I have cheats that I use. Use songs and melodies that you already know to identify certain intervals. Always the first two notes.
Minor 2 is easy. Theme from "Jaws".
Major 2: "Happy Birthday" melody, first two notes.
Major 3: same thing or I sing the major triad as an arpeggio.
Minor 3rd: I have several songs that I reference the melody like Ozzy Osbourne's "The Wizard" (harmonica part).
Perfect 4: "Oh, Tannenbaum" melody.
Flatted 5th (aka "tritone"): "Maria" from West Side Story". Perfect 5th: "2001: A Space Odyssey".
Minor 6th: I don't really have anything special. I just recognize the interval natrually. But I'm sure you can find a melody that fits.
Major 6th: The "NBC" network chime which is basically three notes but the first two are a major 6th apart.
Dominant 7th: Typical blues note from the root.
Major 7: Another interval I don't have a particular hack for but again, there are dozens of melodies that reference it.
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