In this lesson we will look at inverted intervals. All intervals are a measure of distance between two notes. This is the case whether you are analyzing simple, compound or inverted intervals.
What is important to remember before tackling inverted intervals is that intervals are given a numeric value, such as a 4th or 5th, and a quality value which is either major, minor, diminished or augmented.
Inverting an interval is simply flipping the order of the top and bottom notes. The top becomes the bottom and the bottom becomes the top. The lower note of the interval is placed one octave above. Conversely, the upper note is placed one octave below.
When the arrangement of notes within the interval are switched around, this interval is known as an inverted interval.
For example: The interval of C - E with C as the lower note is inverted to E - C. The inverted interval makes E to the new lowest note.
There are no hard and fast rule as to which note is flipped. There are two choices:
- The bottom note, C, is moved an octave above the E
- The upper note, E, is moved an octave below the C
The important fact to understand is that one of the note positions has been displaced or relocated by one octave.
Measuring Inverted Intervals
The diagram above shows the major 3rd inverted to E - C, a 6th. The quality of this inverted interval is now minor. Lets investigate why this is so.
We accept undoubtedly that C - E is a major 3rd. It would be safe to assume that the inversion of the major 3rd is also major, as these two notes, regardless of their arrangement, belong to the C major scale. What can also add to the confusion is that the letter names of the inversion remain the same, all be it flipped around.
The answer to this can be settled by reciting the golden rule for naming intervals.
All intervals are named from the lowest of the two notes.
The interval E - C must be measured from the lowest note, E, and compared to its relationship with the tonic key, E major.
The E Major Scale
E - C is a 6th. When comparing this interval to E major, the note C is a half-step lower than C#.
In order to arrive at our interval of E - C, we must lower the C # to C, resulting in a minor interval. Therefore, the interval E - C is indeed a minor 6th.
Descending intervals are NOT inverted interval
Some students may be confused when it comes to differentiating between an inverted interval and a descending interval. A descending interval is not an inverted interval.
When measuring intervals, the direction of the melody, be it ascending or descending, is not in question. The distance of C - E is four half-steps whether you approach it ascending from C or descending from E. The distance remains the same.
When we invert an interval, we are changing the pitch of one of the notes by an octave.
Naming Inverted Intervals
When you invert an interval, both the number value and the quality are inverted. The interval of C - E is a major 3rd. Inverting this major 3rd results in E - C, a minor 6th. The quality value of major has been inverted to minor. When you invert the quality of an interval, the following patterns are observed:
- Major becomes minor
- Minor becomes major
- Diminished becomes augmented
- Augmented becomes diminished
When we invert the major 3rd, C - E, the resulting interval is a minor 6th, E - C. An interesting discovery is that if you add the numeric value from each interval together, the sum equals 9. When you invert the numeric value of an interval, the following patterns are observed:
- 2nd plus 7th equals 9
- 3rd plus 6th equals 9
- 4th plus 5th equals 9
- 5th plus 4th equals 9
Inverting Perfect Intervals
As with any rule, there are exceptions. When a perfect interval is inverted, it remains perfect by quality only. The numeric value of the interval continues to be inverted. For example:
- Inverting a perfect 4th results in a perfect 5th
- Inverting a perfect 5th results in a perfect 4th
Below is a table of diatonic intervals and their inversions:
|Starting Interval||Inverted Interval|
|Perfect Unison||Perfect Octave|
|Minor 2nd||Major 7th|
|Major 2nd||Minor 7th|
|Minor 3rd||Major 6th|
|Major 3rd||Minor 6th|
|Perfect 4th||Perfect 5th|
|Aug. 4th||Dim. 5th|
|Dim. 5th||Aug. 4th|
|Perfect 5th||Perfect 4th|
|Minor 6th||Major 3rd|
|Major 6th||Minor 3rd|
|Minor 7th||Major 2nd|
|Major 7th||Minor 2nd|
|Perfect Octave||Perfect Unison|