Glossary
Augmented (A)
An interval quality that, when inverted, transforms into a diminished quality.
Example:
An Augmented 4th (like C to F#) inverts to a diminished 5th (F# to C).
Compound Intervals
Intervals that span larger than a single octave, typically expressed as an octave plus a simple interval.
Example:
A C to the E an octave and a third above is a compound Major 3rd (or Major 10th).
Interval Inversion
The process of flipping an interval upside down by swapping the positions of its two notes. This changes both the interval number and its quality (except for perfect intervals).
Example:
A C to E (Major 3rd) inverts to an E to C (minor 6th).
Major (M)
An interval quality that, when inverted, transforms into a minor quality.
Example:
A Major 6th (like C to A) inverts to a minor 3rd (A to C).
Number Inversion
The rule for determining the new interval number when an interval is inverted, found by subtracting the original interval number from 9.
Example:
A 4th inverts to a 5th (9 - 4 = 5th).
Octave
An interval spanning eight diatonic scale degrees, representing the same note name at a higher or lower pitch. It is the foundational unit for understanding compound intervals.
Example:
The interval from C to the next higher C is a Perfect Octave.
Perfect (P)
An interval quality that remains Perfect when inverted.
Example:
A Perfect 4th (like C to F) inverts to a Perfect 5th (F to C).
Quality Inversion
The rule for determining the new interval quality when an interval is inverted, where Major becomes minor, minor becomes Major, Augmented becomes diminished, and diminished becomes Augmented, while Perfect remains Perfect.
Example:
A Major 3rd inverts to a minor 6th.
Simple Interval
An interval that spans an octave or less (a 2nd through an 8th). Compound intervals are often reduced to their simple interval equivalent for easier analysis.
Example:
A Major 10th is a simple Major 3rd plus an octave.
diminished (d)
An interval quality that, when inverted, transforms into an Augmented quality.
Example:
A diminished 5th (like C to Gb) inverts to an Augmented 4th (Gb to C).
minor (m)
An interval quality that, when inverted, transforms into a Major quality.
Example:
A minor 7th (like C to Bb) inverts to a Major 2nd (Bb to C).