Irregular and changing meters

Tap a steady pulse and count to five, then start again. Two and three are easy to feel: the accent falls every other beat or every third beat, and the measure seems to breathe on its own. Five does not split into equal parts, and neither does seven. The ear does not give up on them, though. It hears them as groups of unequal length, a short one and a long one.

Meters like these, with five, seven, eleven beats, are often called irregular meters. Blatter notes that the older name, "irrational", is wrong on both counts, and that what matters is how they are built and how they feel (Blatter 2007, part 1, art. 4).

Five: three and two, or two and three

A measure of five is almost always two groups: one of three beats and one of two. At a slow tempo you count all five; at a faster one you feel an uneven pair of pulses, one long and one short (Blatter 2007, part 1, art. 4). Lacerda describes it the same way, as a triple measure plus a duple measure, or the reverse (Lacerda 1966, ch. VI).

Hear the passage

Listen for where the second accent lands: on the fourth beat, after the group of three. Now the same count grouped the other way, two and then three, with the second accent on beat three:

Hear the passage

The two versions have the same time signature and sound different. The grouping is part of the music, not of the fraction. The second movement of Tchaikovsky's Sixth Symphony is a well-known waltz-like piece in five (Med 1996, ch. XIX), and Dave Brubeck's "Take Five" made a 3+2 pattern familiar far outside classical music.

Seven: three ways to group it

Seven beats are felt as an uneven three: two short groups and one long one. The long group can come last, in the middle or first (Blatter 2007, part 1, art. 4):

Grouping	Where the long group is
2+2+3	last
2+3+2	in the middle
3+2+2	first

In seven-eight, the eighths are beamed by group, so the grouping can be read at a glance. Here is 2+2+3, first in eighths and then as the three pulses the ear takes away from it, two quarters and a dotted quarter:

Hear the passage

And 3+2+2, with the long pulse at the start:

Hear the passage

Lacerda's version of seven is slower-moving: a quadruple measure plus a triple one, or the reverse (Lacerda 1966, ch. VI). The two descriptions are not in conflict. At a slow tempo, where each beat is a quarter, seven feels like four and three; at a fast tempo in eighths, it breaks into the twos and threes Blatter lists.

Writing the grouping

The beams already show the grouping of eighths, but a composer sometimes wants the time signature itself to say it. One way is to write the parts as a sum: a five-eight measure marked 3+2 over 8, or seven-eight marked 2+2+3 over 8. The same device can regroup an ordinary meter, such as eight eighths in four-four grouped 3+3+2 (Blatter 2007, part 1, art. 4).

Med shows the same idea from the other side. For him, five-four can be a three-four measure and a two-four measure joined together, which he calls an alternating meter, and the grouping can be noted beside the signature (Med 1996, ch. XIX). In what he calls the German theory of meter, a measure built from different simple measures, like 2+3 or 2+2+3, is an irregular compound meter, and one built from equal measures, like 2+2+2, a regular one. The grouping, not the fraction, decides which: eight-eight grouped 2+2+2+2 is regular, grouped 3+3+2 is irregular (Med 1996, ch. XXVIII).

When the meter changes

A piece can also change meter as it goes: a bar of 3/4, then one of 2/4, then 5/8. Each new time signature is written at the bar where it starts, and it holds until the next one. Twentieth-century music uses this a great deal, and Stravinsky's The Rite of Spring is the famous case: the meter changes almost from bar to bar, so the accents keep landing where the listener does not expect them.

When the same alternation repeats all the way through, a composer can announce it once, with both signatures at the start. Med mentions the practice and does not recommend it; he also notes that the alternation is sometimes simply left for the performer to feel, without being written (Med 1996, ch. XIX).

What comes next

Everything here happens one meter at a time, even when the meter changes. When two meters, or two different divisions of the beat, sound at once, three against two, the result is polyrhythm and polymeter.