In the most basic sense, harmonies are tones, or pitches, that sound good together. Knowing what tones to choose in accompaniment to others is a matter of taste and mood as much as any established rules or patterns. The best musicians are able to choose from a broad palette of accompanying pitches to compliment any given situation and provide any range of colours to the sound scape. This ability comes from a careful mix of art, science, and a good portion of patient practice. This page is meant to provide an introduction into a world that holds a lifetime of discoveries and challenges.
Any note played on any instrument or with the voice has a frequency. For example, the concert A is 440 vibrations per second. A series of notes exist which are octaves of this note, meaning they have a frequency of exactly half or double this original note (220 and 880 vibrations per second are lower and higher octave A’s, respectively.) Mathematically speaking, these octave pitches are harmonious because the waveforms match up every second cycle. Pitches between the octaves can match up in other ratios and have similarly harmonious effects, but that’s enough math for now. The main thing to remember is that when we speak of “harmony”, we’re not only talking about personal or historical taste, but also a naturally existing and universally human experience. Many of the same clusters of pitches can be found in every style of music in the world.
The most widely used cluster of harmonious tones is the major triad. These three notes make up any major chord, and are the first, third, and fifth tones in a major scale. For example, the notes of the C major triad are C, E, and G. Similar major triads can be made with all twelve notes in our scale by playing the root tone, going up four semitones to the third, and then going up another three semitones to the fifth. A semitone, or half-step, is the distance in pitch between a note and an adjacent note (for example, between C and C sharp).
It is interesting to note that the common western twelve-note division of the octave is only one of many approaches to dividing pitch, and is called equal temperament. This method is widely accepted because it provides a good compromise between tuning in all twelve keys (the concept of “keys” is explained below) and equally spaced pitches. Having equal distance between pitches is particularly important for fretted instruments such as guitars. It is good to be aware, however, that this is not a perfect system, and often pitch correction is necessary for more delicate pieces. This is where the art, rather than the science of music becomes very important.
In music, when one speaks of a key, what is being referred to is the note to which a song naturally resolves. Think of “Happy Birthday”. Everyone knows the song is over when the last note is sung. That last note is the key of the song, also known as the “tonic”. A common mistake is thinking that the key of a song is the note on which the song begins. This is sometimes the case, but as in Happy Birthday, songs often start a fifth (a distance in pitch of five major scale tones) up from the tonic, on what is commonly referred to as the dominant. The dominant also happens to be the most classically “harmonious” tone paired with the tonic, but more on these terms later. For now it is enough to understand that the key of a song is the tonic, and that all harmonious pitches are established relative to this tonic. Because of this, different combinations of sharps and flats (also known as accidentals, or the black notes on a piano) are used in each key. Accidentals are added in a very methodical way as the key is changed. With each increase in pitch of the tonic by a fifth, another sharp is added to what is called the “key signature”. For example, a song in the key of C has no sharps or flats, while a song in the key of G (one fifth up from C) has one sharp, F sharp, in its key signature. This means that throughout the song, when an F is written, it is always played a semitone up from F, as an F# (shorthand for F sharp). This cycle continues, adding one sharp for every fifth rise in pitch of the tonic, in what is known as the circle of fifths. This is referred to as a circle because after 12 rises in pitch, the tonic returns to the original note. Luckily, when first learning music, it’s usually sufficient to be comfortable in just a few keys. C, G, F, D and A are some of the most common.
Now we’ll move on to the next common chord: minor. The minor chord is made up of the three notes of the minor triad, which is identical to the major triad except that the third is lowered one semitone, or “flatted”. Similarly to major triads, minor triads can be formed in any key by playing the root, going up three semitones to the flatted third, then going up another four semitones to the fifth. Where major chords have their place as strong and happy sounding, minor chords have a different role as more moody or dark.
The word “scale” has been used a few times so far in this piece, and now is a good time to explain it. The most common scale is the major scale. Though cumbersome to write out, I’ll list here the distance in pitch between each tone in a major scale. From the root, go up two semitones to the second, two more semitones to the third, one more semitone to the fourth, two more semitones to the fifth, two more semitones to the sixth, two more semitones to the seventh, and finally one more semitone to the root one octave (or twelve semitones) above where we started. These seven notes make up the major scale, and plenty of good improvisation can be done by using these pitches alone. As an example, a C major scale has no sharps or flats, and so it can be played on just the white keys of a piano. Note that there are no black keys between the E and F, and between the B and C. This is because of the single semitone distance in pitch between the third and the fourth, and between the seventh and the octave root. Clever, isn’t it?
The next most common scale is the Dorian minor scale. This scale is identical to the major scale except that the third scale tone is flatted, as well as the seventh being flatted. For example, a C Dorian minor scale contains the notes C, D, Eb (shorthand for E flat), F, G, A, Bb, C. As with the minor chord, the Dorian minor scale is used to evoke a more dark and moody colour in a sound scape. The word “Dorian” is used to distinguish this scale from other minor scales, which won’t be covered at this time.
As was previously discussed, the tonic of a key is the note to which a song naturally resolves. Likewise, songs typically resolve to the chord corresponding to the key of a song. If a song is written is the key of C major, then the song will naturally resolve to a C note, as well as a C major chord. What makes music dynamic and this resolution pleasing, however, is the process building tension and providing motion before this resolution takes place. If our aim is to use the medium of music to express and explore our perception of life, then we can call on the various tonalities to symbolize the contrasts of pain and joy, peace and discontent, melancholy and happiness. These contrasts are exemplified most simply in the following common patterns of chords, or chord progressions.
In these examples, chords are written out in Roman numeral notation. The I corresponds to the chord of the first note in the scale, or the tonic chord; the V corresponds to the chord of the fifth note in the scale, or the dominant chord, and so on. When numerals are written in lower case, this means that the chord is a minor chord.
IV/V/I – sub-dominant, dominant, tonic
vi/ii/V/I – minor six, minor two, dominant, tonic
Experiment with these, and note how they naturally lead to one another and resolve in the end. Practice playing them in several different keys, and gain fluency with them in a few of your favorite keys. These two examples make up a very large portion of chord progressions used in popular music.
While a chord progression is being played, voices and instruments often add extra colour to the song by creating alternative melody lines. This is the beginning of improvisation, and a true test of one’s comfort with the theories explained so far. While one instrument is on the dominant chord, for example, a second instrument may highlight the tones of this chord’s triad, or any other number of tones that fit within the key of the song. The experimentation that can evolve from here is limitless. Enjoy the journey.