What I want to know is what makes some amps sound the way they sound like the Sunn Model T/Sunn Scepter or the Ampeg VT22. What are the components inside the amps which give it a round, fat , heavy, ruough, "slidy" sound (Sorry it is hard to describe with words). Is this related to the "tubes"? How do they affect the sound of an amp?
Even harmonic distortion is a pleasing sounding distortion where a great tube amp can do very well. Even harmonic distortion helps the sound become wide and strong, like in rock and roll music. As mentioned above, tubes help a great deal, biasing the amplifying circuit even more, and speakers also.
I think I know what you are referring to and there are several possible answers.
As you pointed out tubes have a major effect on the sound of an amp. But the presence of tubes alone may not fully account for what you are hearing.
If you notice that initially increasing the volume of the amp correlates with the sound you are describing then what you are hearing is likely Tube Saturation. This is when the signal through a tube is high enough to begin producing new harmonic overtones that are not present at lower levels or in solid state amps. The result is a rounder timbre with more pronounced overtones.
If you notice that then continuing to increase the volume of the amp correlates with the sound you are describing then what you are likely hearing is Tube Distortion. This is when the signal through the tube is so high that it begins to be clip, producing new inharmonic overtones not present at lower levels or in solid state amps. The result is a rougher timbre with some inharmonic overtones
Though these two effects are not the same they are closely related and interdependent and there is often a sweet spot where the two balance out quite well. Additionally, high volume is not a requirement for producing either of these effects, only high signal. So using a tube preamp may be sufficient for reproducing the sound you are describing. If only a specific amp will do, a classic alternative is to disconnect any speakers and connect the amp's signal output to the input of another, preferably identical, amp for independent volume control.
Be careful not to ever connect the speaker output of an amp to the input of another since this can easily damage both.
One additional consideration is the speaker and cabinet configuration.
As you connect more speakers to the amp you begin to hear the effects of harmonic reinforcement. Though the sound produced by multiple speakers may be very similar they are never exactly the same and also each occupy a unique position in space. As a result the multiple sources reinforce one another in their common harmonics and counteract each other in their differences. The result is fuller sound with a more consistant timbre, less subject to environmental variables.
The frequency response of your speakers also plays a key role in the timbre it produces. No matter how much attention is given to equalization there are often harmonics outside of the response capabilities of a given speaker. As a result the timbre may be dramatically effected by variations in speaker design, materials, and manufacturing.
There are of course many other factors effecting in sound of an amp, some known and many unknown. These four are just those I am most familiar with.