Just intonation is far more mathematically accurate than equal temperament, but it often sounds badly out of tune to listeners who are acculturated to the latte

Just intonation is far more mathematically accurate than equal temperament, but it often sounds badly out of tune to listeners who are acculturated to the latter. 12-TET is a convenient fudge, but it isn't optimal. We have become deeply accustomed to a fairly arbitrary approximation of a somewhat arbitrary set of subdivisions. To complicate matters further, pianos deviate substantially from equal temperament at the extremes of their range. A piano sounds more in tune if the bass notes are tuned slightly flat and the treble notes are tuned slightly sharp, to accommodate for the natural inharmonicity of the strings.