THERE! I said it, and I have been trying to say it for years. Now I am going to use my junkie pulpit to try to explain it in simple terms.
The basic rule of transformers is that the transform the load by the turns ratio squared. This simple function allows an 8Ω speaker to present a 3200Ω load to a 300B by using a transformer with a 20:1 step-down ratio. This makes the world an easy place to live in and keeps everyone sane UNTIL someone then asks a poor transformer winder for a 10K:600 linestage transformer and a hole is ripped into the space-time continuum. The conversation typically goes like this:
Customer: I need an 10K:600 lineout.
Dave: What will this be driving?
Customer: Interconnects and the input of the amplifier.
Dave: Do the interconnects have a 600Ω resistor soldered across them?
Dave: Does the amp have a 600Ω input impedance?
Customer: Of course not.
Dave: What is the amplifier input impedance?
Customer: I dunno... 100KΩ... 10KΩ worst case.
Dave: Then what is the purpose of the 600Ω secondary designation?
Customer: A 5KΩ:10KΩ transformer would have a 1:1.4 step up ratio and I want a 4:1 step-down ratio to lower the output impedance.
Dave: A 4:1 transformer loaded with 10K will load the tube with 160kΩ
Customer: No I want 10K.
Dave: Head hits table.... nappy time.
This is the thing that urban legends are made of. Everyone treats transformers as if they all are used to deliver power to a load. This is perfect for the vacuum tube output transformer since the entire purpose of the transformer is to take the high voltage high impedance anode of a tube and get it to a low voltage low impedance to drive a loudspeaker. Universally applying this to every audio transformer simply leads to confusion and needless conversations like the one above. I will categorically state that the worst thing you can do to a transformer sonically is to load it. In the case of the tube-speaker interface this loading is a necessary evil. In just about every other case in audio, transformers are used to deliver voltage to a high impedance and not current to a low impedance.
I do not begrudge the really smart guys from Bell Labs who did the telephone grid at 600-900Ω. I tolerate the audio engineers who borrowed the 600Ω impedance as a standard so everything played well together when any mismatch could prevent people from properly hearing Duane Allman at the Fillmore East. Using those numbers today in audio where systems are meticulously curated is just begging for confusion and mediocrity.
So back the the 10K:600 step down transformer. The one place in audio where this transformer will really will be loaded with 600Ω is when used to drive the Pultec LCR Riaa module. For everything else in audio, the 10K:600 has little if any relationship other than being a convoluted way to say the device has roughly a 4:1 turns ratio. You will find many who insist that the transformer needs to be terminated with its characteristic impedance in order to work as designed. With vintage stuff, that is often the case, but that is simply due to the fact that it was designed with the intent to be loaded with 600Ω.
Lets assume a 4:1 ratio transformer is needed. I can come up with two very different designs based on its intended use. 99 times out of 100 the actual secondary load will be the grid of a tube so the transformer will be operating essentially unloaded. Rather than use an incorrect device designed for a 600Ω load, why not simply use a device designed to operate into the actual load?
The proper (according to me) way to specify a transformer that operates in the voltage realm is to state the source impedance, turns ratio and expected load and then the proper device can be wound. Using this approach takes what many call a black art back to the nicely ordered oblate spheroid we live on.