English: A comparison of the accuracy of perfect fifths, major thirds, and minor thirds in various equally-tempered and meantone tunings relative to 5-limit just intonation.

In just intonation, the minor and major thirds in the diatonic scale are optimally stable (in the sense of exhibiting the least harmonic entropy) if they have ratios of 6/5 and 5/4, respectively. However, stacking four perfect fifths of 3/2 results in major thirds being 81/64 instead of 5/4, while minor thirds end up being 32/27 instead of 6/5. The discrepancy between the classic 5-limit minor and major thirds and their Pythagorean (3-limit) counterparts are, in both cases, a ratio of 81/80 known as the syntonic comma.

33-Tone equal temperament approximates 1/2-comma meantone. It is a "flattone" (very flat meantone) tuning where the perfect fifths are all tuned approximately one-half of the syntonic comma flat from just so that the whole tone has a ratio of around 10/9 instead of 9/8. The major thirds are flat from just by an entire comma and minor thirds are sharp from just by 1/2 comma. Technically speaking, 1/2-comma meantone is so flat that most familiar minor and major harmonies become supraminor and submajor, and by extension, almost neutral in quality.

45-Tone equal temperament approximates 2/5-comma meantone, another "flattone" tuning. The whole tone is 1/5 comma sharp of 10/9 and 4/5 comma flat of 9/8, leaving the minor third sharp by 1/5 comma and the major third flat from 5/4 by 3/5 comma. 45-EDO is also the only equal temperament that tempers out both the syntonic comma and the classic ennealimma (the amount by which nine major limmas of 27/25 fall short of an octave).

19-Tone equal temperament approximates 1/3-comma meantone, since the fifths are flat from their just ratio of 3/2 by approximately one-third of the syntonic comma. The whole tone is 2/3 comma flat from 9/8 and 1/3 comma sharp of 10/9, leaving major thirds flat from just by 1/3 comma and the minor thirds extremely close to 6/5.

50-Tone equal temperament approximates 2/7-comma meantone. Here, chromatic semitones are almost exactly 25:24, and the minor and major thirds are both flat from their just ratios by almost exactly the same amount.

31-Tone equal temperament approximates 1/4-comma meantone, which was the most popular tuning used during the early and middle Baroque periods. Here, by flattening the fifths from just by approximately 1/4 syntonic comma, the major thirds are almost exactly 5/4 while the perfect fifths and minor thirds are both flat from just by about 1/4 comma.

74-Tone equal temperament approximates 2/9-Comma meantone, a little-known meantone tuning that was proposed by Lemme Rossi in 1666. It is a slightly less tempered form of quarter-comma meantone.

43-Tone equal temperament approximates 1/5-comma meantone, a modified meantone tuning used during the Baroque period. By tuning the perfect fifths flat by one-fifth of a syntonic comma, the major thirds are sharp by almost exactly the same amount, while the minor thirds are flat by twice that amount, or two-fifths of the syntonic comma. This leaves diatonic semitones equal to almost exactly 16/15 and major sevenths almost exactly 15/8.

55-Tone equal temperament approximates 1/6-comma meantone, another modified meantone used in the Baroque period. Here, the fifths are flat by one-sixth of the syntonic comma, major thirds are approximately 1/3 comma sharp from just, and minor thirds are 1/2 comma flat from just. The augmented fourth and diminished fifth are almost exactly 45/32 and 64/45, respectively.

In 12-tone equal temperament, the most commonly-used tuning in the world today, the flattening imposed on the perfect fifths is only one-eleventh of a syntonic comma, leaving the minor thirds significantly flat and major thirds significantly sharp from just.