Does music come from first principles, or is it a cultural product that's a result of a feedback loop between a listener/practitioner and an ambient culture and technological landscape? Parrotting is exactly how we learn music- we hear, and we reproduce what we hear. What you call "deriving music from first principles", I call, "post-facto justification for arbitrary aesthetic tendencies".
Whether the human ear naturally prefers 5/4 (5-limit) over 81/64 (Pythagorean) for the major third, and 6/5 over 32/27 for the minor third, is still something I don’t have solid research on.
As it turns out, the modern western scale is more closely aligned with Pythagorean tuning than with five-limit tuning. In particular, the Pythagorean thirds are closer to modern 12-tone equal tempered thirds than they are to five limit thirds.
>>>Around 1300, the English theorist Walter Odington proposes that major and minor thirds (81:64, 32:27) have ratios close to 5:4 and 6:5 respectively, and that singers lean toward these simpler ratios. His observation may reflect the style of much English polyphony of the period, where thirds often have a pervasive role in the texture and may even serve as closing sonorities.<<<
>>>Beginning with Ramos de Pareja in 1482,Fn11 the simple ratios of Just intonation began to be cited by theorists and used in their divisions of the monochord. [...] an octave is 2:1, a fifth is 3:2, a fourth is 4:3, a pure major third is 5:4, a pure minor third is 6:5. These “six-limit” ratios—the senarius, or senario, as Zarlino calls them—are the basic harmonic intervals. Zarlino attributed almost mystical significance to the senario<<<
This article is paywalled, but to summarize, it makes the case that the 5:4 and 6:5 ratios are ratios musicians naturally drift towards in polyphonic contexts.
Just wanted to say, thank you for the detailed response, I suppose my comment looks a bit glib in comparison. I appreciate this perspective- I knew about some basic elements of tuning and acoustics, but it's fascinating that there's this much structure that you can study in it, I understand the interest.
It reminds me a bit of regular polygons or simple geometry like circles- and it makes sense the Greeks would be interested in both- things that are pleasant and can combine and tile well because of their symmetric and regular properties.
I think my "pushback" was more just at the phrasing of "why" something sounds "good"- I do think when we listen to music, we bring our past and our culture into it, and whether a chord sounds "sad" or "happy" depends on a lot more than just the harmonic structure- I wonder about this concept of "tension" you bring up, I can't tell if you mean something emotional or more mechanical. Is that like something you understand just by crunching the numbers on the ratios?
I've never seen "the n+1 problem" used in a context like this, can you explain what that means? To me "the" n+1 problem is the one where you do your DB queries in a for loop instead of using joins or something like that: https://docs.sentry.io/product/issues/issue-details/performa...
Have you experienced Silvesterabend (New Year's Eve) in a major German city? It feels like a warzone. In the context of fireworks specifically, this image of Germany as an over-regulated nanny state feels particularly at odds with my experience of Germany.
I don't think you have it right- the analogy to woodworking and craftsmanship is a category error and probably misses the broad thrust of the essay.
The goal of a woodworker or craftsman is the production of a finished good. He's arguing that, although it's been convenient to position a mathematician as a
"theorem-producer", that's never really been the aim of mathematics, and that the actual products of mathematics are some kind of "mental software"-
see his references to neuroplasticity. Basically, he's saying that the goal of mathematics is to create abstract structures that allow humans to reason about increasingly complex concepts, and that the "mathematician as theorem producer" is more like a convenient fiction that mathematicians have allowed to persist for too long, and now threatens to endanger the whole practice of mathematics.
"Building an application used to mean orchestrating roles over time: one person designed, another challenged the architecture, a third tested, a fourth deployed."
What? That's not my experience at all, this lost me very quickly.
I'm sure the author means well, but it comes off as someone who lacks real-world experience sharing what they think is an ideal team structure when building apps.
That's just my opinion, but yeah, the article doesn't resonate with my experience at all, and I've been at this a while.
