Diatonic Intervals Continued

When an interval such as C - F is named as a perfect 4th, diatonic in C major, we make sense of this. This is easily understood because we have been taught to compare all intervals to the root of the major key. This knowledge is accepted as being your first stage in naming intervals however it is by no means the end of the study.

The interval C - F, whilst diatonic in C major, is not unique to this key. The perfect 4th, C - F, can also be found in F major and Bb major just to name two. Look at the diagram below to see this in action.

C D E F G A B C
F G A Bb C D E F
Bb C D Eb F G A Bb

The diagram above shows the relationship of the perfect 4th, C - F, in two situations other key than C major. Lets investigate this further.

In C major, the perfect 4th, C - F, occurs from the first degree of that scale. In F major, the perfect 4th, C - F, occurs from the fifth degree of that scale. And last but not least, in Bb major, the perfect 4th, C - F, occurs from the second degree of that scale.

Before we go on to explore this subject in detail, lets take a moment to think about what is being established here.

  1. Until now, we have looked at diatonic intervals where the first degree of a scale is the lowest note. We recognise these as being major (or perfect) intervals.
  2. We will now explore diatonic intervals where the lowest note of the interval is not the first degree of the scale.

Intervals generated from any note within a major scale are diatonic. However, this does not mean that these intervals are exclusively major. In addition, minor, diminished and augmented intervals can be created.

Lets continue with our example of C major to explore this.

The interval E - G is a minor 3rd

The interval E - G is a minor 3rd

The interval B - F is a diminished 5th

The interval B - F is a diminished 5th

The interval F - B is an augmented 4th

The interval F - B is an augmented 4th

How is this so?

Before understanding how different interval qualities exist within a major scale, you must first be aware that we are dealing with two different concepts:

1. The question of harmonic relationship.

What is the relationship of the interval within a given major scale?

Considering our minor, diminished and augmented examples above, we can conclude that these intervals are diatonic in C major, as all the notes are found within the key.

2. The question of naming diatonic intervals.

The challenge in this exercise is naming the intervals. In order to achieve this, you must embrace the following rule. When naming intervals, we must reference the major scale of the lowest note .

Lets consider the example of E - G, a minor 3rd diatonic in C major.

Remember, when naming intervals we must reference the major scale of the lowest note. In this example, the lowest note of the interval is E. This means that we need to reference the E major scale:

E Major Scale

Ask the question, is the upper note of the interval, G, found within the notes of E major? The answer is no. G is not diatonic to E major. G# however is.

The interval of E - G# is a major 3rd. Lowering G# by a half-step results in G, creating an interval of a minor third.

The interval E - G is a minor 3rd

Please note, we are describing the interval E - G in the context of the key of C major. We only use the E major scale as our reference for naming the interval.

In Summary

  1. Intervals within a major scale are called major (or perfect) only if they are fixed to the root note.
  2. Intervals of varying lengths can be generated from any degree of a given major scale.
  3. When naming intervals, we use the major scale of the lowest note as our reference.

Changing the quality of a Intervals using half-steps

In the process of correctly naming intervals, we may need to apply an accidentals to a note. In our example above, we lowered the note G# from E major to arrive at our interval E - G. When altering the notes of an interval, consider the following:

Major to Minor

Major intervals can be changed to minor intervals by decreasing the half-step count by one. For example, C - E is a major interval. It has an interval count of four half-steps. Lowering this interval by one half-step changes this major interval to minor. The result is C - Eb, which has an interval count of three half-steps.

Perfect to Diminished

Perfect intervals can be altered to diminished intervals by decreasing the half-step count by one. For example, C - F is a perfect fourth. It has an interval count of five half-steps. Lowering this interval by one half-step changes this perfect interval to diminished. The result is C - Fb, which has an interval count of four half-steps.

Major and Perfect to Augmented

When you raise a major perfect interval by a half-step you create an augmented interval. For example, C - F is a perfect fourth. It has an interval count of five half-steps. Increasing this interval by one half-step changes this perfect interval to an augmented interval. The result is C - F#, which has in interval count of six half-steps.

In Summary

  1. Lowering a major interval by a half-step creates a minor interval
  2. Lowering a perfect interval by a half-step creates a diminished interval
  3. Raising a major or perfect interval by a half-step creates an augmented interval

Simple vs. Compound Intervals

The term simple in this case does not mean the opposite of difficult. It refers to a class of interval. If intervals are contained within the eight notes of an octave, they are referred to as simple intervals.

If the distance between two notes is greater than an octave, the interval is known as a compound interval.

For example: Lets consider C major as a two octave scale:

C to D is a major second - a simple interval within an octave

C D E F G A B C

C to Dis a major ninth - a compound interval wider than an octave

C D E F G A B C D E F G A B C

Below is a list of all the possible diatonic intervals.

Interval Name Equiv. Steps
Perfect Unison 0
Minor 2nd 1
Major 2nd 2
Minor 3rd 3
Major 3rd 4
Perfect 4th 5
Aug. 4th 6
Dim. 5th 6
Perfect 5th 7
Minor 6th 8
Major 6th 9
Minor 7th 10
Major 7th 11
Perfect Octave 12