Interval Direction and Size: Up, Down, Together, and Past the Octave
So far an interval has been one number: two notes, count the distance. That number is real, and it is not the whole description. The same distance can reach your ear in three different ways, and they are not equally easy to recognise — which is why a drill that only ever plays one of them teaches you less than it appears to.
Up or down
Play C then the G above it and you have an ascending perfect fifth. Play G then the C below it and you have a descending one. Same two notes, same seven semitones, opposite direction.
Your ear does not treat these as the same problem. Almost everyone finds descending intervals harder, and the reason is ordinary rather than mysterious: the reference tunes people learn intervals by are nearly all ascending. If your handle on the fifth is the opening of a fanfare that goes up, a fifth that goes down has no handle at all.
That is a gap worth closing deliberately, because real melodies fall as often as they rise.
Together or one at a time
Two notes played one after the other form a melodic interval. Two notes sounded at the same time form a harmonic one.
The distance is identical and the experience is not. A melodic interval you hear as a movement — a step from here to there, with a direction. A harmonic interval fuses: the two notes blend into a single sound with a character, and there is no direction in it at all, because nothing moved.
This is why the two are separate skills rather than one skill applied twice. Someone fluent at naming melodic thirds can be lost the first time a third arrives as a chord, and the fix is practice on the form that is unfamiliar, not more practice in general.
Past the octave
Every interval so far has fitted inside an octave. Those are simple intervals. Anything wider is compound, and gets a new name.
Go up an octave from C and then two more semitones and you land on the D that sits nine letter-names above where you started. That is a ninth — and it is a second, one octave higher. The arithmetic is the same every time:
| Compound | Minus an octave | Is really a |
|---|---|---|
| Ninth | 9 − 7 | second |
| Eleventh | 11 − 7 | fourth |
| Thirteenth | 13 − 7 | sixth |
Seven, not eight, because the octave note itself is counted twice — once as the top of the first octave and once as the bottom of the second. That off-by-one is the single most common slip in interval arithmetic, and it comes from the same place as counting the starting note as “one”.
Why bother with the larger names at all? Because in a chord they say something the small ones would hide. A ninth chord stacks its ninth above the seventh; calling that note a second would place it next to the root and lose the fact that it sits on top of a stack. The name records where the note is, not only what it is.
Common mistakes to avoid
- Practising only ascending intervals and calling it interval training. It is a third of the job.
- Subtracting eight instead of seven. A ninth is a second, not a third.
- Expecting a harmonic interval to have a direction. It does not, and hunting for one is what makes them feel impossible at first.
Now play
The drill below is set to mixed: each round comes up ascending, descending, or sounded together, and you do not get to choose which. Four distances — minor third, major third, perfect fifth, major sixth.
Expect it to feel unfair after a drill that only went up. That difference is the thing being trained.