I'm working on a 16-bit game. I need to replicate with a synth this sword sound
How can I do?
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Metallic sounds are pretty much impossible with subtractive synth, unless it's subtractive that does analog style fm. Fm is definitely way to go if you want metallic sounds.
Not exactly what you are asking for, but sound of 16bit era can be easily replicated by using just very low quality samples or bitcrusher. Start from 11khz 8bit go lower from there. Amiga sound is about 8khz or 4khz. Not sure about game consoles, but if I remember correctly they often used low samplerate 4bit dpcm.
It's totally possible to synthesize this sound, and you don't need any complex techniques to do it. Andy Farnell wrote a book on this stuff, and you should definitely read it if you're interested. All you need for this are a white noise source, envelope, fixed filter bank of about 8 bands and another sine oscillator to add some ringmod. The key is the ringing sound that metals like this make, and that come from the resonant filters. Of course you can't do this with a regular synth, you will need a modular environment like PD, Max or Reaktor or a text language like Supercollider (or lots of others).
Read the book.
I think it just might be too technical to expect to synthesize a real world sound (or if you do, I expect you to have a solid background in math and EE, because this topic is sort of "cutting-edge" in audio signal processing). The sample you provided is clearly not synthetic. Be serious about what you're trying to ask and do (it's simply not possible, there are no tools for synthesizing sword hits from scratch).
How about just buying a sound pack or recording some of your own sword clashes?
I would like to know the theoretical method to make a sword sound. Then I can replicate the procedure in my own synth.
There's no such thing as "theoretical method" other than the mathematical formalism(s) used to perform physical modelling synthesis of bells and metals. I don't expect that you're looking for that when asking for a "theoretical method" (which the involved mathematics specifically is). There are a few VSTs that do physical modelling synthesis however, like Ableton's Collision. But recording is heaps and bounds better for the use that you specify. Physical modelling synths are generally better suited to be used as percussion instruments.
Andy Farnell's Designing Sound is well worth a look if you're interested in procedural audio but to really understand it takes a lot of time and effort, especially if you're not mathematically inclined. In most cases the results won't often fool anyone into thinking they're hearing the real thing but that doesn't seem to be what you're after here.
If you're just trying to emulate the sounds of retro games I'd suggest that manipulating the audio recording would be the most simple option. Bit crush/ downsample, filter, maybe cut off the tail to give it an unnatural sound, maybe see how "bad" pitch/ time stretching changes the sound, all the general lo-fi techniques.