Learning your intervals will allow your ear to instantly recognize the distance between any two pitches. Harmonic intervals are when both notes are played at the same time, as opposed to "melodic" intervals, where they are played separately. The full playlist is available on my Patreon for 1$ with audio downloads, but will gradually be made available on this channel for free. The $ 5 tier gets audio downloads of each exercise. See below for links and a listener's guide.
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Something that really helps to identify harmonic intervals is to sing or hum the two pitches. The ability to isolate these pitches might be difficult at first, but like any skill, it will get better with practice. This might actually be the most difficult to do with perfect intervals because they lock together so perfectly in tune.
Major 2nd - The first two notes in a major scale, and also the distance between MOST notes in a major scale. The only exception is 3-4 and 7-1. Also known as a whole step or a whole tone. A major 2nd sounds somewhat dissonant when played harmonically, which I call a "soft dissonance."
Major 3rd - The first two notes in a major chord. You might confuse this one with the major 2nd because they are both relatively small intervals. The major 3rd has a brightness that the major 2nd does not. A major 3rd has a bright sound when played harmonically, similar to the major 6th. I call this an "imperfect consonance" because while it sounds generally pleasing, it does not have the perfectly in-tune quality that perfect intervals do.
Perfect 4th - Songs that use a perfect 4th tend to go from the 5th scale degree (dominant, or sol), up to the 1st scale degree (tonic, or do.) This results in a very complete, resolved-sounding interval. However, if a song goes from 1 to 4 (tonic to subdominant, or do to fa), it will sound like it needs to resolve down a half step. This interval has less of a bright sound than the major 3rd, and I tend to describe it as "neutral" or "hollow." Perfect 4ths and perfect 5ths can sound nearly identical to the untrained ear, especially when played harmonically. What I like to do is imagine the top note resolving down by a half step (C-F resolving to C-E). A perfect 5th can't really naturally resolve in this way.
Perfect 5th - It is common to mix up a perfect 5th for a perfect 4th, and vice-versa. However, unlike the perfect 4th, the perfect 5th typically doesn't sound like it wants to resolve anywhere. You could say that the perfect 5th is slightly "more perfect" than the perfect 4th, as it occurs naturally in the overtone series. I've always found it to have a somewhat epic sound, which is consistent with some of the melodies that use it. Power chords on the electric guitar are basically just perfect 5ths and have a heavy, natural sound.
Major 6th - If you don't know what an interval is, just guess this one! People have trouble with 6ths because they aren't nearly as common as some of the other intervals. I like to imagine someone yodeling because yodeling tends to be in 6ths. When the major 6th is used in a song, it tends to be the 5th scale degree (dominant, or sol) leaping up to the 3rd scale degree (mediant, or mi). The major 6th is another imperfect consonance but sounds more spread apart than the major 3rd.
Major 7th - This one is very distinct. It has a dissonant, or unresolved sound. The upper note will likely sound like it really wants to resolve upward. If you see this interval in a chord, such as a major 7th chord, it tends to give it a "dreamy" quality. If you listen carefully, you can hear the "beats" in the sound waves, which is where the unevenness of how each separate note vibrates creates a pulsing sound.
Octave- This is the most perfect of all intervals because it is the first in the overtone series and occurs between two notes with the same letter name. An A on a keyboard to the next A on the keyboard is an octave, and so on. It should sound perfectly in tune. Octaves are most commonly mixed up with perfect 5ths, but you should be able to hear that an octave is a much larger jump. It is the biggest melodic jump you're likely to see in most music. An octave is so in tune because of the overtone sequence that it might not even sound like two notes are being played.
Thanks to @BrandonWalid, Martin Shaw, Tóth Ákos, Austin Kwan, and Rafael Belor for proof-watching this video.
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