[mickael-kerjean]

Roughly speaking, tube amplifier goes in distortion adding pair harmonics when the solid state add odds ones. Odds harmonics aren't nice to the ear (see by yourself by listening to a Sawtooth wave) while even ones are much more flattering (see by yourself by listening to a triangle wave). This distortion relates to the entire theory that's behind the creation of chords and also to psychoacoustics.

[mrob]

Both square and triangle waves contain only odd harmonics, with the high harmonics of the triangle wave rolling off faster. The sawtooth wave contains both odd and even harmonics. You can't have a wave with pure even harmonics because the fundamental is counted as an odd harmonic. If you half-wave rectify a sine wave you get only even harmonics above the fundamental, but to my ears this just sounds like two separate tones: the sine fundamental and a separate higher pitched odd-harmonic wave.