A student counts the interval from D to G♭ and concludes it is a 3rd because the flat 'brings G closer to F.' What is the correct interval number for D to G♭?
A3rd — the flat makes it smaller than a 4th, so it must be a third
B4th — both D to G and D to G♭ have the same generic interval number because accidentals don't change the letter-name count
CDiminished 4th — a special category that counts differently than a normal 4th
D5th — because the flat adds a chromatic step
Generic interval names count letter names, not semitones. D to G spans D(1)–E(2)–F(3)–G(4) — four letter names, regardless of whether G has a flat, sharp, or natural. The flat changes the interval's quality (making it a diminished 4th rather than a perfect 4th), but not its number. This is the essential point: accidentals affect quality, not generic size. The student's error is conflating semitone distance with letter-name count.
Question 2 Multiple Choice
How many letter names are spanned by a sixth?
A5 — you travel 5 steps to reach the 6th pitch
B6 — you count 6 letter names including both the starting and ending note
C7 — because a sixth spans most of an octave
D4 — because a sixth is the inversion of a third, which spans 3
A sixth spans 6 letter names: the starting note counts as 1. From C: C(1)–D(2)–E(3)–F(4)–G(5)–A(6) — a sixth. The number is always one more than the number of steps taken, because you are counting positions, not moves. Option A (5 steps) is the classic off-by-one error from starting the count at 0. The interval name directly equals the number of letter names touched.
Question 3 True / False
C to E♭ and C to E♯ are both thirds, because both span three letter names: C, D, and E.
TTrue
FFalse
Answer: True
Correct. Generic interval size depends only on letter names. Both C–D–E♭ and C–D–E♯ span three letter names (C, D, E), so both are thirds — a minor third and an augmented third respectively. The accidental on E changes how many semitones are in the interval (its quality), not how many letter names are spanned (its number). This is why number and quality are treated as independent layers of interval description.
Question 4 True / False
A unison — the same note played twice — counts as 0 in the interval numbering system, since no distance is traveled.
TTrue
FFalse
Answer: False
A unison counts as 1, not 0. The starting note is counted as the first note, not as zero. This is the source of the pervasive counting error in interval naming: beginners start counting at 0 (like an array index) instead of 1 (like ordinal counting). From C, staying on C = unison (1); moving to D = 2nd (2 letter names); moving to E = 3rd (3 letter names). The interval number is always one more than the number of steps taken.
Question 5 Short Answer
Why are intervals named by counting letter names rather than by counting semitones?
Think about your answer, then reveal below.
Model answer: Letter-name counting preserves the functional identity of intervals in the staff system and in harmonic analysis. Two intervals can have the same number of semitones but different functional roles — C to D♯ (augmented 2nd, 3 semitones) and C to E♭ (minor 3rd, 3 semitones) look identical on a piano but behave differently in voice leading and harmony. Counting letter names captures this distinction and provides the foundation for quality, chord construction, and scale analysis.
The deeper point is that Western music notation and theory are built around the seven letter names, not the 12 chromatic pitches. The staff organizes pitch by letter name; chord symbols name intervals by letter name; scale degrees correspond to letter names. Interval numbering follows this same logic: it maps onto the notational system that musicians use. Semitone counting would be necessary for some purposes but would destroy the functional distinctions that music theory requires.