Rhythmic engraving

These two measures sound exactly the same:

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Both last four beats, and the notes start at the same moments. But in the first you can see, without counting, where the third beat begins; in the second, the third beat is hidden inside a dotted quarter. The first spelling is the right one.

That is what the rules of rhythmic engraving are about. They do not change the sound; they change the reading. Lacerda notes that they belong, strictly, in a book of music calligraphy, and gathers those of most immediate use to a theory student (Lacerda 1966, ch. IX). They all follow one idea: the notation should show the beats of the measure.

The dot

In quadruple meter, a dotted half note should only be written on the first or second beat, never on the weak half of the first (Lacerda 1966, ch. IX). Like this:

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And not like this, with the dotted half starting in the middle of the first beat:

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In that case the long note is written with ties, so that the start of each beat shows (Lacerda 1966, ch. IX):

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For the same reason, when the second beat carries over into the third, a tie is used, not a dot (Lacerda 1966, ch. IX). That is the example at the top of the topic: the middle of a quadruple measure, between the second and third beats, must stay visible.

Measures of five and seven beats

In quintuple meter the division between the triple part and the duple part must also stay visible. If a note of the triple part carries over into the duple part, a tie is used, not a dot (Lacerda 1966, ch. IX). In a five-beat measure grouped three plus two, the note crossing the division:

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And not with a dot, which would erase the border between the two parts:

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The same holds when the duple part carries over into the triple part, and the same rule applies to septuple meter (Lacerda 1966, ch. IX). When the beat unit has no flag, Lacerda suggests showing the grouping with a dotted line between the parts of the measure, or by writing the time signature as a sum, five-four as three plus two (Lacerda 1966, ch. IX).

Beams

Eighth and sixteenth notes can have their flags joined by beams. The rule is not to join beats together: each beat makes its own group (Lacerda 1966, ch. IX). In a duple measure, the notes of the first beat are beamed together, and those of the second:

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Looking only at the beams, you can count the beats. Lacerda allows two exceptions. In triple meter, all six eighth notes may share one beam. In quadruple meter, the first beat may be joined to the second and the third to the fourth, but never the second to the third (Lacerda 1966, ch. IX), for the same reason as with the dot: the middle of the measure has to show.

In meters whose beat unit is the eighth note, the rule adapts: in four-eight, the first beat is joined to the second and the third to the fourth, never the second to the third; and in measures of five and seven eighth notes it is the beaming itself that shows the grouping, three plus two or two plus three (Lacerda 1966, ch. IX).

In compound meters the beat is the dotted quarter, and eighth notes are grouped in threes, one beam per beat:

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In vocal music there used to be a custom of not beaming notes when each has its own syllable. Lacerda thinks it better to follow the general rule and beam them, since that makes reading easier (Lacerda 1966, ch. IX).

Rests

Rests follow the same logic as notes, with a few rules of their own (Lacerda 1966, ch. IX).

A rest can combine whole beats. Two beats of silence at the end of a quadruple measure fit in a half rest:

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But it cannot combine part of one beat with part of another. In duple meter, the rest after an eighth note on the first beat is written as two eighth rests, one in each beat:

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And not as a quarter rest straddling the middle of the measure:

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In quadruple meter, a rest should not combine the second beat with the third. Two quarter rests, not a half rest in the middle of the measure (Lacerda 1966, ch. IX):

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In triple meter, a half rest is not customary; two quarter rests are written (Lacerda 1966, ch. IX):

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In compound meter, a rest may be dotted or split, as long as it respects the beats (Lacerda 1966, ch. IX):

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A whole measure of silence takes a whole rest, whatever the time signature: in two-four, in three-eight, in five-sixteen (Lacerda 1966, ch. IX). Here the whole rest is not worth four beats; it means "the whole measure".

Other writing rules

Lacerda gathers in the same chapter a few rules that are not about rhythm but serve the same end (Lacerda 1966, ch. IX):

• in vocal music, when one syllable stretches over several notes, those notes are covered by a curved line;
• when there are many ledger lines, reading is easier with the notes written an octave lower or higher and marked 8va;
• sounds without definite pitch, from percussion instruments or spoken passages, can be written on a single line, or with special noteheads.

What comes next

With the rules of engraving, rhythmic notation is complete: the note values, the meters, the anacrusis, and now how to lay them out so that reading is immediate. What remains are irregular divisions, tuplets, which have writing rules of their own.