Intervals (aka Music Theory Primer part 2)

This post follows on from the Music Theory Primer post so I’d recommend reading that one first if you haven’t already.

In that post I introduced Keys as a way of arranging notes to make them sound more musical.  We saw that the notes in a Key determine the basis for which chords can be used and whether they are major or minor in nature.

Chords are essential building blocks for songs, but a Key can also identify the scales which can be used to provide harmony, melody lines or solos.  In essence, a scale is basically a specific arrangement of some or all of the notes in a Key.  The major scale, for instance, has exactly the same notes and order as the major Key i.e. the key of C major C, D, E, F, G, A, B, C is also called the C major scale.

It’s useful to listen to the major scale and also to listen to the intervals for each of the scale tones from the root note.  This can help you identify tonal changes which can help with ear training over time.  The major scale is easy to play on a keyboard, it is basically all of the white notes which are shown in the Music Theory Primer post.  On a guitar, the major scale can be played in several different positions, three of these are shown  using tablature:

E||------------------------------------------|  1 octave scale
B||--------------------------------0----1----|
G||----------------------0----2--------------|
D||-------0----2----3------------------------|
A||--3---------------------------------------|
E||------------------------------------------|

|------------------------------------------|  1 octave scale
|------------------------------------------|
|---------------------------2----4----5----|
|------------2----3----5-------------------|
|--3----5----------------------------------|
|------------------------------------------|

|------------------------------------------------------------------------7----8--|   2 octave scale
|-------------------------------------------------------------8----10------------|
|---------------------------------------------7----9----10-----------------------|
|-----------------------------7----9----10---------------------------------------|
|-------------7----8----10-------------------------------------------------------|
|--8----10-----------------------------------------------------------------------|

Intervals from the root note are shown for the Key of C major below, represented on a keyboard and on a guitar using tablature.  They are summarised in the table underneath.

E||--------------------|--------------------|--------------------|
B||--------------------|--------------------|--------------------|
G||--------------------|--------------------|-----------4--------|
D||--------------------|-----------1--------|--------------------|
A||--3--------4--------|--3-----------------|--3-----------------|
E||--------------------|--------------------|--------------------|
     C - C#  minor 2nd    C - D#  minor 3rd     C - F#  augmented 4th/diminished 5th

|--------------------|--------------------|
|--------------------|--------------------|
|----------1---------|-----------3--------|
|--------------------|--------------------|
|--3-----------------|--3-----------------|
|--------------------|--------------------|
  C - G#  minor 6th     C - A# minor 7th

|--------------------|--------------------|--------------------|--------------------|
|--------------------|--------------------|--------------------|--------------------|
|--------------------|--------------------|--------------------|-----------0--------|
|------------0-------|-----------2--------|-----------3--------|--------------------|
|--3-----------------|--3-----------------|--3-----------------|--3-----------------|
|--------------------|--------------------|--------------------|--------------------|  
   C - D  major 2nd     C - E   major 3rd    C - F  perfect 4th   C - G  perfect 5th

--------------------|--------------------||
--------------------|--------------------||
-----------2--------|-----------4--------||
--------------------|--------------------||
--3-----------------|--3-----------------||
--------------------|--------------------||
 C - A major 6th       C - B  major 7th

Interval summary table:

Note from C	Interval	Consonant	Dissonant	Number of notes
C – C#	Minor 2nd (m2)		X	Semitone
C – D	Major 2nd (M2)		X	Tone
C – D#	Minor 3rd (m3)	X		Tone + semitone
C – E	Major 3rd (M3)	X		2 x tone
C – F	Perfect 4th (P4)	X		2 x tone + semitone
C – F#	Augmented 4th (aug 4th) / Diminished 5th (dim 5th)		X	3 x tone
C – G	Perfect 5th (P5)	X		3 x tone + semitone
C – G#	Minor 6th (m6)	X		4 x tone
C – A	Major 6th (M6)	X		4 x tone + semitone
C – A#	Minor 7th (m7)		X	5 x tone
C – B	Major 7th (M7)		X	5 x tone + semitone

A word on sharps and flats.

In Music Theory Primer I referred to the black notes as sharps (#).  In practice, the note between a C and D  can be described as C# or Db, they are both describing exactly the same note.  Which one you use is partly determined by the harmonic context and relation to Key.  Well that’s the ‘official’ explanation, feel free to use whichever way you find easiest to remember.  (I must admit I tend to think in terms of sharps regardless of what the ‘official’ terminology should be.)

In these examples, the Key of C doesn’t have any sharp or flat notes but if we consider a minor 3rd interval we tend to say that is a flattened third i.e. Eb.

In the next post we’ll consider the other major Keys using the circle of fifths and circle of fourths.