An interval is the distance between two notes.
Let’s start with a scale.
Scales are made up of steps, meaning each note is next to each other. Steps are either whole or half. Steps are also called seconds. Whole step = major second. Half step = minor second. The G major scale above is WWHWWWH: G-A, A-B, C-D, D-E, E-F# are all major seconds or whole steps, and B-C and F#-G are both minor seconds or half steps. Sometimes we use a number of half steps within a larger interval to identify it; for example, a whole step is two half steps.
Even numbered intervals, seconds, fourths, sixths, octaves, etc., all have a line and a space note:
Odd number intervals, thirds, fifths, sevenths, etc., all have both lines or both spaces:
Intervals can be harmonic (stacked, as above) or melodic (sequential, as below).
Seconds, thirds, sixths, and sevenths can all be major or minor:
Minor second: 1 half step
Major second: 2 half steps
minor third: 3 half steps
Major third: 4 half steps
Minor sixth: 8 half steps
Major sixth: 9 half steps
Minor seventh: 10 half steps
Major seventh: 11 half steps
However, this is not necessarily the easiest way to think about it. Using solfège helps me a lot. Major thirds are Do-mi, fa-la, or so-ti. Minor thirds are mi-so, la-do, re-fa, and ti-re. Sixths are inversions of thirds, so they use the same solfège, just going a different direction – here’s do up to mi, and mi up to do:
An inversion will be the opposite quality – a major third inverts to a minor sixth, and a minor third inverts to a major sixth. Seconds are inversions of sevenths and work the same way. If you mostly work in contexts of major keys you’ll want to identify intervals by solfège for each type – or what interval any two given solfège make, as another way of thinking. (Post on solfège: https://functionalanalysis.blog/2017/06/13/solfege/ and following post on hearing intervals with more solfège: https://functionalanalysis.blog/2017/06/21/intervals-2/ )
If you’re working on reading intervals, I recommend making flash cards with every possible third, second, etc. in a given clef on one side, both stacked and separate. Make sure to use sharps and flats: if you have a minor third, increase the top note by one half step by adding a sharp (or the bottom note down with a flat) to make a major third, and vice versa with making major into minor. Larger intervals are often trickier, because the notes don’t touch on the page, so you might want to spend more time on sixths and sevenths.
Fourths and fifths are either perfect, diminished (smaller), or augmented (larger):
P4 (5 half steps), aug4 (6 half steps), P5 (7 half steps), dim5 (8 half steps)
There are lots of possible solfège for perfect intervals, but the aug4/dim5 is often ti-fa.
Augmented and diminished intervals are a bit weird and definitely harder to sing. Besides augmented fourths and diminished fifths, two common weirder intervals are diminished sevenths and augmented seconds:
dim7 (9 half steps), aug2 (3 half steps)
Both of these intervals are commonly ti-le from a minor key.
A multitude of uncommon diminished/augmented intervals are possible, but we’ll start with that for the moment.
Here are some intervals to practice identifying:
Next post will be hearing intervals (and more details, so ask any questions in the comments!)