Major and minor are one single note — the third as a switch

The smallest possible difference

A C major triad consists of C, E and G. A C minor triad consists of C, E♭ and G. Two of three notes are identical; the third is shifted by a semitone. That is the smallest difference the system allows at all — and it decides whether a sound is felt as radiant or shadowed.

This disproportion between cause and effect is the remarkable part. You can halve the volume of a piece, change the tempo, swap the instrumentation — the effect stays smaller than that of one displaced inner voice. The third is therefore the most discussed note in Western harmony.

The difference can be named physically but not fully explained. The major third has the ratio 5:4 and appears as the fifth partial in the harmonic series of every note; the major triad is therefore already latent inside each single tone. The minor third at 6:5 does not occur at a comparable position in the series. In that sense major is the more natural event — which does not explain why we hear minor as sad. Cultures without the major–minor association do not hear it either.

How composers use the switch

The most conspicuous use is the Picardy third: a piece in minor ending on a major triad. The final chord of a movement in A minor is then not A–C–E but A–C♯–E. From the sixteenth into the eighteenth century that was the rule rather than the exception — a minor ending counted as unfinished. Bach closes numerous chorale settings this way; the effect is a sudden brightening at the last moment, and it works on listeners who know nothing about thirds.

The opposite move, switching from major to minor on the same degree, is called the variant, or in one common case the minor subdominant. Schubert is its most famous user: in many of his songs a phrase tips from major to minor mid-sentence without the melody changing direction. The harmony darkens beneath an unchanged vocal line — musically exactly what the text tends to describe at such moments.

A third use is the third-change as a means of modulation. Because major and minor triads on the same degree share two notes, you can move from one to the other without a break. From there you are in another key although only a single note moved. Grieg’s Albumblatt lives off this technique, and you can pick it out within a few bars.

The third in a setting — where it belongs

In four-part writing the third is the most sensitive note, and two practical rules follow from acoustics. First: do not double the third. Doubling it brings the colouring out too strongly, and in equal temperament it also doubles those 14 cents of deviation. Double the root instead, or at a pinch the fifth.

Second: the third sits better above than below. A major triad with the third in the bass — first inversion — sounds buoyant and light, because a major third above the bass makes a weak foundation. For a firm final chord you therefore use root position.

And third, for wind players and singers: in just intonation the major third sits 14 cents lower than on the piano and the minor third 16 cents higher. Playing the third of a chord in an ensemble means tuning it by ear rather than following the display. When the beating disappears, it is right — and the needle then simply is not on zero.

From practice

The quickest exercise needs an instrument and thirty seconds: a familiar tune, played in major and then with the third lowered. A nursery song in minor is a small shock and gets a laugh almost every time — but that moment sticks. Afterwards every child knows which note is the switch.

For guitarists it gets even more concrete. An open E major chord becomes E minor by lifting a single finger: the one on the third string, first fret. One finger, one semitone, complete change of mood — you cannot make the relationship more visible than that. The same works for A major and A minor.

As a public-domain score example, Tchaikovsky’s “Old French Song” from the Album for the Young, op. 39, works well: a plain eight-bar melody in G minor whose effect rests almost entirely on the minor third. Play the same melody with B natural instead of B flat and every note stays in place — while the piece loses everything you play it for.

A frequent misconception: “minor is sad” is a rule of thumb, not a rule. A great deal of dance music is in minor, from the tarantella to klezmer, and nobody hears it as sad. What minor actually does is raise the tension of a sound and keep its resolution open. What comes of that is decided by tempo, rhythm and context.

Hearing the third in the overtone spectrum

That the major third is already contained in every note can be verified on the instrument. The fifth partial of a fundamental is the major third, two octaves above. On the guitar you reach it as a harmonic just above the fourth fret — a point that deliberately does not sit exactly over the fret wire, because the pure third does not fit the equal-tempered grid.

From this follows an argument that regularly brings clarity in rehearsal. When an ensemble plays a major third purely, it sits 14 cents below the piano value. The third does not then sound flat, it sounds beat-free — and the check is not the tuner but the disappearance of the pulsing in the chord.

For the minor third it is the other way round: pure, it sits 16 cents above the piano value. A minor chord intoned purely by a wind section therefore sounds higher in the inner voice than on a keyboard. Hear both at once and you are hearing exactly the compromise a keyboard has to make.