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This is a client-side WebGL-based spectrogram tool that allows to edit the wavelet function (in GLSL). As a result, it supports custom wavelets.

Another method of visualizing birdsongs is interpreting pitch as direction:

https://github.com/soundshader/soundshader.github.io/tree/ma...

I suggest to call this field of science "birdographics" and its researchers "birdographers".

FWIW, I've been exploring ideas of what bird songs really are. One idea I came up with is "birdglyph" - a distinctive hieroglyph-like picture produced by a birdsong. A few examples:

https://github.com/soundshader/soundshader.github.io/tree/ma...

> how someone can overengineer a solution

If his solution doesn't work with arbitrary number-like objects (matrices at the very least), doesn't support voice input, can't send results via email and can't seamlessy resume the calculations after a hardware failure, it's far from overengineered.

Great map. I suggest to paint active subreddits as bright circles and stale ones as dim circles, so the map would look like Europe viewed from satellite at night.

It writes very convincing pop-sci articles about high energy photons and the like. I see no way how even a proper AI can distinguish it from similar articles written by journalists.

Try green people, blue people, yellow people. Even 'transparent people' returns relevant results.

It sounds this is what I'm doing: taking ACF at equally spaced offsets. Not sure what the sum of ACFs would achieve, but this might turn out a good idea.

It does, but ACF[X] at 0 is the sum of X[i] squares, so when sound gets louder, ACF at 0 also gets higher.

Well, I don't know. My personal reason is that 432 has at least some connection to reality, e.g. half day = 43,200 sec, or speed of light = 432 x 432 miles/sec, or Sun's radius = 432,000 miles. This means that if we take distance that light covers in 1/432 sec, then Sun's radius is exactly 1000 such distances, which is pretty cool.

On the other hand, 440 Hz seems just a random number to me picked by someone with little imagination.

432 vs 440 Hz in music is the equivalent of the C++ vs Java battle. Vivaldi was a proponent of 432 Hz, so it's only when he died, newthinkers had recalibrated pianos to 440 Hz. I believe the newthinkers are simply lacking taste, and rounding 432 to 440 is same as chopping off a chunk of Parthenon to "fix" its proportions from the golden phi ratio to 3/2.

Not really. ACF is defined as a convolution of signal X with itself: XX. But FFT turns a convolution into a dot product: FFT[XX] = FFT[X]·FFT[X], or just |FFT[X]|². But what is this really? If X is a sum of A·cos(2πwt+φ) waves, then FFT[X] is a set of A·exp(iφ) complex numbers. What does |FFT[X]|² do? It turns those complex numbers into A². Inversing this FFT gives a sum of A²·cos(2πwt) waves, so in effect ACF has dropped the phases and squared amplitudes. This is also why ACF have this bright vertical line - this is cos(x) functions piling up together.

Interpreting ACF images:

1. Time progresses from the center to the edge of the circle.

2. Color means note, e.g. A4=432Hz is red, but so is A1, A2 and all other A notes. B is orange, C is yellow, D is green and so on.

3. The amount of fine details is frequency: the higher the frequency, the more fine details you see. If notes of different colors and different frequencies sound simultaneously, e.g. a A2 with a G5, you’ll see a red belt with a few repetitions mixed with a blue belt with 8x more repetitions, so the result will be a purple belt with a fine structure.

For example, on one image below there is a green belt with 10 repetitions. One repetition correponds to 13.5 Hz here (55296 Hz sample rate, 4096 FFT bins), so 10 repetitions is 135 Hz, which corresponds to C3. On another image there is a curious red cross in the center, it’s a red belt with 2 repetitons. That’s 27 Hz, or A0, almost infrasound.

The only way right now is to use the demo and download the sounds yourself (you can use the meows from my link to get the same images):

https://soundshader.github.io/?n=4096&img=2048&acf.lr=5&sr=5...

