Intervals: Size & Quality

You’ll be able to

Measure an interval’s size by counting letter names inclusively
Assign quality — perfect, major, minor, diminished, or augmented
Invert an interval and predict the resulting size and quality

Size: counting letter names

An interval is the distance between two pitches, and it has two parts: a size (number) and a quality. To find the size, count letter names from the bottom note to the top inclusively — both notes count. C up to E spans C-D-E = three letters, a third; C up to G spans five letters, a fifth. The accidentals do not change the size: C to E, C to E♭, and C to E♯ are all some kind of third because they cover three letter names.

Quality: perfect, major, and minor

Quality refines the size by exact half-step count. Unisons, fourths, fifths, and octaves come in a perfect flavor; seconds, thirds, sixths, and sevenths come in major or minor. The intervals of the major scale above its tonic are the reference: P1, M2, M3, P4, P5, M6, M7, P8. A minor interval is one half step smaller than major (M3 = 4 half steps; m3 = 3). Widen a perfect or major interval by a half step and it becomes augmented; shrink a perfect or minor interval by a half step and it becomes diminished.

Inversion and the tritone

To invert an interval, move the lower note up an octave (or the upper note down). Sizes always add to 9 (a third inverts to a sixth, a fifth to a fourth), and qualities flip in a fixed way: major ↔ minor, augmented ↔ diminished, while perfect stays perfect. One interval is its own special case: the tritone (three whole steps, 6 half steps), spelled as an augmented fourth (F–B) or its inversion the diminished fifth (B–F). Its instability drives much of tonal harmony.

Half steps per interval quality

m2=1 · M2=2 · m3=3 · M3=4 · P4=5 · TT=6 · P5=7 · m6=8 · M6=9 · m7=10 · M7=11 · P8=12

Count half steps between the two pitches, then match the number and the letter-name size to this table. Inversions of any pair sum to 12 half steps (and size numbers sum to 9).

Worked example

Identify the interval from C up to A, then invert it.

1.Count letter names inclusively: C-D-E-F-G-A = six letters, so the size is a sixth.
2.Count half steps from C to A: C→C♯→D→E♭→E→F→F♯→G→A♭→A = 9 half steps.
3.Nine half steps spanning a sixth is a major sixth (M6).
4.To invert, put C above A: A up to C spans A-B-C = a third, with 3 half steps = a minor third. Note the sizes add to 9 (6 + 3) and major inverts to minor.

Answer: C up to A is a major sixth (M6, 9 half steps). Inverted, A up to C is a minor third (m3) — sizes summing to 9, major becoming minor.

Checkpoint

What is the interval from E up to B?

Watch out

Do not judge quality from half steps alone — the letter-name size decides the name. F to G♯ and F to A♭ both span 3 half steps, but F–G♯ covers two letters (an augmented second) while F–A♭ covers three letters (a minor third). Same sound, different interval, because the spelling differs.

Checkpoint

What is the interval from F up to B?

On the exam

Memorize the two ways the tritone appears: augmented fourth (fa–ti, e.g. F–B) and diminished fifth (ti–fa, e.g. B–F). Spotting the tritone between scale degrees 4 and 7 is essential for identifying the dominant chord and voice-leading its resolution.

Answer the 2 checkpoints as you read.