What makes some music so enjoyable, and can science help us engineer the perfect pop song?

A group of researchers who statistically analyzed tens of thousands of chord progressions in classic U.S. Billboard hits say they have found the answer, and it lies in the right combination of uncertainty and surprise.

The data could even assist songwriters trying to craft the next chart topper, Vincent Cheung of the Max Planck Institute for Human Cognitive and Brain Science in Germany told AFP.

"It is fascinating that humans can derive pleasure from a piece of music just by how sounds are ordered over time," Cheung, who led the study, said.

Composers know intuitively that expectancy plays a big part in how much pleasure can be derived from music, but the exact relationship has remained hazy.

Writing in the journal Current Biology on Thursday, Cheung and his co-authors selected 745 classic U.S. Billboard pop songs from 1958 to 1991, including "Ob-La-Di, Ob-La-Da" by The Beatles, UB40's "Red Red Wine" and ABBA's "Knowing Me, Knowing You."

They then used a machine learning model to mathematically quantify the level of uncertainty and surprise of 80,000 chord progressions relative to one another, and played a small selection to around 80 human test subjects connected to magnetic resonance imaging brain scanners.

The scientists found that when the test subjects were relatively certain about what chord to expect next, they found it pleasant to be surprised instead.

By contrast, when individuals were uncertain about what to expect next, they then found it pleasurable when subsequent chords weren't surprising.

Musical pleasure itself was reflected in the brain's amygdala, hippocampus and auditory cortex. These regions are respectively associated with processing emotions, learning and memory, and processing sound.

Contrary to previous research, the team found that the nucleus accumbens – a region that processes reward expectation and had been thought to play a role in musical pleasure – only reflected uncertainty.

Cheung explained that he and his colleagues decided to strip the music down to just chords because lyrics and melody could remind listeners of associations attached to songs, thereby contaminating the experiment.

But, he added, the technique could equally be applied to investigate melodies. Cheung is also interested in understanding whether the findings remain similar for other genres such as jazz, or non-Western musical traditions including those from China and Africa.

Future research does not need to be confined to music: "When we look at somebody doing a very cool dance move, that's also linked to expectancy," said Cheung. Joke-telling also falls in this category.

The study falls into the relatively new field of computational musicology, which sits at the intersection of science and art.

So, could data help unlock the magic formula for song writing?

"It is an important feature that could be exploited but it wouldn't be the only thing that could be used to create a pop song," said Cheung, cautioning that the work looked at pleasurable chord progressions in isolation.

In the study, the team found the three highest rated chord progressions appeared in "Invisible Touch" by 1980s English band Genesis, 1968 hit "Hooked On A Feeling" by B. J. Thomas and The Beatles' classic "Ob-La-Di, Ob-La-Da."