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原始链接: https://news.ycombinator.com/item?id=40442595

傅里叶分析表明，拨动的琴弦会产生各种泛音，而不仅仅是主音。这些泛音由于其独特的频率和形状而携带不同量的能量。根据个人的观点，要么： 1. 将这些泛音可视化为正弦波，较高的泛音在电桥附近具有更大的能量集中度，或者 2. 假设高音泛音拥有更多的能量，这让我们得出这样的解释：由于物理原理，它们看起来呈正弦曲线。从本质上讲，傅里叶分析揭示了复杂声音（包括乐音）的潜在正弦特性。这一发现对信号处理、物理学和音乐制作等领域具有重大意义。此外，开发人员不断探索实现字符串模拟的新方法，从应用程序到 API，增强用户对这一有趣现象的理解和互动。例如，考虑探索以弦振动的细微差别为中心的教育、音乐、艺术甚至游戏项目。请联系 murat@ayfer.net 或 @moyfer 了解潜在的合作机会。此外，Rust 和 WebAssembly 等编程语言的技术进步有助于改进字符串模拟结果，与现有方法相比，可以实现卓越的音频质量。查看此示例：https://jackschaedler.github.io/karplus-stress-tester/。此外，glicol.js.org 上提供了一个用于 Rust wasm 音频的简单 API。此外，Pluck 是 Apple App Store 上售价 1.99 美元的应用程序，它提供了一个数学弦乐模拟器，具有引人入胜的音频和视觉表示，可以准确描述弹拨的弦乐及其产生的和声。其功能包括仅基于数学计算生成声音，无需外部 MIDI 文件或隐藏音频源。相反，所有方面——从最初的拨弦到随后的泛音——都源于纯正弦，确保了弦乐行为的真实表现。

Plucking strings is usually synthesized using Karplus-Strong synthesis which is a very short delay line loop with a low pass filter. The delay gets excited with a short burst of noise. The length of the delay line tunes the string.

Karplus-Strong can be extended in ways to simulate different types of plucking, acoustic pickup at bridge, or electric pickup at any point along tbe string, and plucked at any point along the string. Body resonance can be simulated etc. It's a pretty fun synth technique to play with. Amazing to take beyond simulating conventional instruments.

Karplus Strong sounds kind of bad though, if your goal is accurate sounds of instruments. The reason it works at all is that the noise generates the initial high harmonics of a pluck, then a low-pass simulates the frequency-dependent decay of those harmonics.

But this is very primitive compared to a massive body of research on better simulation. The delay line works great though, that part hasn't changed.

The algorithm was discovered in 1983, and for how computationally cheap it is, I'd say it's pretty convincing. Waveguide synthesis is a generalization of the same idea, often with more realistic results.

Variations on Karplus-Strong synthesis can yield some pretty wacky, dry and plucky types of sounds. In the original paper, the authors propose a variant of the algorithm which involves randomly alternating the sign (+/-) of every sample in the feedback loop, which creates a lot more atonal information in the signal. There’s also a variation floating around which uses an allpass filter in the feedback loop to introduce inharmonicity in the signal, see for example https://www.youtube.com/watch?v=SpC3t1EVF_Q.

It is great that the author included some known pieces for you to "watch" (click the music icon on the bottom right). Of course one first goes to Bach to test the mettle. While "watching" BWV 578 one thing I immediately noticed was how the rhythm of the counterpoint stood out to me in a new way. I have seen many visualizers (the great https://www.youtube.com/user/smalin/videos deserves mention), but I have found most to have some sort of constant object moving around to visualization the tones (i.e. a ball moving up and down). In this case, there is no "moving object" that we follow and we are instead left with the tones in isolation. I greatly enjoyed seeing how this increased my appreciation of Bach's rhythmic counterpoint as I could see when multiple strings were plucked at the same time with the clear purple coloring. Amazing work!

What I found weird is that there's only one guitar piece in the list: Asturias. The rest is keyboard music. And unfortunately, that piece shows weaknesses in the system. Notes get cut off, the rhythm is wrong, and there was one very loud buzzing sound, which suggests the buffer can't be filled fast enough.

