Air core is ok, but.
1. Self inductance in an unmitigated field clumps. You can easily see this by unwinding a hockey puck style air core inductor and measuring the inductance with each turn removed. Never will you have the smooth loss of inductance that model / theory of Maxwell promise.
2. Amorphous, metglass, core is not an answer I would propose for anything but the huge power station devices it was designed for. Especially if it is combined with the usual massive amounts of mylar in the coil, as is typical Lundahl practice. What follows is hotly denied by individuals whose calculators are much more active and refined than their senses.
The core provides the potential of a magnet, each sheet or turn making one potential field strength magnetic map. The coil provides a bunch of turns of wire that act in three discrete categories.
1. First is to carry the constituent parts of the voltage signal, this signal goes through numerous stops and starts with each change in tangence of that signal. With every stop, called static electricity by some, called an E Field print by me, a complete magnet is formed in the window of the core inwhat ever shape it holds. When this occurs the electron cloud, that all of the electrical names really are, prints across dielectric membranes, air, water, vacuum, etc., to find place holder electrons that are free to accept an opposite charge. If the various members of this dielectric / E Field circuit have too high a linking threshold some of the E Field print will be lost If the E field print reaches too far afield, the print will be distorted in time / phase in its reconstitution and B Field activity, towards the next change in signal vector. This finding of free electrons gets easier as the initial charge threshold is breached. This is the only ageing that occurs in a transformer. (here come the quiet and calm refutations that this is not proven and does not follow accepted models of electomagnetic behaviour) Bah!!
These E Field print and B Field release characteristics are essentially occurring within the entire confines of the amplifier and if connected by Litz cables to a fast preamp, there also. The time boundary for a good amplifier is under 2000 nanoseconds so one E Field print happens at a time, for a given signal trace, within the amp. Of course, there are an impossible to comprehend number of signal traces, in different stages of their activities, during a moment of a symphony passage.
2. Second is to charge the potential magnets to their field strength map potential by electrons moving in wires and creating flux. As the flux links to form the actual flux charge, that resonates within the core, any discontinuity in the shape of the field strength map, for each of these thin magnets, distorts that flux charge and changes the vector of those force "lines", which are actually a field gradient, but that gets difficult to think about, so, back to lines.
Regular E/I core, laminated as in a power transformer in a 1X1 alternating pattern, displays a diamond shape of linear transform volume of flux lines rather than the rectangular shape of the window. This occurs because the fringe flux lines balloon, as they cross the E/I gap, and constrict the adjacent E's on both sides. This causes the field strength map potential, from the E Field, to be distorted by a non uniform activity in the core. These flux charge lines cut the secondary and create an instantaneous B Field that also stops and starts.
3. The E Field links to all adjacent dielectric materials and if the barrier between the primary and secondary has a high threshold for electron linkage, large scale, low amplitude signals are going to link elsewhere. This means a slight displacement in time when they release to the resultant B Field and the potential of them not being understood by the correlator in your brain and ignored as noise. High threshold materials can be discovered by rubbing them in your dry hair and seeing how long they will stick to a wall. Mylar and Kapton being among the worst in this sense.
If the dielectric circuit provides a high threshold (dielectric constant number) throughout the primary, very little space not occupied by wire in the secondary, and an abundance of free electrons, but with a low dielectric constant number, in the material used as the barrier between primary and secondary, then the E Field electrons print very clearly and at breathtakingly low field strengths.
When you have an unmitigated primary and secondary and the E Field cannot effectivly print field strength map magnets, the extreme low level, low frequency content, of high frequency signals, is compromised and the position in the time stream of the impact of hitting a Glock, for example, will be compromised, as will the decay of the notes resulting, due to the clumping of unmitigated flux fields in an air core. The E Field will print in the same fashion as with core but again, the low frequency compliment to all transients will go askew in time. This can be obscured to some degree by sharp cut off of signals and careful tuning and driver alignment, but....
