intervals (harmony)

So far we have only examined musical progressions where only one note at a time was played: we have examined how the different notes relate to each other while the progression is played, therefore in a horizontal time pattern.

This is one aspect of music of course, but let's not forget that more often we listen to more than one note at a time in a single piece of music, which means that many notes are layered 'vertically' in time.

This vertical disposition of notes, called harmony, follows rules that are very similar to the melody. So, as scales are used to give a melody some coherence, they are also used to properly structure a harmony.

As harmony only applies when more than one note is played, the most basic situation is when the notes are two: a bichord.

Every bichord expresses an interval of course, so the following are the 13 possible bichords in a chromatic scale:

notation	interval	sound
	unison	Listen
	minor second	Listen
	major second	Listen
	minor third	Listen
	major third	Listen
	fourth	Listen
	diminished fifth	Listen
	fifth	Listen
	minor sixth	Listen
	major sixth	Listen
	minor seventh	Listen
	major seventh	Listen
	octave	Listen

You may have noticed that some intervals sound better than others, especially the ons related by a fraction of small whole numbers, such as

major third (5/4)
fourth (4/3)
fifth (3/2)

and so on. These sounds are also called consonant. When the relationship is expressed by a fraction with bigger terms, often the two sounds are dissonant.

Minor second (25/24)
Diminished fifth (45/32)

If more than two notes are involved, we are dealing with a chord. The most basic chord is a triad. A triad is made by a fundamental note (or 'tonic') and by two other notes related to the tonic by specific intervals. As it happens with the scales, the variations of these intervals can change the mood of a chord very much.

There is quite a large number of possible combinations of three or more notes, so we will not examine all of them, but just a few ones that are most commonly used. All the following example has to be intended in G clef.

A very basic triad is made by the tonic, a major third, and a fifth: this is called a 'major chord', and the notes that are part of them belong to its tonic's major scale. Let's see and hear a few of them:

	C major	Listen
	D major	Listen
	F major	Listen
	G major	Listen
	A major	Listen

Now, the 'third' in a chord, is a very important note: by changing it, we can modify the mood or emotions that the chord conveys. If we change it to a minor third, for instance, we will have a 'minor chord':

	C minor	Listen
	D minor	Listen
	F minor	Listen
	G minor	Listen
	A minor	Listen

Minor chords sound totally different from majors, but we have only changed one note!

If we take the third away and, for example, use an interval like an octave, we cannot say if the chord is major or minor anymore:

	C octave	Listen
	D octave	Listen
	F octave	Listen
	G octave	Listen
	A octave	Listen

See how important is the third?

If we use an interval of a fourth instead of a third, we will achieve a particular chord, called 'suspended' (sus.). Also in this case, we cannot tell wether the chord is major or minor:

	C sus	Listen
	D sus	Listen
	F sus	Listen
	G sus	Listen
	A sus	Listen

A variant of suspended chords is to use a second just interval instead of the fourth, but it is less common.

Now, let's take a minor chord and use, instead of a just fifth, a diminished fifth: we will have a 'diminished' chord

	C dim	Listen
	D dim	Listen
	F dim	Listen
	G dim	Listen
	A dim	Listen

Of course we do not have to limit to three notes: in facts, by adding a fourth note we can further shape the mood of a chord. A very common note to add to a is the minor seventh, which gives a sense of tension and incompleteness and leads the way to another chord for proper conclusion (very often the chord whose tonic is the fourth of the tonic of the first chord). The seventh can be added either a major or a minor chord. The following are some major chords with a seventh, or simply 'seventh' chords.

	C major seventh	Listen
	D major seventh	Listen
	F major seventh	Listen
	G major seventh	Listen
	A major seventh	Listen

These are minor chords with a seventh added, or 'minor seventh chords'. Note that the seventh grade is always minor, whether we add it to a major or to a minor chord!! What makes the difference is the third!

	C minor seventh	Listen
	D minor seventh	Listen
	F minor seventh	Listen
	G minor seventh	Listen
	A minor seventh	Listen

For brevity, chords are usually indicated by the name of their tonic note, so we will find for example:

C : which means 'C major'

C-, or Cmin, or Cm: which mins 'C minor'

C4 or Csus: which means 'C suspended'

Cdim: which means 'C diminished'

C7: which means 'C major seventh'

Cmin7, Cm7, C- 7: which mean 'C minor seventh'

Major chords are actually called with the name of the note only, without adding 'major'. That attribute is only specified if the chord is not major.

As we said, there are many other combinations, but it will be out of the scope of this course to examine them.

We do not need to be able to recognise the pitch of every single chord by ear, but it we can definitely recognise if a chord is major, minor seventh, etc.

This is what we aim for, so make sure you do plenty of tests and that you are familiar with these chords.