Man, I didn't even notice the icons in the bottom corners. I thought it was just a quick toy on first pass which is a shame because loading existing songs is really cool.

I wonder how many other people close the tab without noticing the buttons like I did.

It does, and very cleverly too. The '?' button explains what's going on - he just takes the fourier analysis of the shape of the string when it's released, and plays tones from that.

The way strings resonate means the tone you hear contains the fundamental tone and a number of higher harmonics of that tone. Depending on where (and how) you play the string you can emphasise the harmonics more or the fundamental tone more.

Here for example is a piece made up largely of the harmonics (Portrait of Tracy Jaco Pastorius) https://www.youtube.com/watch?v=nsZ_1mPOuyk That's an electric bass and the bell-like sounds are harmonics. Basically he's just lightly touching the string in specific places to suppress the fundamental tone so you just hear the harmonics.

Whereas here (Stir it up - Bob Marley and the Wailers) https://www.youtube.com/watch?v=1hwL3S3Gtzs when the bass comes in, the player is holding his hand near the bridge (back of the strings) with the side of the palm resting on the strings to suppress all the harmonics so you only get the fundamental tone and it has this sort of muffled quality (because a lot of the brightness comes from harmonics).

> the player is holding his hand near the bridge (back of the strings) with the side of the palm resting on the strings to suppress all the harmonics so you only get the fundamental tone and it has this sort of muffled quality (because a lot of the brightness comes from harmonics).

Palm muting is one big technique to the more aggressive and chunkier metal sounds[1].

Even if you take out the music theory - or blatant disregard for - except kinda not, it's complicated, the different way you can create sounds with an electric guitar[2] in weird ways is quite amazing.

1: https://www.youtube.com/watch?v=yg4tKoiGoyM

2: https://www.youtube.com/watch?v=H4ax35i6aIY

It's not just where you pluck the string: most electric guitars have a "neck" pickup and a "bridge" pickup (sometimes a third in the middle). The neck pickup is closer to the middle of the string, and the bridge pickup is close to the end of the string. Regardless of where you pluck, the bridge pickup has a significantly more prominent high-end, to the point of being a bit shrill when played in isolation. Typically rock guitarists play rhythm with the neck pickup so they don't overpower the vocalist, then lead with the bridge pickup so they cut through the mix without needing to amp the volume too loudly.

Why is this the case? It is funny that my guitarist's intuition seems very clear about it - "the string is tougher and clickier at the bridge compared to the neck, of course the tone is more shrill" - but in terms of actual analytical evidence I just have to say "something something Fourier coefficients" :) Refining the physical intuition a bit: I believe the boundary at the end of the string dampens lower-frequency (i.e. lower-energy) vibrations faster than higher-frequency vibrations, so the lower harmonics die off more quickly than the higher "nasal" harmonics.

Isn't it just the geometry of the guitar constraining the ends of the string to have zero amplitude? The fundamental has peak amplitude only at the center of the vibrating part of the string. Higher harmonics have peaks in amplitude at multiple places along the string, and the higher the harmonic the closer one of those maxima is to the bridge.

The fundamental result of Fourier analysis is that we are saying the same thing :) Though I should have clarified that the kinetic energy is zero at the "boundary" (ie bridge).

IMO which answer you prefer depends on perspective:

- if you assume a wave can be broken down into sinusoidal overtones then your geometric approach is much more immediate and intuitive: sinusoidal overtones => higher overtones clearly have more kinetic energy near the boundary, just draw a picture.

- if you assume that higher-pitched overtones have more kinetic energy then the physics approach explains why they are sinusoidal. Not the specific shape unless you do the math, but the "gist" of the slope. If the overtones were more like square waves, with no real difference in shape between frequencies beyond the length of the rectangle, then the pickup position wouldn't matter. But they can't be, the overtones have to be more "trapezoidal." And in particular, the lower overtones must have a more gradual slope than the higher overtones.