The typical amorphous core is a cut, squashed, doughnut shape and this places the gap in the middle of the coil. Means that the potential field strength map is disturbed into a figure 8 shape. This is not worse than the mess with power transformer stacking of E/I core, but, not as good as a gapped core E/I where all E's and I's are butted together rather than interleaved. This core style provides a D or bread loaf shape of linear flux transform. So the cut core has to provide a higher Mu material, with less gap induced ballooning of flux lines, to equal the performance of the Butt gapped E/I core, made of much more prosaic materials. This brings it's own bag of problems as the mu of the field potential has less latency and to stretch out the resultant B Fields so we can, with our electrochemical speed sensors, understand the signals, a "slow" high threshold material must be used for the coil construction.
This brings us to the notorious ageing of Lundahl and other amorphous core transformers. They can sound good.
An important thing to know is that the first half wave of every inductive event is constrained only by the mu of the material and storage mechanisms of the core construction, so they can excurt and overshoot an E Field potential, in a high mu material, to the detriment of the resulting flux transfer between primary and secondary.
Finally, the area under the window of the core has a built in amplification factor of about 1000. This means that the floor where signal turns into uncorrelatable noise will be much lower, in a core coil than an air coil transformer. And, of course, any core induced problems are going to stand right out. My E/I output transformers do not have this non linear flux transform problem, well 4 pieces of lamination do, but they are acting as wave guides for all of the rest and so my potential magnet fields are much more uniform than in other constructions. Since I follow the theory of coil design that admits that there is a differential circuit, in E Field linking, that can be manipulated, I adjust my coil's effective mu to that of my core and get some pretty nice results. Here is an email copied to me, by Island Pink, who is on this and other forums, after replacing a Lundahl PP transformer with one of my PP designs.
"If I was unscrupulous, I'd try to sell you the Lundahl 1620s, saying they're pretty good, not bad for the money, etc. Actually, the O-Netics level 1's are so much better, they are INSULTINGLY good (in the words of 'Romy the Cat' ). It took about 30 sec to realize they were, they had more detail and much more finesse, no usage, straight out of the box and onto the chassis. They got distinctly better for a couple of hours after that, and may improve for a week or two in small ways. The top-end detail, and treble tone-differentiation is astounding, maybe 2 -3 times better than the Lundahls, to the ear. Even the bass tone seems better, bass lines are easier to follow. The overall effect is to reveal new things on every track you play, including basic stuff like lyrics that were muffled and uncertain before, backing vocals you never knew existed, tone on things that were just noises before, etc, etc. For example, on Chieftains stuff, I noticed Derek Bell breathing (huffing and puffing actually) as he worked away on the harp, never noticed it before. The very quiet track 'Small Hours ' on John Martyn's album 'One World' is a revelation. It was recorded at night, outdoors, near a lake (Chris Blackwell's estate ? ) and has lots of lovely ambient sounds including the breeze blowing and ducks honking on the lake. There's loads of extra small sounds, more space and more convincing REALITY going on there, you can just sit there immersed in it, wonderful."
I have chosen this excerpt for it's name dropping cachet ... of course. But I received this long before I had encountered the good sound club and the spontaneous erruptions of laughter..... and knew Romy the cat was not a rude British cartoon.
And, now that I have whipped up your interest, or bored you to death, I only make SE outputs for a guitar amp mfg. I do this only because he is willing to use a spark gap arrestor in the primary circuit, to eat the "carbon tracking across the tube socket" voltage spike, created by the ultra low storage SE coil and core configuration getting the DC B+ turned off with a switch! The designer claims that the spark gap provides an interesting tone .....
I am about 3 weeks away from supplying 3 Kz ohm to 4,8 & 16 ohm SE outputs for 300b or 2A3 tubes to George Wright, of Wright Sound, and Gary Pimm of Pimm CCS fame (constant current controls to buffer stages from each other in amplifiers). They are going to test and report on the modified and hopefully less violently "high performance" SE Audiophile outputs. If my plan works I will be able to participate in your SE hi frequency OP contest with composure. Unless, you are using a parafeed hookup that blocks the DC from the primary. If that is the case, I can whip up two transformers for a moderate or high price that will help you out without loss of composure or any need to cover my Emporial nakedness.