Music And Power Laws

Piano Quintet by Andrew Gustar

Mohamed Kamal

CEO and Cofounder of Unbias

Today, we are focusing on power laws, a mathematical principle widely observed in nature and human systems, and how power laws play a key role in decoding patterns of success in the music industry. 

Understanding these power laws not only provides insight into music consumption trends, but also points to the intricate balance between cultural significance and individual preference in shaping our musical landscape.

To begin, let’s define what a power law is. In simple terms, a power law is a relationship where a change in one quantity leads to a proportional change in the other. Examples of systems where power laws exist include web pages, the intensity of wars, terrorist attacks, wildfires, the population of cities, and the wealth of individuals.

In music, power laws help us describe how often songs are streamed on various platforms. When analyzing streaming numbers of wildly popular songs, we find their patterns exhibit surprisingly similar characteristics. This is indicative of fundamental principles at play.

One such principle is the concept of positive feedback loops, where success breeds success. This effect can also exacerbate inequality within the system by causing a disparity in the popularity of songs. If a song is played frequently, it’s likely to gain even more airplay, while less popular songs tend to remain obscure. This amplification of success is also known as “the rich get richer” theory.

The “rich get richer” theory suggests that as a song or an artist becomes more successful, they are more likely to gain further success regardless of quality. The theory also explains that very successful people can also fall out of fame the fastest, especially with a scandal. 

UK Researcher Andrew Gustar investigated the existence of power laws in the world of music across three distinct contexts: friend’s playlists, concert promoters, and music streaming platforms. He found these laws could emerge through various mechanisms like repeating familiar things, copying others, or making random choices.

I was intrigued by Gustar’s experiment that showcased power laws through random choices. This musical experiment involved 1,000 listeners and a playlist of 1,000 different songs where each listener was able to follow and play songs the other listeners played. 

In week one, every listener picked a random song. In the following weeks, each listener chose a song in one of two ways: 

  1. There was a 5% chance they selected a song at random
  2. There was a 95% probability they picked a song played by a random person the previous week.

After 20 weeks or more, a distinct pattern emerged. The distribution of listeners per song wasn’t even. A few songs had many listeners, while many songs had a few listeners. This pattern signifies a power law distribution and, in this case, emerged from our basic song selection rules. For example, after 20 weeks:

  • A small set of songs, say 10, might each have about 200 listeners
  • Around 100 songs could each have about 50 listeners.
  • The majority of songs, about 890 of 1,000, might each have fewer than 10 listeners.

In addition to the effect of power laws in music, a song’s success can greatly vary with time, quality and genre. For instance, a song’s popularity on Billboard can fluctuate quickly, while at the same time higher quality songs tend to linger longer. Similarly, the popularity of Jazz artists and classical composers changes slowly over time. (I wonder, who’s collecting Beethoven’s royalties?)

My takeaways are A) Obscurity is the norm, not the exception. This is a normal occurrence in the music industry and in nature. Artists shouldn’t be discouraged if they don’t immediately reach high levels of success. This doesn’t necessarily reflect on the quality of their work. (B) Repetitive exposure matters: The three models discussed in the Gustar’s study all have elements of repetition and familiarity influencing success. This means that getting your work heard as often as possible, and through different channels, can significantly contribute to success. This is why the strategy for artists to release a track a week on streaming platforms can increase listeners and fans. It’s a form of repetition.

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