A chord is composed of three or more different notes. That is to say, a chord is simply two intervals. Ordinarily, one builds a chord by superposing thirds. The simplest chord (and the one we will be studying in this chapter) is the triad. The triad is a chord which is composed by superposing two thirds. Each of the notes in a chord (from lowest to highest) has a specific term by which they are named:
Historically, towards the ends of the Renaissance period, music shifted from the horizontal (melodic) approach to a more vertical (harmonic approach). Apropos, chord progressions were developed. This is what established the triad as the building block of Western harmony. We will discuss the nature of chord progressions in later chapters.
As we have already established, a triad consists of two intervals - a third and a fifth. As there are different kinds of thirds (major and minor) and different kinds of fifths (perfect, diminished, and augmented), there exists different kinds of triads. There are four kinds of triads:
All of these triads are important to understand, however the major and minor triads hold the most importance. This is because they contain only consonant intervals. Therefore, they are consonant chords. Oppositely, the diminished and augmented triads contain dissonant intervals, and therefore dissonant triads. Of the two dissonant triads, only the diminished has importance at the beginning stages of the theory.
In a given diatonic scale (heptatonia prima), there are seven degrees, as discussed in the previous chapter. Apropos, there are seven natural triads. The following diagram shows all of the triads in a C major scale:
You will notice that it consists of three major triads, three minor triads, and one diminished triad. A major triad has tendencies to be the most stable chords. So one must ask: "why don't we just use all major chords, if they are stable". The reason is because this would diminish the sense of continuity in a given piece of music. In any given major scale:
The previous example shows all the triads of a C major scale. Indeed, this works for any given major scale, but neglects the rules of triadic quality with respect to the natural minor scale.
With respect to quality, this is how natural minor triads are grouped:
What is interesting is that I, IV, and V are major in the major mode, and minor in the minor mode.
When the root of the triad is the lowest tone, it is said to be in root position. As we discussed in the previous chapter with respect to intervals, triads can also be inverted. When any other tone besides the root is in the bass (lowest position), it is inverted. When the third of the triad is the lowest tone, it is said to be in the first inversion. Consequentially, when the fifth is the lowest tone, the triad is said to be in second inversion. The inversion of the triad depends solely upon the lowest tone. This means that the upper tones can be arranged in any way. Each of these have functions in chordal harmony, and these will be discussed in detail in the chapter on voice leading.
Once may ask the following question: In any given standard chorus, there are four parts (soprano, tener, alto, bass), but there are only three tones to a triad, so how can this possibly work? The answer is, of course, that one of the tones is doubled. But this doubling procedure is not by random process, but rather by careful selection. When a composer doubles a given triad, he or she tries to achieve clarity and balance. This procedure is achieved in a variety of ways, but a basic guideline as to what composers generally do is this:
1) If the root is in the bass, double the root.
2) If the triad is in first inversion, double the soprano voice.
3) If the triad is in second inversion, double the bass voice.
This is applicable to major and minor triads. In a diminished chord, it is generally advisable to double the third. With respect to augmented triads, it is generally observed that composers will double the bass. Please do not take these are absolute rules. The purpose of music theory is to summarize what composers do, based on a theorists observations. One can break these rules at any time, provided it will achieve a greater musical effect to do so.
The last important concept to understand is that of triadic spacing. Like intervals, triads can be either closed or open. A closed triad is when the notes are not spread out more than an octave. An open position triad is when the voices are spread out more than an octave. Compositionally, it is best to put wide intervals at the bottom, and closed intervals in the upper voices. This procedure achieves a sense of clarity an balance. Although, it is quite often seen that composers will leave closed position intervals in the bass. This can leave a very murky and heavy feeling, such as what is often used in the piano sonatas of Beethoven.