Answers to this question, which I first asked on Writers' SE, suggest that's the case.
Is this a standard in general use? If so, what's the theory behind it? Is it something like one chord and one extra note?
And how are "four notes" defined? Does A, B,C,D constitute "four notes," or is that true only if the are in the same times? E.g. Is four quarter notes different from a half note, a quarter note and two eighth notes, when both sets of notes include ABCD in that order?
This started with Yes, we have no bananas, which shares four notes at the same timing with the famous Hallelujah chorus. Even though no sane person would see the two songs as the same, they were able to convince the court, thus setting the legal precedent. The song actually stole quite a few phrases from different songs, but most of them didn't have any copyright. Here's the lyrics, with every stolen part's lyrics changed to where they were stolen from.
Hallelujah, Bananas Oh bring back my Bonnie to me I dreamt that I dwelt in marble halls the kind that you seldom see I was seeing Nellie home to an old fashioned garden, but Hallelujah, Bananas Oh bring back my Bonnie to me
Unless the four note sequence is already in the public domain (not that uncommon if it was used in classical music from last century or earlier), supposedly it's Prima facie evidence of infringement. This case was unique in that those four notes were the only thing copied from that song and they successfully got royalties.
TO be fair, they DID steal a large number of snippets to make their novelty song.
So while this isn't a law, it is a legal precedent, set by that case.
This four note rule is why "I Am Man" from ninja gaiden arcade changed the third note note of each riff it ripped off to attempt to be legally different from "Iron Man". (iron man was the entrance theme of the wrestlers their boss was totally ripping off of) And is the foundation for many of what is known as "Suspiciously Similar Songs". Most courts are more sane, and can certain make decisions in the spirit of the copyright law, and say "stop trying to rules lawyer, it's an obvious copy!" And sure enough the virtual console version fo this game removed the offending track.
According to the portion of https://en.wikipedia.org/wiki/Lead_sheet that cites "Krasilovsky, M. William; Shemel, Sidney; Gross, John M.; Feinstein, Jonathan (2007), This Business of Music (10th ed.), Billboard Books, ISBN 0-8230-7729-2":
Together, the melody, lyrics and harmony define what a song is. In the music industry and entertainment law, a lead sheet is the document used to describe a song for legal purposes. For example, a lead sheet is the form of a song to which copyright is applied—if a songwriter sues someone for copyright violation, the court will compare lead sheets to determine how much of the song has been copied. Or if a song is considered for an Academy Award or a Grammy, the song is submitted for consideration in the form of a lead sheet.
FYI, a lead sheet consists of a melody, its chord progression, and lyrics (if it has any).
I don't know "how much of the song" is required to be copied for the court to conclude that copyright violation or plagiarism has occurred. It's possible that the precise proportion is very subjective and highly dependent on what song has been copied.
And then there's the mess of how to define a (distinctive enough) arrangement of other composers' works (e.g. "Night of Nights", which is a somewhat drastic arrangement by COOL&CREATE of compositions by ZUN of Touhou fame) for copyright purposes...
