> which is the wire diameter you used?
The biggest that will fit.
Just like the first post of the thread says:
Pick a core that looks big enough.
Wind a few turns and measure the inductance. It is best to measure around 50Hz. Laminated iron-cores do funny things at high frequency, and mostly that is not very important. The important thing is the inductance at the bottom of the audio band.
Inductance increases as the square of the turns. So if 10 turns gives 1 milliHenry, 100 turns is 200mH, 1,000 turns is 10 H. Figure for 20Hz cut-off with your intended source impedance.
For a voltage step-up/down transformer, just figure the secondary turns from the voltage ratio. The inductance and the impedance will automatically be right.
In any practical audio transformer, copper resistance will cause 5% to 20% dead loss. You usually want as little as possible. That means using as much copper as you can fit in the windows of the core.
For a 2-winding transformer, divide the window area in half. That is how much space you have for each winding. You already know the number of turns. Divide the half-window area by the number of turns: that is the area of the wire, including the gaps between round wires, winding slop, and insulation. You will only be able to fill 70% to 50% of the area with round copper. Some test-winding on a stick with wire of an estimated size will help you guess how much copper can really fit.
Oh: estimate the average length of turn of wire. Turns in the middle are shorter than turns around the outside of the winding, get an average.
Now: use the estimated wire size, the resistance per foot/meter of that wire size, and the number of turns, and calculate the copper resistance. If it comes out about 5% of the working impedance (30Ω on a 600Ω winding), you are good. If you started with too many Henries and too many turns, you will have long thin wire and high copper resistance: you should revise your goals and recalculate. If you arrive at a very low copper resistance, you probably miscalculated something.
Windings up to 5KΩ are not that hard to do well.
At 600:600Ω, you can just wind the whole primary, wrap with paper, and wind the whole secondary. The secondary resistance will be higher than the primary resistance; that is not a problem.
Above 1KΩ, you should wind some primary, some secondary, more primary, more secondary. This reduces Leakage Inductance which begins to hurt high frequency performance. A simple P-S-P winding is fine for a few KΩ.
Windings above 10K (as you need for high levels into a tube grid) become tricky: Leakage Inductance is a problem, but so is capacitance. And capacitance gets worse when you inter-layer the windings. Ideally you do a LOT of fancy calculations. As a practical matter: a lot of good transformers use the simple P-S-P layer scheme. Yes, there are trannies with 7-way and 27-way interleaving, but some iron guru must have spent long nights over a hot slide-rule optimizing both the theory and how he would get the winders to do it right.
Also: windings above a few KΩ use VERY fine wire. This may not be readily available except at an audio transformer specialist. Very high impedance windings need wire smaller than US #40, which is already so thin (a fat hair) that it breaks a lot. Also the insulation on the winding is small compared to large wire, but does not get much thinner on thin wire, so the thinnest wires tend to have a lot of varnish for their copper. If the design is going wrong this way, allow more window area for the high-impedance winding.
> searching for siemens transformer in the flea markets...
Siemens is good but not magic. For line output transformer, you actually will be fine with common power transformer iron. CJ proved recently that he can hardly tell the difference between an audio transformer and a "2-4-1"brand 120V:28V 20VA power transformer. And I have used power transformers as mike transformers. Many-Watt output transformers usually are wound very much like power transformers, just more turns and more interleaving. A transformer guru has "better" ways to do it, but with a little care and experimentation I think you can use common power transformer technology. And there are a lot more power-iron re-winders around than audio iron specialists.
There is one kind of ready-made power transformer that is NOT a good audio transformer. Many cores use "E-I stampings", like the one on top of this thread, and both windings are in one lump. The other way uses "U stampings" and has two windings in two lumps on separate legs of the core. It is possible to custom wind a great U-core. But the ordinary power transformer has primary on one leg, secondary on the other leg. This gives good insulation against line-faults, but above a few KHz the magnetic flux from the primary doesn't fully flood the secondary on the other leg. I got about 2KHz cutoff, when a very similar 1-lump transformer was well over 50Hz-15KHz (yes, a small power transformer can have good bandwidth; and I was not optimizing source and load impedances yet).