The xkcd is half-right. Cats are ACFs, not FFTs, because they are even functions in polar coordinates, I mean the left half of the cat mirrors the right half, and the two halves merge nicely, without discontinuities. I probably don't want to know what cats look like with the phase components restored.

Wikipedia is great at obfuscating simple ideas in complex math. The "Efficient computation" explains the idea well, but it could be made even simpler. The amplitude squaring step drops the phase there.

Here are vowels: https://soundshader.github.io/vowels

Hi HN!

I used the meow sounds from https://soundspunos.com/animals/10-cat-meow-sounds.html. I expected to see very little variability in the meows, maybe just 4-5 different types for basic emotions. To my surprise, each “cat meow” has astonishingly colorful, complex and unique structure, unlike human vowels that follow a more or less predictable pattern: https://soundshader.github.io/vowels.

The algorithm behind these images is fairly simple. It computes FFT to decompose the sound into a set of A·cos(2πwt+φ) waves and drops the phase φ to align all cos waves together. This is known as the auto-correlation function (ACF). Before merging them back, it colorizes each wave using its frequency w: the A notes (432·2ⁿ Hz) become red, C notes - green, E notes - blue, and so on. Finally, it merges the colored and aligned cos waves back, using the amplitude A for color opacity, and renders them in polar coordinates, where the radial coordinate is time.

Yep, that's the idea.

Amplitudes are normalized locally, using something like a moving average. Global normalization rarely works because most sounds have high dynamic loudness range.

Hi HN! In my previous post, https://news.ycombinator.com/item?id=25037784, I presented so-called ACF images, where the auto-correlation function of a sound waveform is drawn in polar coordinates. It turned out that ACF images capture a good deal of sound symmetry.

This post is a natural extension of that idea. I've been thinking how to introduce colors into ACF images. ACF splits a waveform into a set of pure cosine waves and aligns them together by removing the phase. The idea is to color each cosine wave with the note it corresponds to, so when these waves are aligned, not only the amplitudes of the waves add up, but also their colors.

Population grows exponentially, housing grows quadratically (as circles around towns and cities). About 20 years ago the two curves had met and since then they've been rapidly diverging.

I'm not a linguist and I don't even know any greek (other than the alphabet I've memorized once), but if "epi" means "above" and "ousia" means "essense", then the meaning of "epiousios" trivially follows.

https://en.wikipedia.org/wiki/Ousia

Are there large Ulam spirals? e.g. 100k x 100k, where each pixel is the density of prime numbers there. Do they show any interesting structure?

Price for the Pro version? I'd buy so long as it comes with Ubuntu/Debian.

Not sure I get the idea about triads. Say the three notes are just sine waves with frequencies 200Hz, 300Hz and 500Hz. What will the graph look like?

I've been trying to find the "true and correct" visualization of music that would reflect its "inner symmetry". I started with an assumption that music is a much simpler entity than drawings, simply because it's one-dimensional. Now I think it's actually more complex because it represents an abstract entity that has no shape, yet has symmetry and for this reason it's so difficult to "draw music". Schopenhauer apparently knew this well:

"Absolutely direct experience of the will is impossible, because it will always be mediated by time, but in first-personal experience of volition and the experience of music the thing in itself is no longer veiled by our other forms of cognitive conditioning."

Yeah, it was mostly mp3 and ogg files. If you're suggesting flac would be better, I don't think flac adds much clarity over a decent 320 kbps mp3.

Compressing that boilerplate into one sentence: "under pressure, contact-electrification occurs between its conductive and dielectric layers, creating an electric charge."

A relevant off-topic: there is a living "meta material" called planarian[1].

[1] https://en.wikipedia.org/wiki/Planarian

I wanted to add that the nature of those thin horizontal layers and the patterns they form is similar to diffraction. A laser beam passing thru a thin slit forms a pattern with the sinc-wave distribution of intensity, and so is FFT of a rectangular window used in these spectrograms makes a sinc-wave shape that "diffracts" the "true" sound frequency.