How to create large inductors (1H) for audio use?

The primary of a smallish power transformer is on the order of 1 H.

Magnetizing current for such a transformer is on the order of 0.35 A, which means that its inductive impedance is

$$Z = \frac{V}{I} = \frac{120\ \mathrm V}{0.35\ \mathrm A} = 343\ \mathrm{\Omega}$$

This means that the inductance must be

$$L = \frac{Z}{2\pi f} = \frac{343\ \mathrm{\Omega}}{6.2832 \cdot 60\ \mathrm{Hz}} = 0.909\ \mathrm H$$

Inductors in that range, for low frequencies, use the same construction techniques as transformers, but with just the one winding.

They were wound like transformers, as Dave Tweed mentioned. But they were of specific construction that is different from typical power transformers: the laminations were thinner, so they would be low loss at audio frequencies, and they may well have been gapped for linearity.

It may be worth it to look at the audio transformers available for tube amps (such as the ones that Hammond makes, available from www.tubesandmore.com), and either just use them as-is, or rewind them.

It may also be worth it to investigate using the biggest E cores that you can find, and possibly even gapping them with Kapton tape or similar (to do it really right you get the inner leg precision ground, but I'm assuming this is a hobby project, not for production).

Pot cores. The winding was on a simple bobbin - much easier than a toroid - and it is likely to be nearer 3000 than 300 turns (of very fine wire).

The bobbin is then fitted between two ferrite cores which are tightly clamped to virtually eliminate the air gap. Some variants had a moveable slug for fine tuning over a few percent, rather like a radio IF transformer.

Signal levels had to be strictly controlled to limit harmonic distortion as the core started to saturate. (As with today's switching supply cores, there were different ferrites with different characteristics, allowing e.g. lower distortion if you didn't need the highest values of specific inductance).

Useful search term : Vinkor was one of the common makes. I may dig out some datasheets later on...