Questions: Determining Interval Quality by Semitone Count

Question 1

A student measures the interval from C up to A♭. They count letter names: C, D, E, F, G, A — six letters (a sixth). They count semitones: C to A is 9, but A♭ is one lower, so 8 semitones. What is the correct interval name?

• A. Major sixth — because it spans six letter names
• B. Diminished sixth — because 8 semitones is two less than a major sixth
• C. Minor sixth — because 8 semitones with a sixth span gives minor quality
• D. Augmented fifth — because 8 semitones also matches that interval

Answer: (C)

Both steps are required. Step 1 gives the interval number: six letter names = a sixth. Step 2 gives the quality: 9 semitones is a major sixth, so 8 semitones — one semitone smaller — is a minor sixth. Option D is the trap: C to G# is also 8 semitones, but G# spans five letter names (C–D–E–F–G), making it an augmented fifth — a completely different interval. The letter-name count determines the interval type first; semitones then determine quality.

Question 2

Two notes are 7 semitones apart. A student immediately labels the interval a 'perfect fifth.' Could this identification be incorrect?

• A. No — 7 semitones always means perfect fifth, regardless of the notes
• B. Yes — the notes could span six letter names, making it a diminished sixth (also 7 semitones)
• C. Yes — 7 semitones could also be an augmented fourth depending on enharmonic spelling
• D. No — semitone counting is always sufficient to determine the complete interval

Answer: (B)

Semitone counting alone is insufficient. Consider C to A♭♭ (A double-flat): this is 7 semitones, but A♭♭ is enharmonically G. C to G spans five letter names = fifth (perfect fifth). But C to A♭♭ spans six letter names (C–D–E–F–G–A = sixth), making it a diminished sixth — same pitch, different interval name. Letter-name counting must come first to get the correct interval number, and only then does the semitone count determine quality.

Question 3

C to D♯ and C to E♭ have the same number of semitones but are different intervals.

• T. True
• F. False

Answer: True

C to D♯: letter names C, D — two letters = a second. 3 semitones with a second span = augmented second. C to E♭: letter names C, D, E — three letters = a third. 3 semitones with a third span = minor third. Both are 3 semitones and sound identical on an equal-tempered instrument, but they are named differently because interval number is determined by letter-name count. This is precisely why semitone counting alone cannot identify an interval.

Question 4

The word 'perfect' can be applied to any interval that sounds particularly consonant and stable, such as a major third or major sixth.

• T. True
• F. False

Answer: False

'Perfect' is a specific quality term that applies only to unisons, fourths, fifths, and octaves — intervals that appear with a single natural form in the diatonic scale. Major thirds and major sixths are consonant but are described as 'major,' not 'perfect.' The major/minor distinction applies to seconds, thirds, sixths, and sevenths. The terminology is a formal system, not a description of perceived consonance.

Question 5

Why are two separate operations — counting letter names and counting semitones — both necessary to identify an interval completely?

Model answer: Letter-name counting determines the interval number (second, third, fourth, etc.), while semitone counting determines the quality (major, minor, perfect, augmented, diminished). Neither operation alone is sufficient: different intervals can share a semitone count (C to D♯ and C to E♭ are both 3 semitones but a second and a third respectively), and different intervals can share a letter span (C to E♮ and C to E♭ both span three letters but differ by a semitone). Only the combination of both counts uniquely identifies an interval.

Musical notation encodes two independent pieces of information: the diatonic letter name (position in the scale) and the chromatic alteration (accidentals that modify pitch by semitones). Interval quality is the relationship between these two dimensions — how many semitones a particular letter-span contains compared to its default diatonic version. Mastering this two-step process is the foundation of all subsequent harmonic work, from triad construction to ear training.