The harmonics are a function of your particular motors, drives, and the RPM. Tormach's whitepaper about their series 3 upgrades describes the harmonics - not in great detail, but very understandable.
Take this with a grain of salt, as I am no expert... As I understand it, stepper motors are noisy for a number of reasons. One of these is the cogging effect when one of the poles lines up with the coil. The pole snaps in to position, overshoots slightly, bounces back past, and then settles after some number of decreasing amplitude oscillations. At certain speeds this causes detectible noise from a harmonic and Tormach indicated about 10-15IPM is typical given a 5mm (or 0.200") pitch direct drive ballscrew. Think "thump thump thump" and then increase the frequency until the sheet metal vibrates.
On my mill its about 12IPM and the motors are groaning. 12IPM is 60RPM with my 5mm screw No lost steps and no surface finish issues at my level of precision and measuring ability. But they sound horrible. Slower speeds and they are noisy but not annoying; much faster and they just whine a bit.
Here's what I've read or tried myself that can reduce it (or eliminate it):
1. Increasing microsteps. My drives (cheap, but not garbage) are set at 10x microsteps with 200 pole (step) motors. This smooths things out considerably from 5x, but there's still a (lesser) groan around 10-12IPM.
I'm not sure how this can be reconciled with Norppu's statement above because, according to that theory, if you change the pulse p/sec (switch from 1x to 5x to 10x) then the resonant frequency should result in a harmonic at different RPM depending on the microstep setting. Assuming I understand his statement, of course.
I've not found that to be the case in my limited experience - I find that the noise happens at about the same RPM regardless of the pulse frequency; only the amplitude changes with pulse frequency changes.
2. Change drives to a modern, digital version. I'm no electronics guru, but many of the newer name-brand drives claim to reduce noise through various magical sprinkles. I won't begin to speculate what they're doing, but the more expensive ones are probably using some back EMF as a feedback source to constantly adjust the motors to reduce harmonics. Do a search for Trinamics and see what some clever Germans have done with stepper drives.
3. Switch to 3-phase motors & drives. These have 300 poles (steps) and three coils, and I've heard them run and they're much, much less likely to 'groan' - in addition to having a significantly higher top speed before all torque disappears. What I heard may be a combination of the 3-phase motors and high-quality drives and not just the motors themselves, but I'll leave that debate to others.
Note - Tormach changed all three axis motors to 3-phase Leadshine motors & drives when they developed their Series 3 upgrades.
4. If you really want to dive in to black magic, Galil Motion Controls has an interesting video (long) on youtube where they discuss driving a stepper motor a different way. No 'pulses' are sent to each coil; instead they use an encoder and back EMF to continually adjust the energy sent to both coils at the same time. At that point it's not really a simple, cheap stepper motor. They've essentially turned it in to a 2 (or 3) phase high pole-count AC (DC?) servo with potentially infinite positioning (depending on encoder resolution). Very cool, and way over my head. I'm probably butchering the theory, but watch the video and go to Galil's web site for some engineering articles. Those guys are seriously clever.
Anyway, if you want to fiddle around I'd suggest changing to 10x microstepping if your drive supports it. You'll also need to make sure your controller and BOB can support the increased pulse frequency, as you might run in to problems during rapid moves if the commanded motor RPM bounces off the optocoupler rev limiter. I've got no clue about your hardware, but if you were running at 1000 pulses per rev, I'll hazard a guess that was at 5x microsteps. And now you're at 16x - have you tried moving at high speeds yet?
Articles from Gecko Drive indicate there's really no benefit beyond 10x - either with smoothing or positional accuracy since it's impossible for the drive to hold a motor between two poles with that precision (it wants to oscillate). Even with a fine resolution encoder the motor will possible be dithering - or worse you'll command a number of steps and it won't/can't move that tiny amount - then bang, it moves all xxx number of little microsteps all at once.
I'm hoping there are some folks who can correct any gross errors I've put down here.
Good luck,
Ralph