Learning your intervals will allow your ear to instantly recognize the distance between any two pitches. Diatonic intervals are intervals between the first note in a scale to any other note in a scale. 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 video. See below for links and a listener's guide.
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I would say that learning intervals without a fixed root (each interval starts in a random place with no relationship to a key center) is not just difficult, but unnaturally difficult. How often do you have to hear things out of the context of a key? Not often for most people. Does this make this exercise useless? I don't think so. There have been times when I have had to think about intervals when finding the individual notes of a chord. I've also had to rely on intervals when learning music that is very chromatic or constantly strays from a tonal center.
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 34 and 71. Also known as a whole step or a whole tone. If the notes sound close together, it's probably this one. "Mary Had a Little Lamb" begins with a descending major 2nd.
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 descending major 3rd sounds like a doorbell.
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, resolvedsounding 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." The timpani part in the "2001 A Space Odyssey" theme, originally known as "Also Sprach Zarathustra" is a perfect 4th that goes back and forth. If you think you don't know that song, just look it up and I'm sure you've heard it at least parodied before.
Perfect 5th It is common to mix up a perfect 5th for a perfect 4th, and viceversa. 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. "The Flintstones Theme" begins with a descending perfect 5th.
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 chorus in "Man in the Mirror" begins with a descending major 6th.
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. I could give you examples of this being used if I reach deep into jazz, but I'm going to be stubborn and just say "This one sounds distinct, just remember what it sounds like." Okay, here's a tune: "I Love You" by Cole Porter has a descending major 7th. Does this help you? No? I didn't think so.
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. I always think of the guitar riff in "My Sharona" which jumps back and forth between the notes of an octave.
Thanks to @BrandonWalid, Martin Shaw, Tóth Ákos, Austin Kwan, and Rafael Belor for proofwatching this video.
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