Pythagoras was wrong: There are no universal musical harmonies, study finds | Hacker News Reader

Pythagoras was wrong: There are no universal musical harmonies, study finds

phys.org

2 pointspseudolus6 comments

Has anyone ever doubted this in the last two hundred years? At least since the invention and spread of the well-tempered tuning, it has been clear that people's aesthetic sensibilities are a matter of habit.

> The researchers were surprised to find a significant preference for slight imperfection, or 'inharmonicity.'

Such findings always remind me of this study carried out by the well-known ergonomics professor Grandjean at ETH Zurich. It was about what most people consider to be the ideal desk height. The result was met with international skepticism, and in fact it turned out that the participants in the study were primarily people who had worked at the ETH with the federal furniture there and were therefore used to this table height as being ideal. The researchers of this study should therefore not be surprised.

> it has been clear that people's aesthetic sensibilities are a matter of habit

It's not as simple as that. It's a combination of universal patterns (for example unexpected loud & deep sound will trigger specific response in most people) and subjective preferences based on past experiences (which also seems to form by following certain universal patterns).

The title of this article is a little clickbaity. What this study finds is that timbre can modify what we perceive as consonant, and it seems that can explain evolution of inharmonic scales in non-Western musical traditions.

> The researchers were surprised to find a significant preference for slight imperfection, or 'inharmonicity.'

Preferences for slight deviations disappeared upon elimination of the upper harmonics:

> We identified a subtle but interesting phenomenon for tones with strong upper harmonics, whereby listeners prefer slight deviations from exact just intonation ... This effect seems explainable by listeners enjoying slow beats, a phenomenon that can be straightforwardly incorporated into interference models of consonance perception. Consistent with this hypothesis, these preferences for slight deviations disappeared upon elimination of the upper harmonics, presumably because this eliminates the slow beating effect.

But I agree that there are lots of ways things can go wrong in studies like these. That table height study blunder is hilarious. I haven't heard of it before.

I've just read the article, not the paper (yet). From the article it's pretty clear that they are talking about chords, not (just) the spectral composition of sounds. Since the invention of tempered tuning in the 17th century, the notes in a chord are no longer in an even numbered ratio, but usually in a multiple of the twelfth root of two. It is rather the case that people today consider a chord to sound strange if it is made up of whole-number ratios, which again indicates habituation. Besides, Pythagoras' theory also referred to specific tone intervals, not the spectral composition of arbitrary sounds. Anyway, let me first read the paper to see what they actually claim to have found out.

Sorry, I wasn't clear. They found out that timbre can modify which intervals/chords/tuning we perceive as consonant.

I have heard that :

if you avoid exposure to equal temperament (western compromise tuning that allows 12 keys with equal deviation from the Pythagorean (integer) ratios) , and only listen to "just intonation" - various tunings that adhere to the integer ratios, you get used to the just intonations and find equal temperament "out of tune". I don't get the impression this study tried to use subjects who weren't still hearing "regular" music.

The study directly investigate this, you will find it in Fig. 8: Dyadic preferences for (mis)tunings of the major 3rd. What you see is that (modern) people preferences are NEITHER to just intonation (integer ratios) OR equal temperament (which they were presumably exposed to). What happens that depends on timbre (and this is new too) participant prefer tuning that slightly deviates from just intonation but NOT exactly equal temperament!!

Full study: https://www.nature.com/articles/s41467-024-45812-z

Reply on news.ycombinator.com