Add to this the quality of the wire used. Is it really copper that you see or copper plated aluminum?
Well, if it's a Hammond part, hopefully copper. There aren't many other places making audio chokes anymore (though I'm sure the Chinese are more than happy to offer their competition).
At high frequency, the applied signal travels as a wave in the space around the wire. To exhibit a choke function, the E-field of that wave must be attenuated or relatively weak, and the H-field enhanced, so that the wave has a high impedance. The ratio E/H has units of ohms: the characteristic impedance of that wave.
Therefore, we can look at the design of a choke, and tell at a glance what its RF properties will be. Not precisely -- the exact waves and reflections at play are very complicated -- but hand-wavingly, we can determine the range of where those complications will lie.
For a simple air-cored solenoid, with a single layer winding, the space around any given turn is dominated by free space (that gives minimum E -- a dielectric constant of 1), and surrounded by neighboring turns. As the neighboring turns will have similar voltages to the given turn, the capacitance (E field) between them is discounted, at least until such frequencies where the circumference of each turn is a sizable fraction of a wavelength. This gives good frequency response, up to the first resonance where the overall length of wire acts as a 1/4 wave antenna (actually, a bit beyond -- choking action is maximal here, because it is parallel resonant, high impedance). At harmonics* above this frequency, there will be peaks and dips in the impedance, and the value as a choke will be diminished (or outright wrong).
(*But note that, because the capacitance discount diminishes as frequency rises, the higher resonances are not harmonic multiples, but actually more closely spaced.)
If we have a tightly packed, multi-layer winding, with plastic (enamel or tape) insulation between turns and layers, we have a poor case on the E-field. These materials have a higher dielectric constant, and so the impedance and resonance will naturally be lower than the electrical length of the winding. The amount of wire needed is also huge to begin with (hundreds of meters, say). We already have two problems, then: the resonant frequency will be low, and the peak impedance will not be very high.
With a laminated iron core, we do have a great advantage on the H-field, because of the high permeability core; but, the core permeability drops quickly beyond a few kHz, until the core's own resistivity (it looks like a shorted turn!) and self-capacitance (it's made of laminated
plates, after all!) dominate in the 10s and 100s of kHz range. Beyond here, the core is basically a lump of iron, irrelevant to whatever impedance the winding exhibits. (Indeed, you can measure this: the impedance of an iron-cored choke is almost identical, with and without the core installed, in the high frequency range.)
For any given turn, deep within a multi-layer winding, it is surrounded on all sides with insulator and metal. The adjacent turns again have some advantage from being at similar voltages, but the layers above and below are more a hindrance to any propagating fields. What's more, because the wave's characteristic impedance is low (maybe 50-100 ohms), and there's so much wire (hundreds of ohms worth, inside a typical 4H 20mA choke, say), the loss of that wave is large. At some frequency, at some point in the winding, the wave simply disappears, and you don't get any benefit from the full depth of the winding -- not only does the core act like a short circuit at high frequencies, but the winding itself does, too!
The effect might be overall similar to the simple solenoid case, but instead of many resonances (impedance peaks and dips), the impedance rises (peaking at a few kHz, perhaps), then falls to a minima (hopefully above 20kHz, where it's still useful for audio purposes!), then just kind of wobbles out to a gently falling impedance (as more and more of the winding becomes inaccessible to the applied wave). The equivalent circuit at high frequency is that of a lossy capacitor.
We can take this mental picture further. Suppose it's not a single choke, but there are two windings on the core, both multilayer. Suppose the inner winding is relatively few turns of heavy wire -- a low impedance secondary, against a high impedance primary, in a tube audio output transformer.
If we apply a signal to the primary winding, at the finish of the winding (on the outside, very distant from the secondary), at high frequencies it will be shielded by the bulk of the primary winding, and the transformation ratio will be extremely low!
If instead, we drive the start of the primary winding, where it is close to the secondary, the wave energy will split and take two paths: one is transformed to the secondary, delivering power; the other burrows deep into the bulk of the primary winding, where (at high frequencies) it becomes lost. Effectively, the bulk of the winding shorts out the (relatively) few turns facing the secondary, and
the turns ratio is unexpectedly high! Indeed, in this situation, the turns ratio rises with frequency, which can cause stability issues for amplifiers (which might expect a simple roll-off at high frequencies, under the assumption that the transformer, well, transforms).
I've not measured this on stock Hammond parts, but I have measured it on no-name "audio transformers", the sort that you'd find in a telephone or transistor radio of old. The ratio might be 1k:8 ohms at low frequency (with a peak winding impedance of 20-50kohms at midband), but the ratio falls by several times in the 100kHz+ range.
Tim