Hearing larger intervals is difficult for most people. After a couple weeks of practicing your intervals, half-steps, whole steps, major and minor thirds, perfect fourths, perfect fifths, and major sixths fall into place, but the remaining few linger on, causing us trouble for eternity.
There’s no reason why we can’t isolate these more difficult intervals and learn to hear them just as easily as we hear a whole-step, we just need to utilize the intervals that we already know well as the foundation to learn these less familiar sounds.
Using the intervals you know to hear more difficult ones: the 2-step method
So you can hear the intervals of a perfect fifth and a half step just fine, but tritones (diminished 5ths, or augmented 4ths) give you trouble. No worries. By using what we’ll call the 2-step method, you’ll quickly grasp tritones.
The idea behind the 2-step method is to hear an interval that is close to the interval you want to hear, and then move via half-step (or whole step in some cases) to the target interval. For instance, if you want to hear a tritone and you can hear/sing perfect fifths and half-steps no problem, then first you sing a perfect fifth, and then sing a half-step below.
The full process would be to sing a note. Now sing a note a perfect fifth above. Now sing a half-step below. Now sing the root again. It looks like this:
We’re calling it the 2-step method because in two steps, you arrive at the target interval. After you practice in the manner just prescribed, you’ll work on just hearing and not singing the second step of the exercise. Sing the first note, hear but don’t sing a perfect fifth above, then hear and sing a half-step below that note. Looks like this:
Once you practice this method for a while, you’ll start to ...