Descending Intervals
In order to create a descending interval, we use inversions of ascending intervals. Inverting the interval means moving the lower note up one octave, or the upper note down an octave. No pitch names change in this process. Once the inversion is found, you then revert the top note back to its position in the bottom resulting in the correct descending interval. There is a simple equation that can be used to find the inversion of an interval.
9-(quantity) down = opposite quality (quantity) up
Example: Minor 6th below C
9 - m6 down = M3 up
A Major 3rd above C is E. Therefore, a minor 6th BELOW C is E.
Chart of Quality Opposites:
Major |
Minor |
Minor |
Major |
Augmented |
Diminished |
Dimished |
Augmented |
Perfect |
Perfect |
*Note - a perfect interval has no opposite
Written examples:
Original |
Inversion |
M7 |
m2 |
P5 |
P4 |
m3 |
M6 |
A4 |
d5 |
Examples on the staff:
Compound Intervals
A compound interval is an interval larger than an octave. To determine the size of the compound interval, you can count all encompassing lines and spaces between the bottom and top note. Or - you can add the basic interval (i.e. "third) plus 7 (number of different notes in an octave).
Written examples:
A 9th is just a major 2nd plus an octave (2+7)
A 10th is just a major 3rd plus an octave (3+7)
An 11th is just a Perfect 4th plus an octave (3+7)
Examples on the staff: