I have a little homemade transmitter I use to transmit to my antique radios. When I look at the antenna out with my Hantek DSo5072P in FFT mode, I see the fundamental frequency of 1140 khz and the 2nd harmonic of 2280 khz. But I also have a harmonic below the fundamental and above at 570 khz.

I thought harmonics were like 1st, 2nd, 3rd etc and always going up from the fundamental. But this shows them below and above. Even on battery I see these.

You aren't starting with an oscillator at 570KHz and doubling to your final frequency are you? That's too easy an explanation.

Could it possibly be an image generated in your spectrum analyzer?

It could also be a parasitic oscillation in your transmitter. That can happen if an RF choke resonates with a bypass capacitor at an inopportune frequency. If that were to happen near half the desired frequency, it would have a tendency to "lock in" with the main signal.

Here's another tidbit, if I adjust the variable resistor from the oscillator section (collector) to the base of the RF amp such that the "half" harmonic disappears, then the radio behind me doesn't sound very good. At the moment the "half" harmonic reappears, the radio sounds better.
All that you suggest could be true. 1st I'm measuring it with a Hantek, it's probable not the best. 2nd the transmitter is fairly simple 3 transistor job, audio amp to Hartley oscillator, to RF amp with a coil and variable cap to "tune" the antenna.
I read last night that Hartley oscillator make a lot of harmonics and wonder if that might be the cause.

At any rate, you answered my question. That is half harmonics can exist, or should I say a second fundamental can be produced, which is what I think this is.

Generally signals that are not harmonically related are called spurious signals. That can happen in any transmitter design. How many dB down are the peaks of the undesired signals? How much output does the fundamental have? You could live with the bad stuff if it is not practical to get rid if them, as long as they are attenuated to the point that they are not an issue. Or additional filtering of the output frequency could be added. You ought to be able to determine if the lower frequency is a real signal or some artifact of the test setup or tester if you have a decent signal generator for comparison. Or another transmitter of some sort. If you have a low milliwatts desired signal and the bugs are something like 30 dB down from that, I would not worry about them. Now if you were a pirate broadcaster, with a substantially powerful radiated signal, you might have a problem.

You need to perform several tests. First is to tune the range of the analyzer
slowly around and make sure all the peaks move one direction. If not, you
you have spurious signals. If they do move together, good, but still no absolute
proof they are real.

Second test is to use a high quality radio (a good boatanchor) to look for the
signals at odd multiples of 570.

The peak at 570 moves when the 1140 is moved up and down.

Surprisingly, (to me a novice), I got a weak signal 570.

So what does that mean, is the Harley oscillator putting out 2 frequencies??

For the most part it's not causing an issue, I just am trying to learn something.

Are they moving at the same rate?

The subharmonic should move 1/2 as fast as the fundamental carrier. The second harmonic should move twice as fast: if the fundamental is moved 1 kHz the subharmonic should move 500 Hz while the second harmonic moves 2 kHz.

Be aware I'm just using FFT on a digital scope. That being said as best as I can get the numbers (the band width would not let me see the second harmonic)
Fundamental Sub
998 507
1120 566
1330 664

These numbers are as close as I can move the horizontal position and get the HZ reading. It does seem the sub is moving at half speed.

This is interesting and I'm in uncharted territory. So what does that mean??

I have not yet been able to get the FFT on a scope to give me useful information. The spectrum analyzer is better.

A lot of money though

However, I did learn about sub harmonics, I never had a clue, I thought all harmonics were upward. Time to hit the books for some learning.

You were right the first time. All harmonics are upward. If you have a subharmonic it's due to a specific cause and not normally present in the waveform.

You can play games as well. For instance if you have a wave with many harmonics and filter out the fundamental, it becomes a puzzle to identify the fundamental. It has a sort of parallel in FM where at certain points the carrier disappears.

Have you tried tuning in your low frequency signal on a receiver? If it isn't there, it is an artifact of the scope.

How about a schematic?

does the picture change when you change the parameters of the FFT and the windowing used to compute it ? It also may be that when you FFT a signal on your scope you’re supposed to ignore everything you see to the left of the peak
of the fundamental.

Peter