Harmony: A Closer Look At The Perfect Fourth

When I was younger I developed a passion for harmony. I started learning how modes, scales and chords work together to create music. Harmony is the teaching of a set of rules to make music audible. Perhaps the word ‘rule’ is wrong since that word implies something immobile, the enforcement of the wills or wishes of a few. That notion is in my opinion incorrect, since the teachings of harmony were to suit the human hearing, conditioned to western music. In this article I will be talking about harmony for western music. After all, there is so much more like Arabic harmony, Indian, Chinese and many other harmonies. For us, those harmonies might sound strange and different but our music has the same effect on people who only know that kind of music, which means the rulebook on how to make music sound good depends on the cultural background of the listener.
When I started getting a feel for harmony, I slowly began to realize why I dislike some artists so much. It wasn’t the lyrical content or even the melody, but the harmony. In a sense I grew ‘allergic’ to the perfect fourth. Every time I hear parallel harmony in the perfect fourth I get a bit twitchy and annoyed. I want to take a closer look at what I call lazy harmony, the perfect fourth. I’ll start off by analyzing the perfect four and its function within harmony, the chord and scale. Then I want to take a look at how to make easy yet interesting harmony. In the mean time I want to show several ways of alternative harmonies within the western musical paradigm.
The perfect fourth is, as the name is actually a dead giveaway, the fourth step in a scale, any scale. To make it easier to talk about the steps of the scale I’ll simply name the steps by number, in other words, the root is I, the second is II, the third is III etc etc. When I write the interval, it should be interpreted as playing two notes simultaneously because, after all, we’re talking about harmony.
Regularly speaking, the IV does not have a place in a chord since a chord is built with the I, III and V, and in special cases like the dominant seventh chord, the VII is also used. Because popular music is still based on the rules of harmony that were developed over the course of hundreds of years, the IV still has no place in a chord.
This is true for normal applications. Take your guitar and play a C major chord barred but with an F in stead of a G. You’ll soon discover that the F doesn’t sound that well. You want to move up to the G, the V in the scale. This is because the IV is still considered a dissonant to some degree (‘does not sound good together) and the V is considered a consonant (‘does sound good together). To understand the reason why, we have to take a look at the historical use of the perfect fourth.
The IV was always used to give the melody a thicker, wider texture and this happened already during the middle ages in Europe. Later though, the IV (together with the V, I and octave) were considered the only ‘proper’ intervals with a diminished use of the III and VI. Note that the seventh isn’t even considered at all since the seventh is always dissonant with the root (or octave), and that was completely unacceptable. As the years progressed, the IV was used less and less because it was considered, as I mentioned before, a dissonant. Later, with the rise of the baroque, classical and romantic era, the IV was being used as a dissonant in a consonant manner, but often followed with a resolution to a V, III or simply to the root, the I.
As stated by Tanner & Gerow in their book ‘A study of jazz’ about chord progression in relation to the fourth:
Common-practice harmony is almost always derived from diatonic scales and tends to follow particular chord progressions that have withstood the test of time. For example, in common-practice harmony, a major triad built on the fifth degree of the scale (V) is unlikely to progress directly to a root position triad built on the fourth degree of the scale (IV), but the reverse of this progression (IV-V) is quite common. By contrast, the V-IV progression is readily acceptable by many other standards; for example, this transition is essential to the “shuffle” blues progression’s last line (V-IV-I-I), which has become the orthodox ending for blues progressions at the expense of the original last line (V-V-I-I).
With relying more heavily on the VI, composers started to reevaluate the IV, and subsequently the IV and V were to influence harmony even further with the rise of the quartile and quintal harmony. Interestingly enough, modern acoustic theory confirms the medieval notion of the perfect fourth being a consonant by a pure mathematical reason. As I explained in another article, all notes in a scale have a relation to the root note in terms of a fracture bigger than one and smaller than two (the frequency of the octave is twice the root, the frequency of the fourth is 4/3 the root, etc etc) and it appears that the intervals we prefer to hear are simple fractures whilst more complicated fractures are frowned upon. Here’s an excellent example of quartal harmony by Ravel. The fourth pops up constantly but dissolves and comes back just as pronounced as before.

As to how to make a song in harmony (i.e.: more than one voice) yet make it interesting, that’s not as hard as it might appear to be. If you take the ‘rule’ no parallel fifths, octaves and widen that rule by saying ‘no fourths’, either, you are left with thirds, sixths and sevenths to make two lines with. One is the simple melody and the other goes over and under the melody, in the same key of course, but with alternating intervals. This poses another complication, though this can be an interesting one.
Modern music consists of a melody that’s founded on chords, and everything has the same key. That is the essence of harmony. But a more amazing way of writing music, albeit a bit ancient, is to write lines of melodies for each voice (for instance, vocals, guitar and bass). Each line has a melody of its own but all share the same key. The lines are not supposed to create chords per se but can be consonant or dissonant as long as they dissolve into consonants. This practice is called counterpoint (coming from the latin puntus contra punctum meaning note versus note). Some composers made enormous pieces using that technique, like Johann Sebastian Bach. Just listen to his Prelude and Fugues; all those pieces are in counterpoint. As a matter of fact, a Fugue couldn’t exist as it does without counterpoint!
A fugue is a very interesting technique of composing and I’ll highlight it briefly. The prelude gives the player (and eventually listener) a basic melody. The melody is then taken over by the several voices, to be repeated, augmented, changed, repeated again and replied to like a question-and-answer game. Since all the voices blend together you need a system to make it clear and audible and thats were counterpoint comes in. It doesn’t neccecerily keep it all as clean as can be, but it provides structure. The voices blend together and the counterpoint ensures that they all sound well together.
Counterpoint is really a difficult way of composing and some are better at it than others. Johann Sebastian Bach and Wolfgang Amadeus Mozart were very good at it, and even in modern music, counterpoint has it’s place. If you listen carefully, you’ll hear a lot of counter point in Jeff Beck’s music, or maybe it should be called pseudocounterpoint, since he doesn’t always follow the rules or write the entire piece in counterpoint. After all, making music is a human affair and musicians in particular don’t like to be boxed off by rules.
Here’s an example of simple counterpoint in writing. See how the two voices never make a full chord and the voices are really melodies.
And here’s a real application of counterpoint in a fugue, by J.S. Bach with a visual analyses.
I want to conclude with two audio clips. One is by J.S. Bach, a prelude and fugue. Propably beaten to death by now, but in my opinion it shows what a fugue is, par excellence.

The second clip is Jeff Beck playing “Cause We’ve Ended As Lovers.” Note how the bass player, Tal Wilkenfeld, isn’t just playing a simple bassline but really a melody. It’s not pure counterpoint, but shows a different way of having a different kind of harmony nonetheless. Notice how her line goes up when his line goes down; just as counterpoint demands. And surely sometimes their notes line up in octaves but only to dissolve to a dissonant and then back to a consonant soon afterwards.

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1 Comment

  1. Worst entry ever.
    “a chord is built with the I, III and V” < no, only a major triad is. A chord in music is any harmonic set of three or more notes.

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