Transformers more important than tubes?

I laughed out loud at that video, not because it was BS but because it was funny. Tubes for warmth - just grab one with your fingers if you don't believe they get warm!
 
My problem is with the word "warmth". Where does that word come from? Like so many audio metaphors, it's borrowed from a visual reference. When a photographer says a print needs to be "warmer", he means it needs more red, red being the closest visible color to infrared, which is heat.
 
It means longer wavelengths, which should by analogous to bass frequencies in audio. But when we talk about the effect tubes and transformers have on audio, we are talking about harmonic distortion - adding high frequencies. This is why "warmth" has never made sense to me in this context.
 
But I do understand what people mean when they use the term. In fact, adding harmonics to low frequencies actually makes those low frequencies more perceptible. If you have Ozone, you can easily hear this effect by creating a band below 120 Hz in the Exciter module (Tube mode) and start turning it up. You'll hear the bass guitar, kick drum and floor tom start to sound deeper and fuller, even though you're not adding more bass to the mix. Waves' RBass and Maxxbass plugins work on the same principle.
 
I can see how people might confuse tubes and transformers, because they usually go together. Tube gear nearly always has transformers. Solid-state gear generally does not (power transformers don't count), unless they've been added specifically for tonal reasons, such as in a microphone preamp or inside a condenser microphone. So if the tube gear sounds richer, which component is responsible, the tubes or the transformers?
 
The answer is "both". Half the harmonic goodness you get out of a tube guitar amplifier is from the high-gain triode stage at the front, the other half from the push-pull circuit at the output that incorporates a transformer. Some of that latter half is from the pentodes' nonlinearity and some is from transformer saturation. The triode gives you odd-order harmonics, while the transformer gives you even-order harmonics. Together, you get the whole set. The same thing a sawtooth waveform gives you in a synthesizer, btw, which is why that waveform is so popular in subtractive synthesis.
 
It's silly to argue whether tubes or transformers are more important. Odd-order harmonics are easier to hear, so they have a more profound impact. But transformers, in addition to supplying even-order harmonics, also act as low-pass filters, which softens the effect of the tubes that precede them.