What output transformer impedance to take?
Some design their own schematics, and know exactly what they want, and why. Most users however take existing schematics, and try to find exactly this transformer which is used there. Finding one with exactly that impedance is difficult, and people are uncertain if they can take a slightly different impedance, and what will be the consequences of that. To understand this better, please be aware that the designer always had to make a choice which was a compromise, and there is no ultimate best way. This is why I always say, some deviation is no problem at all, but you need to see the direction of the deviation, and what that does to the original compromise.
When you read "5700 Ohms" transformer impedance in a circuit you found somewhere, that doesn't mean somebody calculated that within 0.1% and when you take 1% off, it begins to sound bad.
The design reality at the time this number was put on paper, was totally another.
To understand this better, first we need to look at the metrics Rp and Ra.
About the Rp
It stands for Plate Impedance. This is a dynamic number, meaning it refers to AC signal. You can not calculate it from the DC plate voltage and plate current.
Though compressed data sheets seem to suggest it, be well aware a tube does not have one single Rp. All dynamic numbers, like gain and Rp, depend om the DC operating point. And not just a little bit!
Rp depends strongly on the plate current / Plate voltage combination. Even so, you can adapt a tube to an existing transformer by choosing an operating point with another Rp. This follows simple logic, any device at high voltage low current has high im ped a ne, and a device with low voltage high current is low impedance. Here is found the simple relation with the static (DC) operating point. If the tube is biased at higher voltage, and lower current, Rp will go up significantly. And in the same way, you can let Rp go down. There are limits to as how far you can reduce the Rp, because the required high DC current, at low plate voltage limits the output power in two ways. First, to get this high DC current, requires a relatively small grid voltage. This again limits the maximum signal voltage we can apply, because we do not want to have positive signal voltage on the grid. (It would become a diode, and signal clips). Second, the lower plate voltage limits the output signal by default.
So what to do, to get a LOT of output power? You guessed it, we need a high plate voltage. That is the only way to get the signal swing out of the tube. We need to keep the plate dissipation within reasonable limits, so plate current must be low. Now that is helpful, because it requires a large grid voltage, and that allows more AC signal. The compromise is now, you will end up with quite a high Rp, which makes transformers harder to build, or in other words: More expensive. And even so, a lower Rp transformer has a better frequency range.
So you see now, Rp of a circuit is one big compromise, and we have not even talked about the distortion yet, which also relates to Rp. .
We don't need to go too deep into this, or do numerical examples here, but just keep in mind:
Rp is a variable number, and you can change it very much by the operating point.
About the Ra
Ra is the transformer primary impedance. Called Ra for a SE transformer, and called Raa for a PP transformer. (Because it is measured between the two Anode terminals. Which impedance only occurs if you load the transformer with the rated speaker impedance.
So Rp is determined by the DC operating point, and the next question is, what transformer Ra we must take. Is that the same number? Well yes it is, for guitar amplifiers. Here, Ra is chosen equal to Rp. That gives highest efficiency, resulting in highest output power, but on the cost of distortion, which rises rapidly at higher signal is. But what is nice to get distorted guitar sound, is not so nice for HiFi.
With HiFi., we avoid distortion, but we do allow a small content of second harmonics, and perhaps a fraction of third harmonics.
This is the trade off between Output Power and distortion. You just can't have it both optimized. What we call "tube sound" is mainly even harmonics added n for HiFi, and even+odd harmonics added for guitars. If more than 5% is added, our ears hear distortion. Below that we hear another "sound".
About speaker resonance
In HiFi, the frequency range of recordings goes much deeper down than guitar strings. A guitar can't go deep enough to cause a speaker resonance. But electronic tones can go easily at or below the speaker resonance frequency. What is this frequency? Well it is literally the frequency at which the speaker comes in resonance. Causing two things: First, the membrane begins to swing much higher as with all other frequencies. Which of course is fully unwanted. Second, it makes the impedance go up for this frequency, and the effect is because of that somewhat reduced. A problem however comes, when the signal stops. So when the tone disappears, we want to the membrane to stop moving. Bit it will not do so because, it is in resonance. So we experience this effect as "muddy" or "slow".
Can we do something against it? Well yes we can. We are going to drive the speakers with a much lower impedance as would be ideal for efficiency. Best Effiency comes when Rp=Ra. Suppose we use Ra=5xRp, then of course we compromise a lot on efficiency. But the speaker itself, when it is 8 Ohms, sees now a source impedance of 1.7 Ohms. This damps the resonance a lot better than 8 Ohms. We say the damping factor is 5. The lack of resonance will cause the speaker to react faster, and the human ear detects this very good. The faster responding bass will not make the bass louder, but it will make the speaker sound more natural.
But as so often, the numbers are only confusing for people who are only interested in the result and not what is behind it. This is why schematics have always THE Ra written on it, whereas is reality this was just a mandatory choice, somebody made at some moment.
So with the above in mind, please be not too critical with transformer impedance Ra.
If it writes 3k5 in the circuit, and you have a 3k8 transformer available, the maker of this circuit would have taken it just as well if he would have had it at the bench, and the schematic would have been published with 3k8. Though the impedance differs 10%, distortion and output power change only marginally. (Both will be lower). Even so, generally of you have an output power problem, take a little lower Rp as in the schematic, so you get a fraction higher output, at a fraction higher distortion.
Another reason not to blind stare yourself on exact Ra, is the speaker impedance itself. Speaker builders just write "8Ohms" on a whatever they made. Because if they would write 7Ohms on it, people would not buy it. Because they say, 7 Ohms is good, but 8 Ohms is better. In reality, this is not very critical.
To my opinion, any deviation of 10% is not critical at all.