Beat/Pulse Grouping
When talking about odd time signatures, people always talk about dividing the time signature into beat groupings, and those beat groupings are most prominently 2 and 3 (for example: 5/4 being 2+3 or 3+2). Why aren't there other beat groupings such as 1, 4, 5 and so on ( n>3 not being divided by 2 and/or 3, meaning that 5/4 can also be 2+1+2, 4+1, 5, and meaning that 2+2+1 =/= 4+1)?
So - if there aren't other beat groupings, could you explain why (proof), and if there are, could you give examples of cultures and maybe even pieces which use such beat groupings?
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This, at its simplest, boils down to the way humans work.
We are most used to two-beat structures, probably stemming from our walking. One, two, one, two etc... And four stems quite simply from this.
A three is also quite straightforward, and doesnt take much to work with.
Imagine a five beat, or a seven beat measure - while you can count one-two-three-four-five-six-seven, it's much easier to go one-two one-two one-two-three.
Pieces can be grouped however a composer pleases. Traditionally, twos and threes have been used - but that's simply that, because of tradition. Music traditionally falls into twos, threes and fours anyway (the most common time signatures are still duple, triple or quadruple metre), and so old habits die hard. However, there are plenty of examples of pieces which don't group things in twos or threes - here are two:
Aleksandr Scriabin's Prelude no. 14 from his Twenty Four Preludes (Op. 11) is in 15/8, and rather than grouping it into 5 groups of 3, he groups it into 3 groups of 5. Notationally (again because of convention) it is written as three lots of dotted crotchet, crotchet (dotted quarter note, quarter note), but that is seemingly simply because we don't have symbols for 5/2 notes like we do for whole note values and 3/2 note values. The pulse of the piece is definitely in fives - even the tempo marking is given as a dotted crotchet tied to a crotchet. PDF here: hz.imslp.info/files/imglnks/usimg/f/f8/IMSLP75864-PMLP09363-Scriabin_Ausgewaehlte_Klavierwerke_Band_2_Peters_Op_11_filter.pdf (go to page 30). The first prelude also uses quintuplets against triplets, using beats of five against beats of three.
Many of Philip Glass's early pieces are built out of small units which repeat and get longer. As a result, he groups the music largely according by keeping what originally were the short units together. For example, take 'Music in Contrary Motion', the opening bar of which is as follows:
(published by Chester Music)
Hope this helps!
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