The geometric approach makes a big (but correct) physical assumption for an easy analytical argument; the physical approach goes the other way, only depending on Newton's laws + a lot of elbow grease.

There is an acoustic version, you can tune it however you like, and choose from all kinds of chords, but once you chose a chord it has to be tuned precisely to that set of notes or it would be "out of tune".

Each course of strings on the webpage somewhat behaves and sounds like an "ovikannel" when you strum it manually.

Here's one that was found hanging on a wall but they were normally attached to an entrance door so the wooden balls would swing against the strings when the door was opened, and play the chime:

https://www.reddit.com/r/finnish/comments/dvd125/my_finnish_...

One of the commenters was quite curious as to what it would sound like. Well about like this.

I should note that this is the same 4 chords as the '50s progression, but a different ordering (I V vi IV vs I vi IV V). One is associated with more recent pop/punk music and the others is more associated with doo-wop.

To flesh this out, the root notes of C and A minor are not that close in the circle of fifths, but the chords sound similar because they share 2 notes (C is spelled C, E, G, and A minor is spelled A, C, E). A common device in major keys is to take a part played over the "1" chord (C in this case) and play it again, or some close variation, over the chord 2 steps down (A minor in this case) to get a "kind of the same, but sadder" version of the same part.

As others said - they're chords. And not just any chords, but chords we know sound great together. (If you haven't seen the 'Pachelbel Rant' yet, you should, it's an entire comedy bit based on the fact that these chords are fundamental to music: https://www.youtube.com/watch?v=uxC1fPE1QEE)

If you click on the little notes in the bottom right, you can pick other sets of chords, which give a different "vibe". (Me, I'm partial to the Andalusian ones)

That's why common advice to people starting the guitar is "Three chords, you can play anything. Four, you control the mood. Five, you're a god among men"

Pachelbel is slightly more complicated than the default here, five chords instead of four (adding iii - F#m in the key of D that he used, or Em in the key of C which is the key that this defaults to). So I guess that makes Pachelbel a god among men.

FYI, in Chrome on Linux, there's a glitchy crackling noise. Maybe a buffer under run or something. It happens a lot more often if you strum lots of strings quickly.

It also happens in Firefox but a lot less.

I also have serious popping in chrome on my mac.

This shouldn't happen.

The main reason is the use of createScriptProcessor.

This should be replaced with AudioWorklet. Use WASM + SharedArraybuffer for calculation.

The visual of picking the strings is great, I spent a lot of time on it, I believe the vote is also a recognition of this.

Here is a similar idea (karplus) implemented with Rust + WASM, which is much better in terms of audio quality:

https://jackschaedler.github.io/karplus-stress-tester/

I also wrote a simple api to use Rust wasm audio here:

https://glicol.js.org/

If you are interested in doing some use cases, leave a message. I am actively maintaining it recently.

It would be nice if he or she described the algorithm in more detail. A common and simple string-synthesis method is called Karplus-Strong, but this sounds a bit better.

Make sure your phone isn’t on mute. On iPhone, the mute button. I was raising the volume to no avail.

Edit: I don’t know why I’m being downvoted, the mute button is very unintuitive. YouTube will play on a web page with mute on, but this page won’t.

I had a fun time making a game using MIDI with some friends for a game jam. There was a godot extension for MIDI (that I ended up mostly cannabalizing to get more control) and I used it to read and animate musical bars in a sort of guitar hero-y setup.

It was a fun project, although the game was a little rough around the edges to say the least.

I did not look at the source code yet, but is this some sorta physics modeling problem? Treat the strings as a a bunch of interconnected balls, then apply the force at point, compute other forces, interpolate a curve through the new state, then compute frequencies based on where the string was plucked? this is pretty cool

My guess is the strings are not modeled as balls balls as continuous lines with a set tension oscillating based on their length and thickness. It's presumably a bunch of trigonometry, but not the most insane modeling problem I've seen. Very cool none the less

Well, this fixed it. I bet there is a lot of confusion for the people reporting it just works, while their phone is on silent. Seems to work on silent if you have headphones on.

