I have a brand new Jackson JS30, and I am already having issues with a weird fluttering sound when I pull of from 15 to 14, 9 to 8, 8 to 7, etc. I can't seem to find anyone else with this problem, yet I have had this same problem on three guitars. I have tried it on multiple amps, and with different cords, as well as taking it to the shop multiple times. Here is a link to the sound. "https://soundcloud.com/porter-larson/fret-fluttering/s-p9y5f"
I highly suspect that the issue here is inadequate muting technique.
You said that you are muting the strings, but we also know that:
- This problem happens on three different guitars,
- The audio you shared sounds exactly like extra unmuted strings ringing out,
- The extra notes that ring out are G, A, and D, which are easily excitable natural harmonics on the EADGBE-tuned guitar, and
- The fluttering can be stopped with additional muting help from a cloth.
This is strong evidence toward a problem with your muting technique.
Next time you hear a flutter, touch each string with your right hand. Hopefully you will find that touching one of the strings stops the flutter. That's the string that you failed to mute.
This may be a nothing burger, but distortions and beat frequencies can be caused by pick-ups too close to the strings. I had a similar distortion on my Peavey Raptor cured by increasing the distance. I don't know if this applies to Humbuckers, but for single coil pick-ups, a starting spacing of 2mm (at the e string) and 2.4mm (at the E string) between the pick-up's magnet and the bottom of the string (this from a video I watched on a Strat setup). Oh, if you have an electronic caliper for measuring, a cool trick to get that elusive distance between string and fret or string and pick-up is to measure the diameter of the string in question and zero the caliper. This now allows you to measure from top of the string to the fret or pick-up while reading the distance from bottom of string to the fret/pick-up. BTW, these calipers are really cheap these days! I just looked and Amazon shows them for as little as $9.99 (although I'd pay closer to $25 to get some quality) Neiko makes a decent one for $20 (Mine's a $150 Mitutoyo). Good Luck & Great Playing!