Compound Intervals Practice With Worked Answers

Play C4–E♭5 and C4–D♯5 on a piano tuned in equal temperament. Your fingers land on the same two keys, 15 semitones apart. On paper, C4–E♭5 is a minor tenth (m10), and C4–D♯5 is an augmented ninth (A9).

You can do the worksheet on paper. Each pair starts with the lower note. In scientific pitch notation, C4 is middle C, and the octave number changes at C. B3 sits one semitone below C4.

Simple vs compound intervals

In written interval names, simple sizes run from unison through octave. Compound sizes start at the ninth. To reduce one, lower the upper note by an octave and keep its letter and accidental. Each octave you remove takes seven off the interval number and 12 off the semitone count. The quality stays the same. Stop when the written number is eight or less. Open Music Theory’s interval chapter

Give the full name on this worksheet. For example, a minor tenth reduces to a minor third. You may also see the original interval called a compound minor third.

Count letters, then count semitones

1. Count the letter positions, including both ends. For C4–E♭5, count C, D, E, F, G, A, B, C, D, E. The last E is the tenth letter position. D♯5 is one letter position earlier, so C4–D♯5 is a ninth.
2. Lower the top note to find the quality. C4–E♭4 spans three semitones, one fewer than a major third. C4–D♯4 also spans three, one more than a major second. That gives you a minor third and an augmented second. Put the octave back to get a minor tenth and an augmented ninth.

To count semitones on paper, start with the natural notes. E–F and B–C are one semitone apart. The other gaps between neighboring natural notes are two. A sharp raises its note by one semitone and a flat lowers it by one. Lowering the bottom note makes the gap wider, as you'll see in the spelling example below.

Simple interval baseline	Semitones
Major 2nd, 3rd, 6th, 7th	2, 4, 9, 11
Perfect 4th, 5th, octave	5, 7, 12

Compare your semitone count with the baseline for that letter count. Minor (m) is one semitone narrower than major (M). Augmented (A) is one wider than major or perfect (P), and diminished (d) is one narrower than minor or perfect.

Written pair	Reduced pair and quality	Full interval	Total semitones
C4–E♭5	C4–E♭4, m3	m10	12 + 3 = 15
C4–D♯5	C4–D♯4, A2	A9	12 + 3 = 15
B3–C5	B3–C4, m2	m9	12 + 1 = 13
F♯3–C5	F♯3–C4, d5	d12	12 + 6 = 18
G3–G5	G3–G4, P8	P15	12 + 12 = 24

G3–G5 takes just one move. Lower G5 to G4 and stop at the perfect octave. The lower note stays put. You can practice exchanging which note is on top in the interval inversion lesson.

Spell the smaller interval first

To spell a major tenth above D♭3, start with a major third (10 − 7 = 3).

1. Count D, E, F. The third letter lands on F in octave 3.
2. D3–F3 spans three semitones. Starting on D♭3 adds one, so F3 gives you the four semitones of a major third.
3. Raise F3 to F4. D♭3–F4 spans 16 semitones, including the octave you just added.

When the simple interval crosses C, give its upper note the new octave number before raising it again. In the table, B3–C4 is already a minor second. One more octave gives you B3–C5.

Compound intervals worksheet

Copy the four columns from the example table. For each answer, write the pitch pair with octave numbers, the reduced pair and its quality, the full interval name, and the total semitones. For the last three, name the proposed interval before you fix it.

1. Identify E♭3–C5.
2. Spell a minor ninth above E4.
3. Identify A♭3–E5.
4. Spell a perfect twelfth above B♭3.
5. Someone writes A3–C4 for a minor tenth above A3. Fix the pair.
6. Someone writes B3–D♯5 for a minor tenth above B3. Fix the pair.
7. Someone writes A3–B♯4 for a minor tenth above A3. Fix the pair and explain why the piano key sounded right.

Answers

#	Original or corrected pair	Reduced pair	Full name	Semitones
1	E♭3–C5	E♭3–C4, M6	Major thirteenth	21
2	E4–F5	E4–F4, m2	Minor ninth	13
3	A♭3–E5	A♭3–E4, A5	Augmented twelfth	20
4	B♭3–F5	B♭3–F4, P5	Perfect twelfth	19
5	A3–C5	A3–C4, m3	Minor tenth	15
6	B3–D5	B3–D4, m3	Minor tenth	15
7	A3–C5	A3–C4, m3	Minor tenth	15

1. Count six letters from E through C. E♭3–C4 spans nine semitones, so the reduced interval is a major sixth.
2. A second above E uses F. E4–F4 is already one semitone, so raise F4 to F5.
3. A♭3–E4 spans five letter positions and eight semitones. That's one wider than a perfect fifth, so the twelfth is augmented.
4. A fifth above B uses F. B♭3–F4 spans the required seven semitones, so raise F4 to F5.
5. A3–C4 is a minor third of three semitones. The letter and pitch spelling are right. Raise C4 an octave to C5.
6. B3–D♯5 is a major tenth of 16 semitones. The letter and octave are right. Remove the sharp to narrow it by one semitone.
7. A3–B♯4 is an augmented ninth of 15 semitones. B♯4 and C5 share a piano key. Spell that key as C5 to reach the tenth letter position.

Turn a missed step into a flashcard

Pick a question you missed. Try it from memory, then check your answer and correct any mistake. Come back to the card in another session. Spacing retrieval attempts can help you remember the material longer. Research on spaced retrieval

Front	Back
Spell a minor ninth above E4. Give the simple pair too.	E4–F5. The simple pair is E4–F4, a minor second.
Why is A3–B♯4 an augmented ninth?	It spans nine letter positions and 15 semitones. A3–C5 spans ten positions and the same 15 semitones.

If the reduced intervals are where you slow down, the Nibomo music interval deck contains 181 English cards on simple intervals from unison through octave, including spelling, semitone counts, and inversions. Use the worksheet or your own cards for ninths and above. The music theory flashcards guide has more examples of writing prompts you can grade by spelling.

AI tools drafted and edited this lesson and created the illustration. The interval names and semitone counts were checked with a script.