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Victoria Williams

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5. Intervals

Grade Four Music Theory Lesson 5: Intervals

At grade three, we learnt how to identify intervals and to describe them with their full names - a type and a number, for example "perfect fifth".

 

We learnt that the intervals built from the tonic of a major scale are:

1- perfect unison

2- major 2nd

3- major 3rd

4- perfect 4th

5- perfect 5th

6- major 6th

7- major 7th

8- perfect 8ve (octave)

 For example, here are the intervals built from the G major scale, with the tonic G as the lower note:

major scale intervals

We also learnt that the intervals built from the tonic of a minor (harmonic) scale are:

1- perfect unison

2- major 2nd

3- minor 3rd

4- perfect 4th

5- perfect 5th

6- minor 6th

7- major 7th

8- perfect 8ve 

 For example, compare the intervals built from the G minor scale with G as the lower note:

minor scale intervals

The only differences between the major and minor scales are in the third and sixth intervals.

 

At grade 3, all the intervals we had to identify had the tonic as the lowest note. 

At grade 4, we have to identify and write intervals between any two notes in any of the keys for this grade (up to 5 flats/sharps). In other words, the lowest note might NOT be the tonic of the key.

We will also learn two new terms - AUGMENTED and DIMINISHED.

 

Harmonic and Melodic Intervals

Intervals which are written with one note on top of another are called harmonic intervals.

Intervals which are written with one note after another are called melodic intervals.

harmonic melodic

 (These terms have nothing to do with types of minor scales!) 

Harmonic and melodic intervals are worked out in the same way. They are just written differently.

 

Interval Qualities

The words "major", "minor" and "perfect" describe an interval's quality

Major and perfect intervals are those created when

  • the lower note is the tonic of a major scale, and
  • the upper note is also in the same major scale.

Note: it does not matter what key a piece of music is in. The interval between C (lower note) and E (upper note) is always a major 3rd, even if the interval is found in a piece written in the key of F minor, for example. This is because the note E is the third note in the C major scale.

In the grade 4 exam you will normally be told what key the interval occurs in. However, this makes absolutely no difference to anything.

  • Only the intervals of a 2nd, 3rd, 6th and 7th can be major
  • Only the intervals of a unison, 4th, 5th and octave can be perfect.
  • You cannot have a "perfect 3rd" or a "major 4th" for example.

 

Minor, augmented and diminished intervals are only found when

  • the lower note is the tonic of a major scale, but
  • the upper note is NOT part of that major scale

Minor intervals are one semitone (half step) smaller than major intervals. Only 2nds, 3rds, 6ths and 7ths can be minor.

Diminished intervals are one semitone (half step) smaller than minor intervals, or one semitone smaller than perfect intervals. 2nds, 3rds, 4ths, 5ths, 6ths, 7ths and octaves can all be diminished, but unisons cannot be diminished (because a perfect unison is the smallest possible interval).

Augmented intervals are one semitone (half step) bigger than major or perfect intervals. Unisons, 2nds, 3rds, 4ths, 5ths, 6ths, 7ths and octaves can all be augmented.

 

Here are some examples. 

example intervals

  1. F-Bb = perfect 4th. (Bb is the 4th note in the F major scale).
  2. F-B = augmented 4th. (One semitone wider than a perfect 4th).
  3. B-C = minor 2nd. (In the B major scale, the 2nd note is C#. B-C is one semitone smaller).
  4. C-Eb = minor 3rd. (In the C major scale, the 3rd note is E natural. C-Eb is one semitone smaller).
  5. Eb-G = major 3rd. (G is the third note in the scale of Eb major).
  6. Ab-G = major 7th. (G is the 7th note in the scale of Ab major).
  7. Ab-B = augmented 2nd. (The 2nd note of the Ab major scale is Bb. Ab-B is one semitone wider).
  8. D-B = major 6th. (B is the 6th note in the scale of D major).

 

Working out Intervals

1) To find the interval number, first count the letter names of the notes, starting from the lower note. (G-A# is a 2nd, but G-Bb is a 3rd, even though A# and Bb are enharmonic equivalents (the same note on a piano keyboard).)

2) To find the interval type, use the lower note and pretend it's the tonic of a major scale.

3) Write out the scale if you can't do it in your head. Use the pattern TTS TTTS (tone/whole step = T and semitone/half step = S).

4) If the upper note is in the major scale, the interval will be major (2nd, 3rd, 6th or 7th) or perfect (unison, 4th, 5th, octave).

5) If the upper note is not in the major scale, it will be augmented (wider/bigger), minor (1 semitone (half step) smaller than major) or diminished (1 semitone smaller than minor or perfect).

 Here's an example. Name the interval marked with the bracket:

name the interval

First, count the letter names: B-C-D-E-F = 5. This interval is a 5th.

Next, make the major scale using the lower note as the tonic. The lower note is B, so we make the B major scale: B-C#-D#-E-F#-G#-A#-B.

Now check whether the upper note is in the scale: it is not (the upper note is F natural, but the scale contains F#).

Work out if the interval is bigger or smaller than the "perfect" interval. F natural is one semitone (half step) lower than F#, which makes this into a smaller interval. An interval which is one semitone smaller than "perfect" is "diminished", so this is a diminished 5th.

 

Writing Intervals

 Use the same method to write intervals. Let's imagine you are asked to write a harmonic interval of a diminished 7th above this note:

diminished 7th

Start by working out what letter name is needed, by counting out 7 letter names. F-G-A-B-C-D-E. Write in an E (without any accidentals).

7th

Next, work out the major scale from the lower note. In fact, the scale of F# major is pretty nasty though, so if you want, you could ignore the sharp for a moment*, and work out the scale of F major instead: F-G-A-Bb-C-D-E-F.

We can see that E exists in the F major scale, so F-E is a major 7th. If the lower note is F#, then the interval is one semitone (half step) smaller, so the interval we have written so far must be a minor 7th.

We need to write a diminished 7th, which is one semitone (half step) smaller than a minor 7th. This means we need to make our interval smaller by one semitone. We do this by changing E natural to Eb.

diminished 7th complete

 * You can use the same trick when working out intervals, if the lower note makes a nasty scale!

 

 Harmonic Unisons and 2nds

Harmonic intervals are written with one note above the other. If the interval is a unison or a 2nd, you will need to move the higher note to the side a little, so that it can be clearly seen. 

placement harmonic intervals

 

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