Pythagoras Was Wrong About Music

12:12 minutes

A marble bust of Pythagoras surrounded by a graphic of music notes and triangles and math equations
Credit: Shutterstock, composite image by Emma Gometz for Science Friday

The ancient Greek philosopher Pythagoras proposed a mathematical argument for what music sounds best to the ear: According to legend, he said listeners preferred music with chords adhering to perfect mathematical ratios, like 3:2. This concept has persisted in modern Western music, specifically for building harmonies.

But new research out of the University of Cambridge disputes this idea. A set of behavioral experiments with more than 4,000 participants in the US and South Korea found that listeners actually prefer chords with a slightly imperfect mathematical ratio, particularly when played with non-Western instruments.

Tim Revell, deputy US editor of New Scientist joins Ira to talk through this story, as well as other big science stories of the week, including a big change to YouTube’s algorithm, a new battery breakthrough for electric cars, and the Smokehouse Creek Fire in Texas.

Segment Guests

Tim Revell

Tim Revell is Executive Editor at New Scientist in London, England.

Segment Transcript

IRA FLATOW: This is Science Friday. I’m Ira Flatow. Later in the hour, a rundown of Florida’s measles outbreak, and the science behind what makes snakes evolutionary superstars.

First, back in ancient Greece, the philosopher Pythagoras proposed a mathematical argument for what music sounds best to the ear. According to legend, Pythagoras said listeners preferred music played in certain perfect mathematical ratios. This concept has persisted in modern Western music, specifically for building harmonies. But it turns out that Pythagoras was wrong.

Joining me to break this down and other science stories of the week, is Tim Revell, Executive Editor for New Scientist and host of the New Scientist weekly podcast. He comes to us from New York City. Welcome back, Tim.

TIM REVELL: Hi. Thanks for having me.

IRA FLATOW: Well, before we go disputing what Pythagoras said, explain to me what he meant by saying music sounds best when notes are in certain mathematical ratios.

TIM REVELL: Yeah. So there’s this story about Pythagoras, that apparently he was walking along the street in ancient Greece, and he heard blacksmiths hammering on metal and noticed that certain combinations of the ringing metal sounded more pleasant than others. This led him to the idea that there are certain frequencies that sound best to the human ear combined together when they are in simple mathematical ratios.

So for example, when those frequencies are in a ratio of 3 to 2, that’s known as a perfect fifth. And when they’re in the ratio of 4 to 3, that’s known as a perfect fourth. Now, this idea has really become canon for Western musical theory, and so it shapes how instruments are tuned and which chords musicians play.

IRA FLATOW: Studies have shown that that is wrong, is what you’re saying.

TIM REVELL: Yeah. So those notes, they do sound good together. But what is certainly not true is that there is some universal, mathematical rule that says this is the only music that sounds good together. In fact, we’re much more sophisticated than that. So a team at the University of Cambridge, they looked to really study this. And they surveyed over 4,000 people in the UK and South Korea, testing them on their perceptions of music. And to do this, they played them different chords in different ratios and asked them what they thought sounded best.

And if Pythagoras was right, well, it should have been these very simple mathematical ratios that rose to the top. But actually, listeners seem to have a very slight preference for chords in imperfect ratios.

IRA FLATOW: But there’s so many different kinds of musical tastes around the world, isn’t there?

TIM REVELL: Yeah. So that’s why this shouldn’t come as too much of a surprise because non-Western music has long been much more open to chords using less mathematically simple ratios, and they have instruments that are tuned in such a way that makes it more easy. So really, what this says is that across the world, musical tastes are more sophisticated than Pythagoras would have us believe.

IRA FLATOW: Let’s move on to our next story, and this one is about one of my favorite topics, those batteries, especially for electric cars. What’s new here?

TIM REVELL: Yes. As I’m sure you know– this it’s one of your favorite topics, electric car batteries– one of the ways in which they are lacking a little is that when the temperature is very cold, they tend to lose charge very quickly. And this actually happened to a colleague of mine recently on a skiing trip in Colorado where driving an electric car, it ran out of charge a little quicker than she was expected and it left her stranded.

