> *how would I go about measuring the impedance of a speaker*

Use a signal generator. Put the speaker and a 300 ohm resistor in series across the output. Sweep frequency while watching the voltage across the speaker.

Say the signal generator puts out 10V. And say we are not looking for 10% accuracy (we aren't). If the speaker is 3 ohms, the output voltage will be 10V*(3/300)= 0.1V. If the speaker is 30 ohms, the output voltage will be 10V*(30/300)= 1.0V. So you can **very** quickly sweep frequency and see the general trend and the outstanding peaks (and dips if any).

You can calibrate with good resistors and some math. But mostly there are two impedances that matter: the *lowest* midband impedance (which will suck the most power and heat in the amp) and the highest bass and treble peaks (because their ratio to the lowest impedance affects frequency response).

A typical 4-inch speaker in box will be 6Ω at DC and maybe at 20Hz, about 50Ω at 150Hz, about 8Ω at 500Hz, rising above 16Ω above 5KHz.

If the alignment is tuned flat for a zero-Ω source, and you use an 8Ω source (DF=1), then around 500Hz the response will be 8Ω/(8Ω+8Ω)= 1/2 = -6dB relative to the zero-Ω source, at 150Hz it will be 50Ω/(50Ω+8Ω)= 0.86 = -1.3dB relative to the zero-Ω source. In effect the low damping gives a 6dB-1.3dB= 4.7dB bass-bump relative to the zero-Ω source.

DF=1 is kinda like a triode. Most triode amps give DF=2 or 3, so the error is less, like 1dB-2dB. Naked Pentodes give DF=5 or 10 on paper, in practice sometimes limited to 3-5 by transformer losses. A naked pentode can show a BIG bass-boom on a speaker tuned for zero-Ω source. You can tune a speaker different for high-Ω source and get flat response; zero-Ω source design generally gives deeper bass in less box size.

> *speakers whose impedance stays relatively stable under a load?*

The "load" we care about is the air load. For a 4-inch speaker, this will reflect-back as about 10Ω above 2KHz, falling very fast at lower frequencies. We can hardly see that, because the bigger load is the cone+coil mass, which is infinite at DC but falls past 8Ω at 200Hz toward 0.8Ω at 2KHz. So the inside of a speaker is all slanty impedances BUT for low-efficiency (<5%) speakers, the "inside" is a low impedance over the whole working range except its bottom octave. So what we see at the terminals is mostly coil resistance and inductance (and inductance is typically selected for the speaker function).

The main impedance "flaw", then, is the bass resonance. If we could use infinitely limp suspensions in infinite boxes, there would be no bass resonance: impedance would rise smoothly below about 100Hz. In fact we have lots of stiffness, usually selected to tune-up the soft corner of a no-stiffness speaker's response. If the suspension and box had zero losses, the impedance rise would be proportional to midband efficiency, roughly 100:1 or 8Ω for typical 1% efficient speakers. Zero losses never happens, and losses help muffle surround-flap and other incidental flaws, so the impedance peak tends to be 30Ω to 100Ω for 8Ω speakers. Adding loss at bass resonance reduces the impedance peak but also reduces bass output: impedance rise is a necessary part of an optimized speaker.

That's for a single driver. The sins of crossovers are complex. It is possible, with flat drivers, to design a 6dB/8ve crossover with dead-flat impedance through the crossover frequency. If the impedance rose at crossover, total response would dip because less power is being drawn at the higher impedance. In fact we are usually fighting driver droop, which suggests a crossover that dips in impedance to suck more power and compensate the driver droop. But we could go on for 9,999 pages about the complexity of crossovers.