Importance of low distortion

When talking about the distortion of audio electronics such as a DAC or a power amplifier, low order harmonics, particularly 2nd and 3rd, are often considered "harmonious" and "benign". In contrast, high order harmonics, which are not harmonically related to the fundamental tone, are considered noxious. This argument usually supports the idea that tube amps sound better, because tubes only add low order distortion, or that low- or zero-feedback amplifiers sound better because feedback adds higher order harmonics.

Let's conduct a little experiment. Let's say we test an amplifier that adds 0.01% of the 2nd harmonic (H2) and 0.001% of the 3rd (H3):

The distortion is not particularly high and is all low order, harmonious and benign, perhaps even euphonic.

Now let's play a simple chord, A-C#-E:

Oops. In addition to H2 and H3, our benign test amplifier sputters a bunch of intermodulation products, musically unrelated to the chord, with levels comparable or in some cases above those of H2 and H3. These are not euphonic and would not be masked by music. Worse, they will mask the music itself.

So, an amplifier with low order and relatively low level, "benign" distortion may be euphonic with a single tone but not so euphonic with a chord. Practically speaking, such an amplifier would have genre preferences: it might sound fantastic on simple music such as solo vocal, but would get confused with anything moderately complex, and it would mush a full orchestra or, say, a Rammstein recording.