This paper deserves a rant 🧵!

Besides HARKing, there are plenty of other ongoing, institutionalized problems in #science.

Cherry picking, retconning, historic negation &/or narrative reframing to make your results sound surprising (clickbait) all seem to apply here.

www.cam.ac.uk/research/news/pythagoras-was-wrong-there-are-no-universal-musical-harmonies-study-finds

April 08, 2026 - 18:07 UTC

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Agree. That is a very bad click-bait article with overblown conclusions, based on what looks like a reasonable study.
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We asked a lot of people which tones sound pleasant together, which is not quite the same as consonance, which in turn is not a very explanatory concept in harmony. 1/4...
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Part of my complaint stems from the fact that that *is* exactly the definition we've been handed down from Pythagoras, & it ruined (IMO) most research paths that followed since.
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...William Sethares was right about scale choices depending on timbre. Gamelan -> slendro scale. He was right about almost everything in fact. 2/4...
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Listen to the great blues artists of the Delta, or Texas, or The Piedmont, and the Hill music of tge era. We find amazing and pleasurable deviation from western choral standard.
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"pythagoras was wrong" misses that musical understanding was always distributed across cultures.

bianzhong bells (12-tone chromatic, ancient) show parallel discovery across materials and cultures.

what else fossilized into "truth" because the recording language became dominant?
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Yes. Saying that there are "no #universal harmonies" (plural makes it even worse!) really misses the underlying point of harmony describing the coherent combinations of *multiple tones.*

But it also implies (to me) that there is neither a single, unifying explanation to be found through more work.
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Good findings but sensationalist wording.

Enjoyment of small random variations from harmony doesn’t mean harmony doesn’t exist, only that it’s not the whole picture.

Second, Indian music knows thousands of scales. They aren’t western harmonies, but they are still harmonies.
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Right. I guess the 'pop article' (version of the study) at least stays consistently outdated by referencing Pythagoras as if it were still considered valid, with the subtitle arguing against a similar strawman, that I don't imagine many actually believe.

[One True Harmony of the West Fallacy]?
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The famous science communicator/historian Pythagoras passed along many great ideas, as we all know. His original cult ideas include beans & irrational numbers being forbidden.

His argument for those simple ratios is nothing more than literal #numerology. He formed his hypothesis to meet his #bias.
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ICYMI, the "Pythagorean Theorem" didn't come from him, nor "the West."

Nor did anything he said about music intervals.

He repeated what had been known in antiquity for more than 1000 years. He traveled widely, gathered #knowledge & wrote it down.

mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_Pythagoras/
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Subsequently, he presents the terms con/dissonance to frame his simplistic world-view of a type of 'good vs evil' represented in integers. We could replace them w/"delicious & yucky" & capture the same logic.

For the 1st 1000 years or so after this, it's excusable that these were repeated as truth.
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After that, it becomes more pathetic every century.

Was there some truth buried in there? Ofc. But it sure as hell was not number magic. Pythagoras is to Western #jingoism what "Columbus" is to American exceptionalism: a poster boy meme.

#Music history refutes this simplistic, reductionist claim.
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That #history includes the expanding definition for the arbitrary distinction between C/D & increasing # of divisions of the #octave that musicians used & society followed (every song is experimental confirmation!)

"Jazz is Freedom"
~Duke Ellington

Freedom from what? The false dichotomy of C/D!
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#Math refutes this claim, probably most completely by Euler, in Tentamen Novae Theoria Musicae, but even the number 2 was too much for #Pythagorean faulty logic.

The number 2 plays a central role in music & wave interactions. This is lost in the 'harmonic series' that treats integers similarly.
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Further reading:

bsky.app/profile/johncarlosbaez.bsky.social/post/3mffdozhwbs2h
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To expand past the MOAP dichotomy, a relational approach is required, and it's not linear, nor "rational".

This series of numbers contains both C/D relations, aka con/destructive "interference" & co/decoherence, etc.

☂️category = #resonance

#Physics refutes this claim. ⬇️
bsky.app/profile/malthusjohn.bsky.social/post/3mdvjntcts22c
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The actual paper makes the same mistakes as the summary article, just in more academic fashion.

The great problem we have w/our #Information System is that it lacks the kind of #connectivity among sources that would guide later generations past these mistakes, instead of repeating them over & over.
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If there were only some theory that helped explain where "perceptual origins" come from..

#co-evolution

ref
www.nature.com/articles/s41467-024-45812-z
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While this 🧵 starts w/a specific paper & #narrative, it's not meant to imply that it stands alone, quite the opposite.

The #framing by "western science" of Pythagoras as the originator, as well as the numerology-spiritual-emotional narrative by Pythagoras both served to take us down the wrong path.
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As we go back through another 1000 yrs before Greece, the distinction between #musician & shaman or priest blurs, so the spirituality connection is not w/o consistent reason.

AFAICS, the only thing new/different circa Pythagoras was the #language this knowledge was written in & widely translated.
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So not only is "proving Pythagoras wrong" like proving Judas had st to do w/Romans arresting Jesus, just as importantly, there is no western claim on the long search for the mathematical symmetry of 12√2, nor its final calculation.

The Chinese were 1st to recognize that symmetry, so far as we know.
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Using the fundamental #physics phenomenon of #beats, trial & error, and unmatched metallurgy & bell casting skills, the Chinese assembled 12-tone chromatic bronze bell sets like below, 2000-3600 yrs ago.

Essentially 1st uncovering the mass relation to tone as well.

en.wikipedia.org/wiki/Bianzhong
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An excellent source of historical information here, carefully parsed to not include #presentism or the Historian's #Fallacy onto the ancient past.

Digital and physical re-creation of ancient Chinese bells: new understandings and discoveries
Kin Sum Li, 2025
www.nature.com/articles/s41599-024-04133-8
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When I say 'unmatched,' I mean to this day!

The special shape & design of these bells produces a dampened sound that eliminates the normal ringing, enabling them to produce 2 unique & noninterfering (dissonant) tones each.

They had a Norm Tone like modern symphonies, tuned to -20 cents from A440.
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Given that musical instruments pre-date "the west" by 10s of 1000s of yrs, perfected into practice at least 1000 prior to Pythagoras, even his question re. #consonance at the time was misleading. As stated above, he was simply looking to confirm numerology #biases to uphold his cult-like beliefs.
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#History is like this though, a very messy affair, rife w/ errors that can derail progress for centuries.

One last mind-blowing example: because of the subjective focus of Pythagoras, categorical mistakes regarding beats survive to today.

The west credits #Tartini w/discovering beats in 1754!
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This is definitely the most difficult part of the #complex knot to untangle. We find the dangers of reductionism left to be reified by time & convention.

Our inability to compute/utilize nonlinear equations led to #linear workarounds becoming fossilized into hand-wavy, erroneous norms & beliefs.
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< End Part 3 >

You can find the previous parts here

(Pt 1) bsky.app/profile/malthusjohn.bsky.social/post/3md6uv4vkmc2o
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and here:
bsky.app/profile/malthusjohn.bsky.social/post/3mdsqtvbw3s2m
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