Inconsistent octave stretching that leaves partials linear is jarringly unpleasant

Evidence

There are two other ways to stretch, one of which can be done with physical instruments: we stretch all the first partials of the notes, but leave the higher partials of each note equally spaced, as they are naturally in musical instruments. At 2.1:1, this is really just a badly out-of-tune instrument, but out of tune in a special pattern. Even though the musical scale is the same as in the previous case, a remarkable contrast exists. The previous “stretch everything” example is at least self-consistent, and the result is not jarring, although hardly preferable to the traditional octave. However, the 2.1:1 octave with linear unstretched partials is jarringly unpleasant. The explanation is that all the bad collisions of partials have been caused by the inconsistent stretching of the notes without stretching the partials. — Eric J. Heller, Why You Hear What You Hear- An…, 2413

Categorization

• DEFINE: Clarifies how ‘stretching’ operates differently on fundamental partials vs. higher partials, and why consistency matters.