I remember haring about someone creating a musical software model that was supposed to allow you to do things that you normally couldn't do i.e. pluck or strum a cymbal.

I tried to find it but never have.

Does anyone else know what it is?

physical modelling synthesis has been around since the 70s. Some instruments are really complicated and require a bunch of FM oscillators to nicely replicate some physical sounds - things like cymbals and other metallic crashes especially.

Very cool project, I love the drawing function, can bring to interesting ideas. Unfortunately, some songs are broken, MIDI file 404. The code tries to parse the empty response, instead of escaping early.

As a musician, it's super interesting looking at the JS source (if you're a developer) and seeing how he applies musical concepts like notes and progressions to code.

Hey all: don't miss the music button in the bottom right!!

You can play classical music on the simulated instruments. This is the nicest thing I've seen in a long time.

reading some of the reactions to this, it amazes me how many free VSTs just need a web interface of some kind to suddenly become interesting and popular.

If you have a DAW there are so many interesting free sound generators on the internet. Just spitfire audio has their free lab VSTs which give you 60 VSTs to play with - and thats just one company.

https://labs.spitfireaudio.com/

Its all just missing the front end a DAW normally provides but is too complicated for people just looking to mess around with sounds.

Doesn't seem like a gag to me. I find this one to be a lot more musically interesting. The "pluckable" demo makes it kind of hard to do anything musically interesting based on the constraints of the screen-based UI.

The blob one harmonizes in a very interesting way. I would love to know the algorithm. Maybe even enough to pull apart the source code or reverse engineer it.

Interesting idea.

I went to share it with some musician friends of mine, but first wanted to give them a TL;DR.

I tried to copy info out of the "?" dialog so that I didn't have to re-type the details but the page blocked the operation. That was enough for me to pass. I don't have time to do extra work to explain someone else's project.

This seems like a case where a more generous take would be productive. The page itself is a tool that intercepts drags, it seems like an oversight, not intentional, that it also intercepts drags on the help page.

I totally agree. Many folks overlook the UX decisions they make when sharing a project. That's why (in the spirit of HN) I began with a compliment and provided information as to why I made the choice.

While I can cop to the fact that some may interpret my comment as "Please don't complain about tangential annoyances—e.g. article or website formats, name collisions, or back-button breakage. They're too common to be interesting." it seems there is an equal and opposite lack of consideration around "Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith. "

Here's the text extracted from a screenshot of the ? provided to ChatGPT so you don't have to do extra work.

Pluck by Murat

A math-based string simulator.

Download on Apple App Store for $1.99 [Image of Apple App Store download button]

- It's fun to have on iPad with multitouch, especially for kids (even 1 year olds). - Support this project

Both the audio and visuals are generated using the same math, rendered at different speeds so the eye can see.

No tricks or audio files are used: everything is calculated from raw sine waves, with a theory of how energy is released in a pluck. - The vibrations are modeled based on how far down the string you pluck from. - The velocity of midi notes are mapped to both pluck position, as well as pluck strength.

This YouTube video of a slow motion string pluck proves that our simulated result is very close to reality. [Embedded YouTube video of slow motion pluck]

Technical details: - Each string is simulated with 12 overtones (integer multiples of the note frequency) - To calculate amplitude of each overtone, we take the Fourier transform of the plucked string at the time the pick is released - Higher frequency overtones decay faster than lower frequency overtones - 72 strings x 12 overtones x 44,100 samples per second = 52,920,000 calculations per second - Audio buffer of 1024 samples are sent to the GPU to compute in parallel on each tick

There are several directions I can take this project from here: 1. Turn it into an interactive educational tool to teach physics of sound, timbre & music. 2. Turn it into a music learning tool for kids where songs are pre-made as chords that the user can pluck to learn rhythm and feel. 3. Turn it into an interactive art installation 4. Turn it into a game where i.e. a bouncing ball plucks the strings & you try to match the melody

If you are interested in any of the above, please get in touch at [email protected] or @moyfer.

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