Identifying the interval between two written notes

For the first step, the number of the interval is easy to figure out by counting up lines and spaces, including the lowest note (so, a D up to the E right above it is a second of some kind, D up to A is a fifth, etc.). So now that we know whether it’s a 4th or 7th or whatever, we just have to figure out whether it’s minor, major, augmented, diminished, or perfect (the interval's quality).

I’ve run into two ways students are often taught to identify interval quality, and have a third way that might be helpful to some people. Here they are:

1. Seeing whether the top note fits into the major key signature of the lowest note (often taught in schools). For this to work, students have to be very quick with knowing key signatures given a tonic; not just how many flats or sharps, but all the letters that are affected. It also doesn’t work if the lowest note is D#, G#, A#, or a double sharp or flat. But in many situations it’s fine.

2. Counting up the semitones on a keyboard. First, you need a keyboard, either a real, drawn, or mental one. Then, you just count up the notes, so if we count 3 semitones, we know it’s either a minor 3rd or an augmented 2nd, depending on the spelling. The student has to know the numbers of semitones for the different intervals (e.g. 11 for a major seventh), and to keep enharmonic respellings in mind, but this works well for small intervals.

3. (The McCarthy method!) One technique I’ve used with some good results is to first ignore any accidentals (imagining both notes as natural, white-key notes), figure out the quality of this interval, then put the accidentals back in and adjust. Unisons and octaves are always perfect on white notes, and so are 4ths and 5ths except when the notes are B and F, which make a diminished 5th/augmented 4th. So that just leaves 2nds, 3rds, 6ths, and 7ths. The student has to know that B-C and E-F are semitones; then, if the interval is a 2nd or 3rd that contains one of those pairs, or a 6th or 7th that contains both, it’s minor (e.g., D up to F contains the E-F, so it’s a minor third; D up to C contains E-F and B-C, so it’s minor too). Otherwise, it’s major. Remember to put back in whatever accidentals you took out to find the white-key interval's quality! 

Example: given an Ab up to C: we know it’s a 3rd of some kind; since A up to C contains the B-C semitone, that would be a minor third, but the A has been lowered with a flat, so it’s a major third.

Tip 1: Remember that unisons, 4ths, 5ths, and octaves can’t be minor or major; if they’re 1 semitone smaller than perfect, they’re diminished, and if 1 semitone bigger, augmented. And 2nds, 3rds, 6ths, and 7ths can't be perfect.

Tip 2: Sometimes it's easier to figure out the inverted version of an interval (putting the bottom note above the top one), and then use the inversion formula of making the numbers add to 9, with qualities reversing (major to minor and vice versa, augmented to diminished and vice versa, and perfect stays perfect). So, given a Bb up to an A (a 7th of some kind), putting the Bb above the A is pretty clearly a minor 2nd, which means the original must have been a major 7th (2+7=9, and minor inverts to major).

Tip 3: an interval (of any kind) will retain its quality if you flatten or sharpen both notes. So, for example, if you have an F double sharp and a D sharp, just flatten them both by a semitone to make F sharp and D natural, which is easier to figure out. I always imagine "stripping off" a layer of sharpness or flatness, if that helps.

Whichever method you use at first, after a while you will just know by looking what interval it is!