Mnemonics is totally how it works for me. I can hear songs in my head in tune. Through learning to play guitar, I've memorized songs for each note, by the first chord of each song.

A: Jessica, Allman Brothers

A#: In Bloom, Nirvana

B: Out on the Weekend, Neil Young

C: Like a Rolling Stone, Bob Dylan

C#: Say it Aint So, Weezer

D: Moonage Daydream, David Bowie

D#: Woman, John Lennon

E: Melissa, Allman Brothers

F: Smells Like Teen Spirit, Nirvana

F#: Foxy Lady, Jimi Hendrix

G: Santa Monica, Everclear

G#: Brain Stew, Greenday

The only part I'm not completely convinced is a learned skill is being able to internalize the song in the first place.

Intervals are the same.

Minor 2nd: The Jaws theme

Major 2nd: Mary had a Little Lamb

Minor 3rd: What Child is This

Major 3rd: Kumbayah

Perfect 4th: Here Comes the Bride

Tritone: The Simpsons

Perfect 5th: The Star Wars Theme

Minor 6th: Close Every Door to Me

Major 6th: The NBC Theme

Minor 7th: Somewhere(Theres a place for us)

Major 7th: Take on Me

Octave: Somewhere over the Rainbow