It reveals the exact type of mindset that could produce an article like this. All they know is waterfall, so they see agentic coding and think: "you know what we need? More waterfall"
A few examples come to mind: the 20 or so nazi psychiatrists who classified over 200,000 people as "unfit" to justify their "euthanasia". The USSR using the term "sluggish schizophrenia" to institutionalize dissidents without trial. And the whole "drapetomania" thing which was the mental illness of black slaves that kept running away.
This is very common. Psychiatry has been used as a weapon since its very beginning.
Just trying to understand your point here- so non-westerners are primitive and irrational, unlike the West, led by Donald Trump, champion of rational, elevated discourse?
He's right. Moral self-righteousness aside, Hollywood was a window for many of us in "developing countries" to a better world. Yeah, it was an idealized version of reality, but that's how many of us discovered science, athleticism or sexual freedom, for example.
I don't disagree that you got a window into American values, I just don't agree that proximity to American values is the same as civilization versus primitivism.
Revolutionary terror in 1789 wasn't about killing the Bourgeisie- the French Revolution was a Bourgeois revolution- the Revolution was about overthrowing the Aristocracy, the nobles, the people with, as you say, titles- Being Bourgeois generally meant that you're common-born but well-educated and moneyed.
The fact that the Bourgeois of France were growing in real power, but completely unrepresented in the formal political systems in France, was one of the major pressure points that caused the entire system to explode into Revolutionary violence.
I think you're right to point out the irony that revolutionary violence mostly affected the common man, and not the aristocracy, but the "enemies of the revolution" were nobles, clergy, and their sympathizers (perceived or otherwise), not "the bourgeoisie".
Proletarian revolutions against the Bourgeois don't really happen until there IS an urban proletariat in the first place- in pre-industrial 1789, the bourgeois and the sans-culottes were grouped together socially in the "Third Estate".
where a huge amount of influential accounts posing as American patriots were actually essentially content-farmers from the global south?
For my 2 cents, I consider X in 2025 (which is very different from Twitter in 2011!) to be basically an anonymous imageboard like 4Chan, mostly full of straight-up noise and largely decoupled from reality, with the only reliable signal being a bias towards information that is personally flattering or aligned with Elon Musk.
I don't know that I'd ever seriously listen to a place like 4Chan for guidance about how to tie my own shoes, much less how to govern an entire nation.
You would notice that X responded to concerns over such accounts directly, without being forced to do anything by the EU and in a much more sensible way than what the EU is demanding.
>influential accounts posing as American patriots were actually essentially content-farmers from the global south?
Which is why I'd like a button that allows me to geofence the global south from posting on my social media feeds. Their opinions are irrelevant anyway to the political issues happening in my EU country since they're not citizens and can't vote in the elections here, so there's no loss there, same how I'm not gonna go on Indian social media boards and lecture them about how to solve the conflict with Pakistan because it doesn't concern me.
Like for example a popular blogger from my country solved this issue by paywalling his blog behind a 5 Euro monthly Patreon fee. Suddenly, no more bots, trolls, low quality rage baiters and Asian scammers. Gatekeeping is important if you want to maintain quality and don't have massive resources for moderation.
Also this isn't anything new. Spying, botting and farming on the internet aka information warfare in general, has been happening for 50+ years now. We're now just more aware of it because now "others" are doing it to "us", when in the past it was mostly "we" who were doing it to "them".
>I don't know that I'd ever seriously listen to a place like 4Chan for guidance about how to tie my own shoes, much less how to govern an entire nation.
[...]mostly full of straight-up noise and largely decoupled from reality
If it's so decoupled from reality, then how come both X and 4Chan were bang on about how Trump was gonna win the US presidential election both times, despite mainstream media telling otherwise from their "polls" as sources?
You can chose not to listen to X and 4Chan the same way how you can choose to piss against the wind, but then don't be surprised you end up getting wet and covered in piss.
I think mostly Meta's and X's platforms have the big issue with asian posters masquerading as westerners, since they get paid for the engagement rage-bait they generate there, but 4Chat doesn't pay you, so they have no incentive to spend their time commenting there when they can farm on X for cash. 4Chan is mostly infested by glowies though, both US and Israeli.
reply