Anything that uses 9 of the 12 tones in a Western standard equally tempered octave, for starters. So, if it changes key at any point it is very likely to find that it uses 9 tones or more.

Anything written in a melodic minor scale will use 10 tones, as the 6th and 7th of the melodic minor scale are sharpened on ascending movement but not sharpened on descending. Assuming it uses every note in the scale of course - not all melodies do. But if you start off saying 8 tones per octave you're probably not making space for sharpened 6ths by ignoring the 4ths.

Just about anything written by Schoenberg in accordance with his theory of tone rows and atonality, where the idea is to use all 12 tones as a fundamental component of your melody so that you're not constrained by the notion he didn't like of a tonal centre. Okay so this isn't a popular genre, because it turns out most people who aren't Schoenberg really rather like tonal music. (Yes, that's an oversimplification of his ideas, he did a lot more for music than that).

I think the author of the article has exaggerated the claims about "every possible melody", because given the people who did it are musicians themselves they must be well aware that they've ignored a large swathe of music, and that's before we've even considered tuning systems which don't have 12 tones per octave.

You're missing anything that uses notes outside of a typical diatonic scale. Example: The first 2 notes of the popular piano piece Fur Elise. It uses an Eb. The piece is in A-minor/C-major and Eb isn't in that scale. That piece also uses a G#. The addition of the Eb and G# means you need at least 9 tones to represent that melody.

Many Spanish songs use what's called the Andalusian Cadence which will use the equivalent of that G# in melodies too as well as the non-sharped note.

Any blues singing will use that "blue" note that is off the diatonic scale.

A song like Jamiroquai's Picture of My Life has a little color note that feature prominantly in the melody in the opening line "... I can follow through." The note on "through".

Though you asked for an example... but maybe its best to show a counter-example instead? Here's the Imperial Death March played in a Major-scale, instead of a minor scale.

https://www.youtube.com/watch?v=B9MShtCg4fk

If everything was in an 8-note (no accidental, transpositions only) measure, they'd sound like "Vader's redemption".

To sound sad, you MUST shift to a minor key. A minor key has sharps and flats to create tension. Any "sad sounding" song cannot be properly played in a major key.

"Maria, I just met a girl named Maria" in the first two notes; it's Lydian. Or if you pretend it starts on the IV, then the 7th note won't fit for being outside the octave.

Yoda's theme from star wars... first three notes of the Simpsons theme...

Pretty much any song by Nirvana... like Lithium, major 3rd, flat 6, flat 7 - that's not even a normal mode.

"La la la" from Buble's "Everything" for an easy listening example.

If it is all possibilities of 12 beats and below, then presumably it includes a measure + a partial measure of even 7, 9, 10 and 11-beat measures.

But for an example: "Turn it on again" by Genesis is a 13-beat verse. The chorus I think is maybe in 4. You could turn to King Crimson for longer beats.

Shifting meters (Stravinsky's Rite of Spring), quarter tone music (Charles Ives), other alternate scales (check out Okros Ensemble), Take 5 (5/4 meter). The title is absurd because there is virtually an infinite number of melodies.

Anything with a sixteenth note or faster.

Anything not in 4/4.

Anything not in C major.