Ask HN: Teach me something new

I didn’t know about that channel but now I’m hooked. Thanks for the tip!

Ever since I learned that the frequency ratio between adjacent keys on a piano is always a constant twelfth root of 2 regardless of whether you're going black-white or white-white, I've been sort of frustrated with the way pianos are designed. Transposing a song to a different key could have been effortless if keys were structured differently, such as with uniformly alternating white and black keys, rather than the 2 black 3 black groups we have now. By optimizing pianos for C major / A minor, we've made everything else so much more difficult. And no other instrument does this afaik. String instruments don't obscure the constant ratios at all, so it's easier to transpose songs on them.

I suspect someone may reply to this with "it'd be harder to keep track of what notes you're on if keys were uniform like that", but I don't think we actually rely on feeling the keys to know where we are. Would be willing to be proven wrong on that. But I suspect simply coloring/shading each fifth and octave differently should do the job, maybe also texturing them differently for the blind.

An electric guitarist usually has a pedalboard that they use to make different guitar tones. Let's approach this like an electrical engineer might.

Time is a straight arrow: call it t.

The guitarist plays, and their guitar pickup records a signal. At any time t, measure the value of this signal's waveform: call it x.

That signal can go into a pedal that maps each value to create an output signal. Call it f(x, t).

The pedal is a linear system when it satisfies f(x1 + x2, t) = f(x1, t) + f(x2, t). In English, you can blend two guitar signals going into a single linear pedal, and it will sound the same as if you used a separate pedal for each guitar.

The pedal is a time-invariant system when it satisfies f(x, t1) = f(x, t2). In English, a time-invariant pedal does not warble over time.

The magic happens when a system is both linear and time-invariant. These systems are so special, we call them "LTI" for short. Feed an LTI system a single, really loud, POP! Something like a clap, or a gunshot. Record the sound of this gunshot, and call it "impulse_response.wav". This file characterizes EVERYTHING about the system. If you know how the system responds to an impulse, you will know how the system responds to any other sound. All you have to do is convolve the sound with the impulse response, i.e. use the contents of impulse_response.wav as a set of weights and pass the sound through it.

The echoes you hear when you speak in a large room is a real-world example of an LTI system. People will go to a cathedral, an open field, or a large tunnel, set up a microphone, and fire a blank pistol. They can go home, convolve the sound of their guitar or voice or whatever with the impulse response, and it will sound exactly like they're in that space! There are whole communities of people making and sharing impulse responses out there, and I just think it's the coolest thing ever.

For any guitarists reading this, I'll bring this back to the pedalboard. Another cool thing about LTI systems is that when you chain multiple of them together, the order does not matter. Reverb, delay, EQ, and wah are all LTI effects. If you've ever wondered why pedal ordering sometimes matters and sometimes doesn't, this is why.

Our eyes are wired up to detect a limited spectrum of wavelengths. Although those wavelengths correspond to a color, not all colors correspond to a wavelength. That’s why OP stated that color is a brain phenomenon.

In statistics, the mean and median are both averages, but are technically quite different. The mean is the sum of all items divided by the number of them, while the median is the middle item in the sorted list. When they are different, this can have strange effects. For example, when estimating engineering tasks, the mean error is often positive while the median is often negative.

This is why your manager believes that engineers are too conservative and always pad estimates, while projects are always late. Indeed, they can learn both these things from observation without realising that they are contradictory. Because humans learn by the most common observation, which is represented by the median, but outcomes can be dominated by the less common, which affect the mean but hardly affect the median.