, this chord progression includes the entire scale!
This is one of the many uses of the IV chord: To be used with V and I to play any note of a scale with just three chords.
Confirming The Tonic
Playing the dominant and the tonic creates a tonal context. But it is incomplete. If we however include the subdominant, we have the entire scale presented. While the dominant supports the definition of the tonic, the subdominant helps, too. Imagine that we have a very short piece of music where we play only three chords. If we play F first and then G and C, we establish C as tonic.
If we repeat this chord progression, we experienced F as relaxed, G as dominant and C as point of rest.
The Use Of A Tonic
Image we only have two chords, C-major and F-major. How do they relate to each other? We could view C as tonic and F as subdominant. We also could interpret F as tonic and C as dominant. We would have to look on the melody we accompany with our two chords to decide. Or just hear the piece.
The tonic is what we perceive as point of rest. A chord is just a chord, only the progression of several chords can create a tonic. A melody without chords can also create a tonic. A melody accompanied with chords must be composed carefully to make a good song. It however is possible to make clear that a chord is the dominant. A triad cannot do it, but a tetrad can. We will have to save this for later.
The use of a tonic is that we have a point of rest which we can use to create an experience. The tonic is the center, the zero point, the home. The subdominant is a walk away from the tonic. The dominant is the urge to come back to the tonic.
Three Chord Songs
If a guitar player admits than he only plays three chords, he probably doesn't mean it figuratively. I, IV and V are enough to accompany many traditional songs. This is also the reason why we devoted two entire blog entries on just these few chords: As they are so important, we needed a full understanding before we can continue with more chords.
![[image loading]](http://i.imgur.com/wSJQUaq.png)
Four Chord Songs
To get a bit more variety and to fit four-bar songs, an additional chord is quite common: The minor relative of the major scale. For C-major, that would be A-minor. It's degree is VI, as A is the sixth degree in C-major. It is common to use lower-letter numerals for minor chords, so the chord would is written as vi. You can accompany almost every pop song with these four degrees of chords: I, IV, V, vi.
The vi chord is interesting as it can be used as a substitute for the tonic. Usually we will play the vi not with going to the sixth note upwards, but to the third downwards. Remember: We count degrees from the tonic upwards. Not to the tonic, nor downwards. Even though we rather play a third counted downwards, it is the sixth degree because we enumerate a degree always from the tonic upwards.
While vi is a minor chord, it is close to the major tonic chord. The reason is that the according scales, which in C-major would be A-minor, use the very same notes, only in a different order. In addition, the C-major and A-minor triads share two notes.
It is easy to learn all four chords and then sing a song and accompany with the chords. You can play the full triad, add its root as additional bass note, play the chord as note sequence instead of pressing all keys at once, and so on. If you learn piano, I recommend to learn to play triads in all keys, not just C-major. Once you can do it, you developed an harmonic intuition.
Scales For Degrees
C-major and A-minor are closely connected. That is no miracle, they use the same notes, only in a different order. There are other scale connections, too.
Let's say we play the dominant of C, which is G, and want to improvise a melody while we are in G. Now it is a good idea to use the Mixolydian scale instead of natural major, because G-major differs in one note from C-major. However, G-Mixolydian uses all the same seven notes as C-major does! The same is true for the subdominant of C, which is F, and the Lydian scale. We will come back to this when we finally discuss tetrads.
Next blog: Analysing Pachelbel's Canon in D. And Luka from Suzanne Vega.
