There are two tunable, usable major seconds. In moving along a diatonic scale from C, say, to the major third E, one of the major second steps will be a large major second, the other a small major second. In a tonic-dominant environment, the first will be large, the second small.
But as I found in my work on Josquin’s five voice motet “Ave verum corpus”, in an environment less oriented to tonic-dominant, the first step may well be lower. Nearly always in the Josquin the other voices forced the second scale step to function as a subdominant substitute (in modern terms), and to be tuned lower. The Josquin score is here . You will see my dilemma about the second note of the score, briefly discussed in footnote 2.
The larger major second is the Pythagorean second: two fifths stacked. C – G – D. The larger major second is about four cents larger than the equal tempered major second, the two are nearly indistinguishable. Sounding simultaneously as a dyad, there are so many overtone beats, and such rapid beats, that the difference between the two is insignificant.
The smaller major second is rather flatter, differing from the larger by a comma (about 22 cents) and from the equal tempered second by about 16 cents.
If my best laid plans do not go agley, I’ll be writing some tuned major second clusters very soon in new music being sketched now. Tuned Debussy should be a novelty.
In a minor key, the step from the rather high tuned minor third degree to the perfect fourth is also a small major second.
I’m not positive about the best way to tune the lowered seventh in a minor scale (Bb in C minor), but my practice is to tune it high, a perfect fifth above the high minor third. This means, since the minor sixth is also tuned high, that the major second between sixth and lowered seventh is a large major second. Incidentally, when the seventh degree is not flat, the very narrow augmented second (Ab to B natural, in C minor) is not terribly different than the wide major second, 272 cents versus 204 cents, or at least much less different than on the piano (300 cents versus 200 cents) giving, to my mind, more justification for how often the two seem to be interchanged in older music. And as a result the Bb in C minor is tuned differently than the Bb in C major, used for instance in moving harmonically toward F major. The former being a good deal sharper than the equal tempered equivalent, and the latter slightly flatter.
I can remember in my first year of music school learning to sing the harmonic minor scale with its augmented second, and feeling that my voice was wildly approximate: in retrospect, perhaps a modified memory because of these subsequent studies, I think I was basically singing a wide minor third, much larger than the narrow augmented second.