So what’s happened now is that a team at Zhejiang University in China has made a breakthrough that could help prevent this kind of problem in the future. They’ve identified a new electrolyte, which is a particularly important part of the battery in which charged particles flow back and forth, that seems to perform and hold up much better at really cold temperatures.

IRA FLATOW: So how does this work? I mean, how much better is it?

TIM REVELL: They’ve done initial experiments with it and also a whole bunch of simulations. And in some tests at minus 94 degrees Fahrenheit, so extremely cold, the battery performed 10,000 times better than a standard battery electrolyte. So really amazing. That’s obviously way colder than most cars will ever experience, but it really shows the potential of the electrolyte.

IRA FLATOW: Yeah. If you’re driving in the South Pole, this is the battery.

TIM REVELL: Yeah, this is the one you want.

IRA FLATOW: Yeah, but it’s good, interesting research, though. We can always learn more about batteries. Let’s move to some big environmental news out of Texas. And I’m talking about this incredible Smokehouse Creek fire that has become the largest wildfire in Texas history. Tell us about this.

TIM REVELL: Yeah. The fire has burned over a million acres in Texas and 25,000 in Oklahoma. And it’s the second largest wildfire in US history and the largest in Texas’s history. And local firefighting groups are saying that it’s only 3% contained at the moment. And homes have been burned down, lampposts melted, power lines disrupted, and two people have died as well.

IRA FLATOW: And is it near any of the large cities in Texas?

TIM REVELL: Yeah. It’s just north of the city of Amarillo, and it’s in the Texas panhandle part of the state.

IRA FLATOW: And it’s not under control at all, is it?

TIM REVELL: No, it’s not under control. And today, the conditions are meant to be a little bit colder, so slightly better for containing the fire. But in Texas, they’ve been experiencing a high heat, high wind. And that is really contributing to the fire, and those conditions are expected to return tomorrow. So the next 24 hours are particularly important.

IRA FLATOW: Sounds like another piece of evidence for climate change in hot, dry places.

TIM REVELL: Yeah. All those high temperatures, high winds– they are all things that climate change is contributing to and will only occur more frequently.

IRA FLATOW: Yeah. OK. Up next is a tech story about YouTube. In the past, we all know that the platform used to send people down extreme political rabbit holes. But is it true the algorithm has changed now?

TIM REVELL: Yeah. This is a rare, good news story about our algorithmic overlords. As you say, YouTube has long had this problem where the video it recommends seemed to very quickly push people towards extreme political content. But in 2019, it made some changes to its algorithm to try to prevent this.

And what’s happened now is that an independent group of researchers at the Swiss Federal institute of Technology has been investigating whether this actually worked. And so to do this, they compared the paths from video to video of a typical user when they’ve got complete control compared to the path recommended by YouTube’s algorithm. And what they found is that YouTube is now actually much less likely to nudge you towards radicalized content than if you just have free rein yourself to find things to watch.

IRA FLATOW: There’s got to be a monetary reason for this because Google that owns YouTube is a huge moneymaker. I imagine they went through this and said, hey, maybe if we change the algorithms, we might help people a little more. They might like us. We might get more people.

TIM REVELL: Yeah. That could definitely be it. It’s also when these platforms become radicalizing places, obviously, lawmakers look at them a little more closely. So maybe that’s part of it too.

IRA FLATOW: I think you got that. And so this poses the question, How responsible are tech platforms for serving up content that could radicalize users, right?

TIM REVELL: That’s a big question. And one of the things YouTube has said in this is that there’s obviously two parts to this. There’s content that is radical by someone’s view. But then there’s content that YouTube actually says shouldn’t be allowed on its platform at all. And one of the things the company says is that according to its own data, it’s now only less than 0.1% of watches that are actually people viewing content that violates YouTube’s own policies. So they’re doing a better job of weeding out the videos it says shouldn’t be allowed.

