So it wasnât that Pythagoras was wrong, as he was only basing his views on the instruments he had access to. Itâs the western world trying to apply his theories to all musical instruments and styles, since the world opened up and we discovered the world was not just Europe.
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I donât really see that this is a big deal.
âThe researchers were surprised to find a significant preference for slight imperfection, or âinharmonicity.ââŚâ
Just means that Iâm not the only one that prefers live music with all its little imperfections to âperfectâ recordings that are the result of multiple takes and software tweaking (and donât get me started on autotune)
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To be fair, I think Euclid has to take the blame for that one.
However this is why mathematicians have the greatest chance of immortality. Long after Hendrix is forgotten and the guitar, when Einstein has been shown to be a complete crackpot then kids will still be taught Pythagorasâ theorem it will always be correct and important.
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Couldnât have put it better Ian.
How many people would flock to stadiums or festivals to listen to a recording?
Hereâs hoping our kids will be alive to appreciate this, and not have succumbed to the consequences of the crackpotâs beautiful equation E = mc² 
Maths is a useful (and beautiful) tool that physics uses to describe the laws of the universe we live in 
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Iâm glad the physicists find it useful, itâs becoming much more difficult to find branches without applications these days!
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Physics is everything and mathematics is its language
Quote by Miranda Cheng
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This reminds me a bit of a radio segment I heard several years ago about a book called This is Your Brain on Music. In the segment, they talked about how we generally like predictability so that we can groove along with the tune, but we also appreciate little surprises thrown in to get our attention and keep our interest. One example they gave was Stevie Wonderâs drumming at the beginning of âSuperstition;â for the most part, the pattern is the same, but he does occasionally change a beat here or there. They went on to describe how great composers have been doing similar things for centuries.
Thereâs a lot of great neuroscience of music being done today.
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Thanks for sharing Rogier, very interesting reading andâŚIâm very happy with that quote too 
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An old thread, I know, but an interesting subject.
I agree with @jjw, this research largely endorses Pythagorean ideas.
As to the âwhyâ of what we like in music, any answer given to a âwhyâ question simply begs another why question (any parent of a four-year-old appreciates this) that eventually leads back, rather unhelpfully, to the big bang. No âwhyâ answer is ever truly satisfactory or conclusive. But, taking a less purist perspective, we can point to cultural norms or we can go back to evolutionary hypotheses. I might do both.
As for differences between cultures, there is a lot to be said for the simple idea that we like what is familiar to us, what we grew up with, even what we began to experience (in a slightly muffled way, I presume) in the womb. This applies to most things, not just music.
There is an interesting video https://www.youtube.com/watch?v=-penQWPHJzI done by Adam Neely and Paul Davids where they discuss a guitar with true temperament frets. They, like us, are more familiar with standard harmonically compromised guitars. Paul Davids said something that really stuck with me âThe guitar is an imperfect instrument within an imperfect tuning system.â Yet it is what is familiar to us and we seem to like it just the way it is.
On the other hand, familiarity may be boring. I once had an oboist girlfriend who had grown quite tired of the âpredictableâ patterns of historical classical music, and preferred to play ânew musicâ instead. She and her orchestra friends liked what they liked, and didnât think much of what I liked, yet we shared a cultural heritage.
In other words, you donât even have to stray outside your own culture to find tastes that clash with the popular norm. Thatâs our cultural conundrum: some of us are happy with the standard western cultural fare, some want it more harmonious, and some want it less so.
Iâm sure that Pythagoras knew that people varied, but he was searching for something universal under the noise.
Before I move on to the evolutionary question, itâs worth noting that music that has not been pitch-corrected and quantised sounds natural to us. Too much autotune and quantising and anything human can begin to sound like computer music (Paul Davids jokingly called the true temperament guitar an AI guitar). This may be because we are familiar with imperfection, or it may be something deeper - the slight imperfection on a harmonic base could be a useful marker for humanity. OK, time for DarwinâŚ
The book that @grabhorn cited This is Your Brain on Music by Daniel Levitin - Penguin Books Australia concludes that there are two competing evolutionary hypotheses about why we even like music to begin with:
- Darwinâs idea was that music is a vestige of our original mating rituals. The ability to maintain a good song and dance probably indicated strong lungs, good hearing, good balance, well-toned leg muscles and many other characteristics indicative of good breeding genes. No wonder girls seem fascinated by guys who sing and play guitars!
- The other prevailing hypothesis is that of Steven Pinker, who thinks that music is just a side effect of language. As humans evolved to communicate through speech, our hearing became attuned to subtle modulations of sound, and what they expressed. Sound started to have value for us. This is just as plausible as Darwinâs hypothesis.
So, yes, for some reason we like music, and most of it is harmonic, and harmony is a feature of simple numeric ratios. So to say we like the effect of numbers in music is not controversial, even if other cultures differ. Perhaps Pythagoras was wrong insofar as he may have said our harmonic preferences were ordained by the universe or gods, but I donât know why that would be the subject of a scientific study.
What the research seems to suggest is that people adjusted sliders to positions that cluster around simple harmonics. Without musical training, I would not expect them to find perfect tunings anyway, so I think there is an unfounded assumption there - that experimental subjects had perfect appreciation of the slight discords they selected.
PS: @jokuMuu I read the article and played the rising pitches. I found them quite fascinating.
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Wow, Mark you put some time into it⌠
I can only sayâŚ
I love imperfect thingsâŚand oh so lucky my wife does too
Greetings
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Dear all
The article in the link is a non-peer reviewed ânewsâ type article. I have quickly read the news article. However, the actual study they refer to is published in Nature Communications which is a serious peer reviewed study. I didnât look at the original publication yet. However, authors of these news articles often make wild claims that are not actually claimed by the authors of the original study. They can get away with it because they have not been peer reviewed. So as I tell my students, itâs important to check the original source.
Titles like âScientists refute Pythagorus âŚ.â Can just be click bait sensationalism to get people to read their article.
I know this well to my own detriment. I and my team published some research in the journal Nature. A science journalist wrote a news article saying that âScientists at the university of Lausanne overturned the fundamental principles of geneticsâ. This couldnât have been further from the truth. I was then ridiculed by my colleagues for something I never said or claimed.
So never read between the lines in science.
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@prof_thunder
Youâre right to point that out. So I went and read the Introduction, Results and Discussion sections of the paper, and of course it isnât claiming to refute Pythagoras at all.
The authors report on an extensive series of experiments - enough work to generate a small handful of PhDs, I imagine. They refer to competing models of consonance perception (interference model and harmonicity model) and found evidence in support of both, so neither can be ruled out. They do suggest the harmonicity model has less support than may have been assumed.* They wonder whether this is because we have grown accustomed to the prevailing but imperfectly harmonic equal temperament.
There was a surprisingly long list of qualifications. For example, the authors admit that it may have been preferable to analyse the data at participant (rather than group) level, but that this wasnât practical.
* This, I suppose is where the click-bait title about poor old Pythagoras comes from.
EDIT: I just noticed that the âPythagoras was wrongâ article was provided by Cambridge University, one of the participants in the research. Blimey!
Hilarious 
When science communicators get sucked into clickbaity tendencies. I get it, right. As a science communicator, you want to grab the nonspecialistâs attention and get them to read about some science and learn something. So you sensationalize. Except SO MANY PEOPLE read the title and thatâs the only conclusion they get from the text in the deeper article (let alone going all the way to the primary literature).
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Sorry, you all lost me at âPyâ ⌠make mine a steak and cheese thanks.
Sounds like your colleagues need to be told this, too 
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They do 
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