This old adage goes back to when most amps were tube-based and used in systems with limited frequency response. Components like carbon resistors, saggy resistor voltage droppers, and tube rectifiers contributed to this ’tone’ of a rolled off upper treble and woolly bass.
In reality, a good modern tube amp has a certain naturalness which can be attributed to lack of solid state transistor haze caused by switching noise and its associated odd-order harmonic distortion. With modern components, tube amps can sound as cool and neutral as you prefer. Conversely, many solid state amplifiers can sound warm so it’s not a predictable way to classify the type of sound you’re going to get from a specific type of amplifier. To add complexity to the issue, electronic passive component and tube type, configuration and brand selection can also affect how warm or cool an amplifier sounds.
In reality, a good modern tube amp has a certain naturalness which can be attributed to lack of solid state transistor haze caused by switching noise and its associated odd-order harmonic distortion. With modern components, tube amps can sound as cool and neutral as you prefer. Conversely, many solid state amplifiers can sound warm so it’s not a predictable way to classify the type of sound you’re going to get from a specific type of amplifier. To add complexity to the issue, electronic passive component and tube type, configuration and brand selection can also affect how warm or cool an amplifier sounds.