IRA FLATOW: All right. Let’s shift gears a bit and revisit the saga of the Odysseus Moon Lander. Now, it was literally a week ago we talked about the launch. We were going on the air. We talked about a successful landing. But now it appears, under analysis, it wasn’t as successful as we all thought, right?

TIM REVELL: That’s correct. Yeah. So Odysseus– some people have nicknamed it Odie– it landed on the moon, making it the first American spacecraft to land on the moon in over 50 years. But it didn’t quite go to plan. Odie is on the lunar surface but on its side. So its antenna was supposed to be pointing directly towards Earth to transmit data. But it’s not, which means that getting data back from it has been slower than expected.

And its solar panels have been working. That’s one good part of it. But now a week later, it’s actually lunar night on the moon, so it’s experiencing very dark and cold conditions. And that was always expected, but it’s not actually designed to survive, though. So at the end of lunar night in two weeks time, we may hear from Odie. But this may be the last we hear from it.

IRA FLATOW: Wait a minute. So it landed a week ago, knowing that it’s going to be colder than it’s made to operate. And we knew that going in. I mean–

TIM REVELL: Yeah. We knew that going in. The main objective here was really, could it land softly on the moon and send back some data? And I think you can say it mostly did that. Obviously, it wasn’t perfect. But it mostly did that.

IRA FLATOW: Well, we’ll soon be penning an ode to Odie. Excuse me for that. Well, we love speaking of weird stuff here on Sci Fri. And this next story, I know, is no exception. It’s wild. A new genus of plant has been discovered in Japan. And it’s a very strange one. Describe it please.

TIM REVELL: Yeah. I mean, it’s almost indescribable, this thing. It kind of looks more like a squid or an alien than a plant.


TIM REVELL: Yeah. Part of the reason it looks so weird is that it spends the vast majority of its time underground, only pops up once a year for about a week. And it feeds on fungus. So it doesn’t need chlorophyll, that green pigment that many plants have. And so that means it’s pigmentless. And it has this very strange pale color and looks a bit like a star.

It was found on the island of Kyushu in June 2022– that’s in Japan– by an amateur botanist. But it’s now been confirmed as a completely new genus for the first time.

IRA FLATOW: Wow. If it’s just been discovered, I can’t imagine there are many around. I mean, right? I mean, how many do we think there might be?

TIM REVELL: Yeah. So far, they’ve found five of them. And they reckon that perhaps the entire population might just be 50 plants.

IRA FLATOW: 50 plants could live by themselves and still reproduce and keep going. Wow.

TIM REVELL: Yeah. It’s pretty amazing.

IRA FLATOW: That is amazing. OK. Speaking of amazing, we have a bonus question time. Our last story is about jeans and more environmentally friendly ways to dye them. I mean, is the jeans dyeing industry not quite a perfect fit?

TIM REVELL: Yeah. That’s correct, jeans. There are 4 billion pairs of jeans manufactured every year. So it’s a huge industry. And the dyeing process itself is actually not very environmentally friendly at all. Blue denim in particular is dyed using indigo, along with quite a few harmful chemicals that are part of the process. And that leads to toxic fumes and pollution in wastewater.

What’s happened now is that a team from the Technical University of Denmark has come up with a new process for dyeing jeans that uses a natural precursor to indigo called “indican.” And they estimate that the environmental impact of this new process is 92% less than the usual one.

IRA FLATOW: Wow. So what are the chance we’ll be seeing this anytime soon?

TIM REVELL: Well, with all of these things, there’s a huge industry already using this other process. So there’ll be some time to convert it into something that could be manufactured on a much bigger scale. But one really interesting part of it is, rather than the jeans actually being dyed initially by indican, once the indican has been applied, the color changes afterwards. So you could imagine a future where you buy a pair of jeans that are not yet blue, but once they’ve been out in the sun, they turn the blue color that they will eventually stay.

IRA FLATOW: Wow. That is cool. Tim, you always bring us good stuff. Thanks for taking time to be with us today.

TIM REVELL: Thanks very much for having me.

IRA FLATOW: Tim Revell, Executive Editor for New Scientist, and host of the New Scientist’s weekly podcast. He comes to us from New York.

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