Complex rhythms - Introduction

After a self- inflicted couple of months of chaos through moving from a moderately large house with garden etc. to a  spacious but much smaller flat, the rhythm of life for both me and my wife is very slowly returning to normal albeit without a sound system yet; but, soon that also will come to pass as well.

In his stimulating discussions of rhythm Ken covered quite a bit of ground. There are many questions in each blog and I am almost certain that these questions will lead to further interesting discussions. One of the fascinating aspects of rhythm is the consideration of the organisation of music using rhythmic sentences as the basis of a composition. This idea is not new and perhaps it was one of the most important aspects of ancient music which lasted well into the High Baroque era. Even as late as the17^th century, the instrumental tuning  in use was very uncertain and it was locale specific. Although later  in the Romantic era an agreed upon tempered scale ( A4 = 440 Hz) increased the emphasis in favour pitch related properties of a composition, rhythmic structure of music was and still is a very important property of any musical work.   

If we consider many forms of dances, folksongs, and immediately approachable popular music, the rhythmic sentences that repeat in more or less regular intervals are short and readily identifiable. In general, in these types of composition, the rhythmic content of musical expressions could be readily expressed within the context of the meter associated with the composition and the repeated patterns rarely exceed a few measures at most. In a structure like this, a change in the rhythmic structure acts like a caesura and one of the structures (sequences) can be used repeatedly (refrain).  If the purposes behind the composition of these types are examined; we would conclude that this is a very logical structure. This is also applicable to any section of a musical work where an immediate recognition of that section is an important concern. There are many interesting theoretical aspects of rhythmic structures that are discussed extensively in G. W. Cooper and L. B. Meyer The Rhythmic Structure of Music (University of Chicago Press Chicago, London 1960).

There is a practical matter for the composer, players and audience alike; as the musical sentences become more complicated, rhythmic structures become more divorced from the easily recognisable forms, both the comprehension and interpretation  of the rhythmic structure demand more careful listening. If one considers from the oldest existing music, through Renaissance, Baroque, Classical, Romantic eras to our own time, the importance of the rhythmic structure becomes much more apparent.  In this respect, it may be claimed that there is more commonality between a Bach fugue and quintessentially 20^th Century pieces such as Messaien's Turangalila or Takemitsu's Colours than  it is apparent in a casual hearing. One might probably be more correct than not stating that this has always been so, because considering the music of a vast geographic area extending from Iberia to a virtual meridian just east of Myanmar, the similarity of the rhythmic structures – highlighted by linguistic differences – provide an evidence that the rhythmic similarities are so much of the defining property of music the this has always been the case, from the first attempts at singing by our earliest ancestors to our own creative musical efforts.  Naturally, included in this notion, there is the relative influence of the language and/or dialect based prosody on the rhythmic structures of any locally or nationally identifiable music. This important observations lead to a vast area of knowledge and investigation, unfortunately too far afield from our discussions. Thus we'll leave this to linguists and ethno-musicologists, who are much better equipped to discuss these topics and limit our discussion to considerations of musical rhythmic structures of the music normally discussed here.

A generalised rhythmic language:

A rhythm can be fully defined by two relative properties of a sound: length, stress. The length is long, medium and short and the stress is strong and weak. The basis in terms of the note length can be extended to any commonly used notes (Breve, semi-breve, minim etc.), for the purposes of this article we will use a minim based system with:

Symbol            Length             Strength          ''Sound''

h                      Long                Strong             Boom

H                     Long                Weak               Baah          

q                      Med                 Strong             Ta

Q                     Med                 Weak               Ti

e                      Short               Strong             Ka

E                      Short               Weak               Ke

Rule I. A rhythmic pattern is the expressed using the least amount of weak notes

 Example:   Q Q = H  but  q Q ≠ h                                                                                                                                                            

Rule II. A rhythmic sentence is the sequence of rhythms that occur at least twice

Example:   < H Q h Q E q E q h H Q h Q E q E q h  >   is a sequence with a sentence repeated once. The sentence has a most unusual meter of 11/ 4 :  < H Q h Q E q E q h >. The partition by the unusual meter is not necessary and within the context of the music it can be any convenient partition. A sentence can be any length, but the composer must keep in mind that very long sentences are hard to interpret, perform, or listen to. One of the musical examples is a long sequence to demonstrate this difficulty. In fact, one can calculate the appropriate length easily. A sentence with a meter 120/4 is about a minute of allegro music, which asks the listener to recall the details of a whole minute in order to understand the rhythmic structure.  I would not be surprised to find such a composition to be beyond the reach of most audiences.

Common short  rhythmic sentences can be used as building blocks for long sentences. For example:

a) 1. <  h e > 5/8   2.  < H Q h >10/8   3. < Q E >3/8  Caesura or cadence 4 / 8

      1 + 2  + 3  + 3  = < h e H Q h Q E q E>  16 / 8

 Sequence:   < h e H Q h Q E q E  C  h e H Q h Q E q E  C >  =>  5 / 8:6 h x 6 H E ¦E h 6 Q E q 6 E h 6 h x 6 H E ¦E h 6 Q E q 6 E Q Q 6