Binary and ternary form

A piece's form is the shape it makes on a large scale: which sections appear, in what order, and which come back. The topic on form introduced the letters, A, B, A, that name that shape. This one deals with the two oldest and most used forms, binary and ternary, and with what they do to the key.

Repeat, return, vary

Blatter divides forms into two broad groups. Sectional forms have clear phrases and distinct cadences that audibly mark the important points of the structure. Continuous forms seem, on first hearing, to flow without clear cadences or predictable goals (Blatter 2007, part 5, art. 4). Binary and ternary forms are sectional.

In a sectional form, after presenting a section, the composer has few choices: repeat it, vary it, or bring in new material. Blatter names each one (Blatter 2007, part 5, art. 4):

Term	What happens	Letters
repeat	the material just presented comes straight back	A A
return	the material comes back after other material	A B A
variation	the material comes back changed	A A′
new material	something not yet heard in the piece	A B

The first section is always A; new material gets the next letter; material that comes back changed gets a prime for each variation (Blatter 2007, part 5, art. 4).

Open form and closed form

What separates binary from ternary is not only the number of parts. It is the path the key takes.

A form is open when the first section ends away from the tonic, most often on the dominant. A form is closed when each section ends with a cadence on its own tonic (Blatter 2007, part 5, art. 4). In an open form the first part leaves a question; in a closed one each part resolves on its own.

Binary form

In binary form the piece divides into two sections. It is an open form: the first section leaves the tonic for another centre, most often the dominant; the second starts in that new centre and returns to the tonic. If the key is minor, the second centre is usually the relative major. In short pieces the first section may end on no more than a half cadence; in larger ones the composer modulates (Blatter 2007, part 5, art. 4).

The harmonic path of a short binary piece might be this. The first section leaves the tonic and stops on the dominant, reached through its own dominant:

CITonicDiatonicFIVSubdominantDiatonicD7V7/VDominantSecondary dom.GVDominantDiatonic

Hear the progression

The second starts from the dominant and comes home:

GVDominantDiatonicG7V7DominantDiatonicCITonicDiatonicFIVSubdominantDiatonicG7V7DominantDiatonicCITonicDiatonic

Hear the progression

In binary pieces the material of the second section is usually closely related to the first, so the form is written as A A′ rather than A B. And both sections are commonly repeated: A A, A′ A′ (Blatter 2007, part 5, art. 4).

Rounded binary

Rounded binary is a variant of binary. The second section starts with new material but, near the end, brings back some of the opening material (Blatter 2007, part 5, art. 4). The shape becomes: A, then B followed by a piece of A.

That return "rounds off" the piece: the ear meets again what it already knew, which gives a sense of closure (Blatter 2007, part 5, art. 4). The difference from ternary is subtle and lies in the proportions: in rounded binary the returning A is part of the second section, usually shorter than the first A, and the repeats still group B and the return together.

Ternary form

Ternary form, or three-part form, has three distinct sections and is usually closed: each part begins and ends on its own tonic. The middle section sits in its own key and usually brings new material rather than material derived from the first. The relative major, the relative minor and the dominant are the commonest choices for it (Blatter 2007, part 5, art. 4).

A ternary piece with its middle section in the relative minor. The first section, closed in C major:

CITonicDiatonicFIVSubdominantDiatonicG7V7DominantDiatonicCITonicDiatonic

Hear the progression

The middle one, closed in A minor:

AmiTonicDiatonicDmivSubdominantDiatonicE7V7DominantDiatonicAmiTonicDiatonic

Hear the progression

And the first again, closed in C.

Since the third section is often identical to the first, instead of writing it out again the composer can put da capo, "from the head", at the end of the middle section, and the performer goes back to the beginning (Blatter 2007, part 5, art. 4).

Some authors call ternary form arch form: the point of greatest tension tends to fall in the middle of the B section, and the piece traces a curve, rising to it and coming back down (Blatter 2007, part 5, art. 4).

Minuet and trio, and the da capo aria

Binary and ternary forms nest inside each other. The classic case is the minuet of symphonies. The minuet is usually binary or rounded binary and is followed by a trio, which is another minuet made from different material and also binary. After the trio, a da capo brings the first minuet back (Blatter 2007, part 5, art. 4). On a large scale, minuet, trio, minuet is ternary; looking closely at each part, they are binary.

The da capo aria of Baroque opera is another variant of ternary. The A section is long, with parts for the orchestra and the singer and a modulation away from the tonic and back; the B section is shorter, in another key; and at its end the music goes back to the beginning and the whole A is repeated (Blatter 2007, part 5, art. 4).

Neighbouring forms

Three other short forms complete the picture (Blatter 2007, part 5, art. 4).

• Song form, A A′ B A′. Common in popular song of the early twentieth century, about 32 bars long. A ends on a half cadence, A′ repeats A with a full cadence, B contrasts and is often called the bridge, and the final A′ closes the piece.
• Bar form, A A B. The two A sections are called, in German, Stollen, and the B section Abgesang. Many Lutheran chorales, of the kind Bach harmonised, are in this form.
• Through-composed. A piece in which no material returns, A B C D and so on. The term was first used for songs in which each verse had a different melody, and since the eighteenth century there have been relatively few examples.

What comes next

Binary and ternary forms are the bricks of larger forms. The rondo, which alternates a refrain with episodes, theme and variations, and sonata movements are built from the same choices: repeat, return, vary, or bring in something new.