Introduction to Harmony
Intervals, Triads and Chords

Intervals, Triads and Chords

Some basic terms used in this introduction to harmony 

An interval consists of 2 notes. Usually a lower note followed by a note that is higher in pitch or the reverse, where the higher note is written first and followed by the lower note. An interval can be measured using a unit of measurement such as the semitone.

As we proceed you will see that the two important things about an interval is its size and type. 
Typical measurements of an interval can be, unison, 2nd, 3rd, 4th 5th 6th, 7th and 8th. Intervals that have a measurement of an eighth and lower are know as simple intervals. 
Compound intervals have sizes larger than an eight, such as a 9th, 10th, 11th, 12th, 13th 14th and 15th, and are known as compound intervals. In this introduction we will learn about simple intervals first and later on compound intervals. 
The type of an interval is usually one of the following: major, minor, perfect, augmented and diminished. 
We will discuss each of the above in detail, later on.

See some examples of intervals below.

Harmonic Interval of a Perfect fifth

When notes are written as above in a vertical arrangement, they are usually excuted / played simultaneously forming harmony, in this example a perfect 5th.

Melodic Interval of a Perfect fifth

In the example above the note are written melodically. They are played one after the other. This serial arrangement means that the notes form a melody and on their own do not produce harmony. The interval remains a perfect 5th.

Harmonic Interval of a Perfect 8th

An example of a perfect eighth interval that is written harmonically. The notes will be executed together. The type and size will be discussed in greater detail later on.

Melodic Interval of a Perfect 8th

Another example of a melodic interval, which is a perfect eighth. The second note is an octave higher than the lower note and is played serially..

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Getting ready to learn basic harmony

Here are a few considerations when starting out with harmony. Know the intervals formed by the adjacent notes of the scale as well as other permutations. Initially we will learn to create intervals from the tonic (root or first note of the scale) to each of the other notes of the scale.

In the example below, you will see intervals in the major scale, all starting on the tonic (first note / root note)

How to calculate the exact size of an interval

In the illustration above, there are eight intervals, unison, second, third, fourth, fifth, sixth, seventh and eighth. This size does not completely describe the interval, we also need to know its type such as, major, minor, perfect, diminised or augmented. Each type of interval has a specific size measured in semitones.

Unison - 0 semitones
There is no movement in the unison interval, since both notes are exactly the same pitch. The size in semitones measures, zero.

Major second - 2 semitones / Minor second - 1 semitone 
The interval of a second may be major or minor depending on its semitone count. The major second as in our example above measures, 2 semitones, C to D natural. The minor second measures, 1 semitone, e.g. C to Db.

Major third - 4 semitones / Minor third - 3 semitones
The interval of a third also comes in two flavours, the major third and the minor third. The sad-sounding minor third has 3 semitones, C to Eb, while the happier-sounding major third has 4 semitones, C to E natural. 

Diminished fourth - 4 semitones / Perfect fourth - 5 semitones / Augmented fourth - 6 semitones
The interval of a fourth may be a diminished fourth with 4 semitones, C to Fb, and a perfect fourth with 5 semitones, C to F natural, and an augmented fourth with 6 semitones, C to F#.

Diminished fifth - 6 semitones / Perfect fifth - 7 semitones / Augmented fifth - 8 semitones
The diminished fifth has 6 semitones, C to Gb, while the perfect fifth interval measures 7 semitones, C to G natural, and the augmented fifth, 8 semitones, C to G#.

Major sixth - 9 semitones / Minor sixth 8 semitones
The major sixth interval measures 9 semitones, C to A, and the minor sixth measures 8 semitones, C to Ab

Diminished seventh - 9 semitones / Minor seventh - 10 semitones / Major seventh - 11 semitones
The diminished seventh measures 9 semitones, e.g. C to Bbb, while the minor seventh measures 10 semitones, C to Bb and the major seventh 11 semitones, C to B natural.

Perfect Eighth - 12 semitones
The perfect eighth interval measures 12 semitones, C to C octave.

The example below shows intervals formed on the tonic degree of the scale of C major.
You will notice that the tonal structure of the major scale makes the following intervals possible, 5 major second intervals and two minor second intervals. 

Intervals in the diatonic major scale

Adjacent notes in any scale will produce intervals between themselves. These intervals are a result of the tonal arrangement of the note, viz. tone, tone, semitone, tone, tone, tone, and semitone. The following example will make these intervals clear.

C to D forms an interval of a major second and measures 2 semitones
D to E forms an interval of a major second and measures 2 semitones
E to F forms an interval of a minor second and measures 1 semitone
F to G forms an interval of a major second and measures 2 semitones
G to A forms an interval of a major second and measures 2 semitones
A to B forms an interval of a major second and measures 2 semitones
B to C forms an interval of a minor second and mesaures 1 semitone

Diatonic and Chromatic Intervals

Diatonic intervals are made up from the notes of the scale such as notes in the major scale. When it is found that a note in an interval does not belong to the scale, it is called a chromatic interval. 

The interval C to G in the C major scale is diatonic because the note, G, is the fifth note in the scale of C major. The interval C to G# is a chromatic interval because the note G#, does not belong in the C major scale.

In our examples we used the C major scale to form intervals. Learners need to form intervals in the other 14 major scales. In the G major scale, the interval G to F# is a major 7th interval with a measurement of 11 semitones. The note F# is diatonic, because it belongs to the G major scale. 
If we take a minor 7th interval, G to F natural, the interval becomes a chromatic interval since the note F natural does not belong in the G major scale.

In the next section on intervals we will begin to examine compound intervals. These intervals are larger than a perfect eighth.

Intervals in the C chromatic scale

The C chromatic scale has the following notes:
C, Db, D, Eb, E , F, F#, G, G#, A, Bb, B, C

The notes in parentheses have the same pitch as its neighbouring note and are included here to ensure that all the basic intervals are mentioned. 
C - 1st, Db - 2nd, D -2nd, Eb - 3rd, E - 3rd (Fb - 4th), F - 4th, F# - 4th (Gb - 5th), G - 5th, G# - 5th (Ab - 6th), A - 6th (Bbb - 7th), Bb -7th, B - 7th, C - 8th

E has the same pitch as Fb
G# has the same ptich as Ab
Bbb has the same ptich as A

Bbb is pronounced B double Flat and Cx is pronounced C double sharp.

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A more advanced example of intervals in the scale of F sharp major

Working with a key like F# major which has 6 sharps in the scale, helps learners to understand the correct usage of accidentals in describing each interval. The table below includes diatonic and chromatic intervals for the scale of F# major.

A more advanced example of intervals in the key of Db major

Working with a key like Bb major which has 5 flats in the scale, helps learners to understand the correct usage of accidentals in describing each interval. The table below includes diatonic and chromatic intervals for the scale of Bb major. Try other keys with flats such as Gb major and Cb major.

Interesting intervals occur in the melodic and harmonic minor scales

With the raised 7th degree in the harmonic minor scale, and the raising of the 6th and 7th degrees in the melodic minor scales, they produce interesting intervals. Examples in minor keys.

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