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This topic has interesting aristas.

davidpenalosa wrote:An argument as to whether Indian rhythm or African rhythm is more complex probably cannot be resolved because the two systems are based on different criteria. Indian music is based in additive rhythm, while sub-Sahrana African music is based in divisive rhythm. Within their respective means of generating rhythm, each system is supreme.

It would be optimum if David could illustrate this to us the newbies.
I'd also like to know if he is referring to indian classical percussion or to indian folk percussion.

african percussive music:
http://www.youtube.com/watch?v=FMs3LTtgwY8

indian classical percussive music:
http://www.youtube.com/watch?v=N81oMTvvX3o

My understanding of Indian and other south Asian music is vey limited, but my statement which you quote, has been affirmed in every discussion I've had with those who are intimately familiar with south Asian music. It is also affirmed in the book Music in South India by T. Viswanathan and Mathew Harp Allen (Oxford Press 2004).



Odd meters are perceived in additive terms (7 + 1 + 2), (3 + 2 + 2), (3 + 2 + 2), (2 + 3):



An eight-beat cycle is also perceived in additive form (4 + 2 + 2):



My statement applies to both the folk and classical music of India.

The clearest example I can think of to illustrate my point is the figure known in Cuban music as tresillo:

X . . X . . X .

In Asian music this is counted as: 3 + 3 + 2 (additive rhythm):

1 2 3 1 2 3 1 2

Here is an example of Indian music where the "tresillo" figure is periodically sounded:

http://www.youtube.com/watch?v=f1TxzE3erv8

In African music, the figure is not traditionally counted of course, but it is generated through a specific type of cross-rhythm (a form of divisive rhythm). The eight pulses are divided by three. The result is two cross-beats, with a remainder of a partial cross-beat consisting of two pulses:

8 ÷ 3 = 2, r 2 (divisive rhythm).


1 e + a 2 e + a

The African musician and scholar Kofi Agawu addresses the mistake of writing African expressions of "tresillo" in additive form:

Kofi Agawu, Representing African Music wrote:Although the difference between the two ways of notating this rhythm may seem small, they stem from fundamentally different conceptions. Those who wish to convey a sense of the rhythm’s background [main beats], and who understand the surface morphology in relation to a regular subsurface articulation, will prefer the divisive format. Those who imagine the addition of three, then three, then two sixteenth notes will treat the well-formedness of 3+3+2 as fortuitous, a product of grouping rather than of metrical structure. They will be tempted to deny that African music has a bona fide metrical structure because of its frequent departures from normative grouping structure” (2003: 87).

The triple-pulse correlative of tresillo is the cross-rhythm three-over-two (3:2). There are two main beats within a span of six triple-pulses:

1 . . 2 . .

To generate cross-beats you divide the six pulses by two. The result is three cross-beats:

X . X . X .

In other words:

6 ÷ 2 = 3 (divisive rhythm).

1 + a 2 + a

Notice that the pulse names of tresillo and the triple-pulse cross-beats are identical: 1, 1a, 2+.

-David

The result of all this is in the "feel" and how one dances to the music!

windhorse wrote:The result of all this is in the "feel" and how one dances to the music!

. . . which is expressed most clearly by the steps of the dancer's feet.





“For cultural insiders, identifying the . . . ‘dance feet’ occurs instinctively and spontaneously. Those not familiar with the choreographic supplement, however, sometimes have trouble locating the main beats and expressing them in movement. Hearing African music on recordings alone without prior grounding in its dance-based rhythms will not necessarily convey the choreographic supplement. Not surprisingly, many misinterpretations of African rhythm and meter stem from a failure to observe the dance” (Agawu 2003: 73).

davidpenalosa wrote:8 ÷ 3 = 2, r 2 (divisive rhythm).

1 e + a 2 e + a

Very clear and illustrative, David.
Although I don't understand the equations, what do e and a represent?

shor wrote: I don't understand the equations, what do e and a represent?

Hi Shor,
Thanks for asking. There are probably several people who don’t understand the abbreviations, or that particular equation.

When the main beats (1, 2, 3, 4) are divided by four pulses each, they are often counted in this way:

“One, e (‘ee’), + (‘and’), a (‘ah’), Two, e, +, a, etc.

So, a single measure of 4/4, where the main beats are represented by four quarter-notes, and the regular pulses (subdivisions of the main beats) are represented by sixteen sixteenth-notes, is counted like this:

1 e + a 2 e + a 3 e + a 4 e + a

For those of you who read standard notation, this is the basic metric structure when clave is written in a single measure of 4/4.

Concerning the equation, if we take the eight pulses that span two main beats:

1 e + a 2 e + a

. . . and divide those eight pulses by three (grouping pulses in sets of three), we get a result of two cross-beats (consisting of three pulses each):

[1 e +] [a 2 e]

. . . with a remainder of a partial cross-beat, consisting of two pulses:

[+ a]

The resultant pattern is what is known in Cuban music as tresillo (highlighted in red below).

1 e + a 2 e + a

Expressed as an equation, it's eight pulses divided by three, resulting in two cross-beats, with a remainder of two pulses. Or: 8 ÷ 3 = 2, r 2.

I hope that helps. If you need more clarification, or if my answer raises more questions, please let me know.
-David