Dots, ties and fermatas

Each note value is worth two of the next, and that is all. A half note lasts two quarter-note beats, a whole note four. But what about a note of three beats? There is no value for it, and melodies ask for that length all the time.

Notation solves it with signs added to the note value. Lacerda counts four ways to lengthen a note: the tie, the dot, the double dot and the fermata (Lacerda 1966, ch. V). This topic goes through all four.

A tie adds two values together

A tie is a curved line joining two notes of the same pitch. It says: play the first and hold the sound to the end of the second, without playing again. The two values become one sound, as long as both together.

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A half note tied to a quarter: three beats of G, then one of E. Listen. Two sounds, not three.

Ties can follow one another, to add up as many values as the length needs. Each note is tied to the next:

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Whole note, plus half, plus quarter: seven beats of a single G.

A tie also crosses the barline. A note that starts at the end of one measure and carries on into the next can only be written this way, because a note value cannot reach over the barline:

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A rest is never tied. Two rests in a row are already one continuous silence, and there is no sound to hold (Lacerda 1966, ch. V).

A dot adds half

A dot written to the right of a note value adds half of that value. A half note is two beats; dotted, it is three.

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Both measures sound the same. In the first, a half note tied to a quarter; in the second, a dotted half. The dot is a shorthand for the most common tie of all: a value tied to half of itself.

The rule holds for every value. A dotted quarter is a quarter plus an eighth; a dotted eighth is an eighth plus a sixteenth.

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It holds for rests too: a dotted rest is a silence half as long again as the rest without the dot.

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There is a consequence that will matter later. A value without a dot divides naturally into two smaller values; a dotted value divides into three. Lacerda calls the first a simple value and the second a compound value (Lacerda 1966, ch. V).

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That difference, between dividing by two and dividing by three, is what simple and compound meters are built on.

A double dot adds another quarter

A second dot adds half of what the first one added. The first dot adds half the value; the second, half of that half. Altogether, a double dot adds three quarters of the value.

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A double-dotted half note is a half, plus a quarter, plus an eighth: three and a half beats. Both measures sound the same again.

Med goes as far as the triple dot, which adds a further eighth, and Blatter notes that one can go further still, but both agree it is rare: in practice almost everything is written with one or two dots (Med 1996, ch. VI).

Dot or tie?

If the dot is a shorthand for the tie, why do both exist?

Because the dot only covers two sizes: half again, and three quarters again. A note of five beats, a whole note plus a quarter, has no dot to write it. Only a tie will do (Lacerda 1966, ch. V).

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And a dot does not cross the barline. If the added value falls in the next measure, the tie is the only way (Med 1996, ch. VI). So the choice is simple: within the measure and at the right size, the dot is quicker to read; everywhere else, the tie.

A fermata leaves the length to the performer

The first three devices say exactly how long the note lasts. The fourth does not. A fermata is an arc with a dot inside, written over a note or a rest, and it means: hold this longer than written.

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How much longer is exactly what the books leave open. Lacerda speaks of roughly twice the value, and adds that it all depends on the tempo and the performer's judgement (Lacerda 1966, ch. V). Blatter gives half again as a rule of thumb, then says there are many exceptions and that musicians usually hold it for as long as seems right (Blatter 2007, part 1, art. 6). Med places the fermata among the tempo signs, because it suspends the regular beat for a moment (Med 1996, ch. XXX). In the example above, the sound holds the last note for twice its value, Lacerda's reading.

Over a rest, a fermata lengthens the silence in the same way.

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Med gives the sign different names by where it sits: fermata over a note, suspensão over a rest, and parada over a double bar, where it marks a short break between two sections of the music.

What comes next

A tie across the barline already assumes the measure: the regular groups of beats that barlines divide. And the difference between dividing by two and dividing by three, which the dot brought out, is what separates simple meters from compound ones.