4.1M views · Sep 17, 2015 · 4:20 · 2 HN recommenders · 4 mentions · discussed 2015–2026
A minutephysics video explaining why a piano cannot be perfectly tuned, comparing equal temperament with just intonation and the math of harmonics.
Why Hacker News points people here: Commenters link it as a quick, clear explanation of why twelve notes only approximate simple ratios.
“minutephysics had a nice video about the mathematics that go behind piano tuning too.”HN comment, 2019
“A related video on the numbers behind piano music, on why it is mathematically impossible to perfectly tune a piano”
Explains why a piano cannot be perfectly tuned mathematically.
A related video on the numbers behind piano music, on why it is mathematically impossible to perfectly tune a piano : this video
“minutephysics had a nice video about the mathematics that go behind piano tuning too.”
The mathematics behind piano tuning.
minutephysics had a nice video about the mathematics that go behind piano tuning too. "Why It's Impossible to Tune a Piano" this video
“I like this video for explanation”
Explains why 12 notes approximate simple ratios.
I can help with a couple of these. 12 notes is a kludge, because powers of 2^(1/12) well approximate simple ratios. These simple ratios (such as 3:2) sound good. I like this video for explanation: this video Also, the reason that the letters are in the wrong order is that we're playing the wrong scale. The monks who invented the scale usually sang in A-minor (so we use the first letter for that scale). Nowadays, we use the major scale, which has the same spacing between notes, but in a different order. It just so happens that C-major has the same notes as A-minor, so that's why we count from C. A great channel for this is Michael New, he explains everything very clearly: link Music, much like language, has a lot of technical debt.
“have a MinutePhysics take on how the common 12 note western scale falls apart”
Example of how the 12-note western scale falls apart.
To +1 the "no objective foundation": browse music theory research a bit! There's a ton of caveats and poor-sounding fits and whatnot for literally every approach, and there's endless discussion of it. E.g. have a MinutePhysics take on how the common 12 note western scale falls apart: this video And that's before even getting into completely alternate approaches, or how strongly harmonics affect perception: link or link (maybe to clarify: there are objective aspects , in that sound is measurable. but there is nothing like a "grand unified theory" that covers all music, nor are roughly any of the popular ones internally consistent - it's far, far too varied for that, and physics often doesn't allow the desired consistency, causing more variety)
