Intervals: the distance between notes
Measure the distance between any two notes in half steps, give it its proper name, and predict whether two notes played together will sound restful or tense.
WHAT A TUNE REALLY IS
You remember distances, not notes
Someone starts "Happy Birthday" too high, someone else starts it too low, and you recognise it instantly both times. Not one note is the same. What is the same is the chain of distances from each note to the next. The distance between two notes is called an interval, and harmony is built out of intervals.
This is also why the scale patterns worked from any starting note. W W H W W W H is nothing but a list of intervals.
Interval
The distance between two notes. It has a size, counted in half steps, and a number name, counted in letters. For the number name you count both ends: C to E covers C, D, E, three letters, so it is a third. C to G covers five letters, so it is a fifth.
You already know two intervals from lesson 5. A half step (1) is a minor second, and a whole step (2) is a major second.
| Interval | Half steps | Example from C |
|---|---|---|
| Minor third | 3 | C to Eb |
| Major third | 4 | C to E |
| Perfect fourth | 5 | C to F |
| Perfect fifth | 7 | C to G |
| Octave | 12 | C to the next C |
Check yourself
"Twinkle Twinkle" begins C C G G. Nika wants to name the jump from C up to G. What is it?
- 5 half steps, so a perfect fifth
- 7 half steps, a perfect fifth
- 8 half steps, because G is the eighth key
- 4 half steps, a major third
Show the answer
7 half steps, a perfect fifth
Yes. C#, D, D#, E, F, F#, G: seven moves. And C D E F G is five letters, which is where the name "fifth" comes from.
"Happy Birthday", first line, started on G.
Hap py birth day to you
G G A G C B
G -> A up 2 major second (whole step)
A -> G down 2 major second
G -> C up 5 perfect fourth
C -> B down 1 minor second (half step)Shape of the line: same, up 2, down 2, up 5, down 1.
The big reach, from "day" to "to", is a perfect fourth.Start on any other note and keep this list of distances. The note names all change and the song does not.
Check yourself
If you start "Happy Birthday" on D instead of G but keep every interval the same, people will still hear "Happy Birthday".
Show the answer
True
True. A melody is its intervals and its rhythm. Moving all of it up or down together is called transposing, and singers do it every time a song is too high for them.
The two thirds
Major third · 4
C to E. Wide and bright. It is the distance from home to the third note of a major scale.
Minor third · 3
C to Eb, or A to C. One half step smaller, and noticeably darker. It is the distance from home to the third note of a minor scale.
TOGETHER
Restful intervals and tense intervals
Play two notes at the same time and the interval has a character. Octaves, perfect fifths, fourths and thirds sound restful; musicians say consonant. Notes one half step apart, and notes six half steps apart, sound tense, or dissonant. Tension is not a fault. It is the feeling of wanting to move, and music uses it all the time.
C and G together: open and stable. C and C# together: a rub, like two people trying to go through one door. Move the C# up to D, or down to C, and the rub is gone.
Check yourself
Two notes played together: restful or tense?
- C and G (7 half steps)
- C and C# (1 half step)
- C and E (4 half steps)
- F and the B above it (6 half steps)
- A and the next A up (12 half steps)
- E and F side by side (1 half step)
Show the answer
Restful: C and G (7 half steps), C and E (4 half steps), A and the next A up (12 half steps)
Tense: C and C# (1 half step), F and the B above it (6 half steps), E and F side by side (1 half step)
Name any interval in four moves
- Find both notes on the keyboard
Picture them, lower one on the left.
- Count the half steps
Count moves from the lower note to the upper one, black keys included. Don't count the starting key.
- Count the letters
Include both ends. Three letters is some kind of third, five letters is some kind of fifth.
- Put them together
Three letters and 4 half steps: major third. Three letters and 3 half steps: minor third. Five letters and 7 half steps: perfect fifth.
Check yourself
Omid plays D and the F above it, both white keys. What interval is that?
- A minor third: three letters, 3 half steps
- A major third, because both keys are white
- A major second, because only one white key lies between them
- A perfect fourth, because F is the fourth letter from C
Show the answer
A minor third: three letters, 3 half steps
Right. D, E, F is three letters, and D#, E, F is three half steps, because E–F has no black key between. Two white keys a third apart can be major or minor.
Check yourself
Match each pair of notes to its interval
Show the answer
- E up to F → Minor second
- C up to E → Major third
- G up to C → Perfect fourth
- C up to G → Perfect fifth
- A up to the next A → Octave
Lesson recap
- An interval is the distance between two notes; a melody is a chain of intervals, which is why it survives being moved up or down.
- Size is counted in half-step moves; the number name is counted in letters, including both ends.
- Minor third = 3, major third = 4, perfect fourth = 5, perfect fifth = 7, octave = 12.
- Fifths, fourths, thirds and octaves sound restful; a half step or a tritone (6) sounds tense.
- Tension is useful: it makes the music want to move.