Several of you have quite a different take on tube bloom than I do. I certainly wouldn't paraphrase is as being "un-natural", as it is a very natural occurrence for the tube to have a very lightly rounded off edges to the music, which to me is as natural as the music itself.
Yes we can say that anything done to the signal other than the original signal is distortion, but there are good distortions and bad distortions.
For example, harmonic distortions of the odd order in a high percentage can be downright awful to listen to.
For some, the razor sharp presentation of poorly designed solid state may be a distortion to them as it sounds "un-natural" or very mechanical...that old "transistor sound" if you will.
I think historically, tube gear has had a reputation for glorious midrange, while being slightly gun shy in the lower and extreme upper end. However, listening to well recorded music, especially classical or jazz really tends to allow the orchestra to build and decay in power in a more natural order. The midrange pierces the soul and it becomes very emotional because it sounds very real and what's even better, it's in your home and you can control it, it sounds like a gift from above.
The tube bloom isn't so much a sound as it is an effect. While your listening to the music, a certain passage comes along and grabs your attention. You focus on it and you become a part of it and while it lingers, blooms to a climax of totally suspended reality. You have forgotten about your life, your troubles and woes and this music and it's tubes captured your very attention, your very soul and took you away.
That is what I call the "Tube Bloom"
Wayner