Time signatures, polyrhythmics?
For time signatures, the top number is purely the number of designated "beats" worth of music in each bar as defined by the lower number. For example, in the time signature 4/4, there are 4 beats in each bar (that's the top number telling you that) and each beat is worth a quarter note or crotchet (that's what the bottom number tells you).
In 21/16 there are 21 (top number) semiquavers (bottom number) worth of musical time in each bar.
To work out a time signature from a piece of music (ie you have the notation but not the time signature and you want to work it out), you need to look at how it's written. You can't just add up the number of crotchet or quaver beats in a bar and decide on a time signature cos it's not always as simple as that. For example, 6/8 and 3/4 both have the same number of quavers worth or crotchets worth of music in each bar (if quaver = 120bpm for both of them, then they would both last the same length of time) so how do you know if it's in 6/8 or 3/4? Look at how the notes are grouped - if they are grouped in groups that give 3 quavers worth of music with stems joined together, then it's 6/8. The grouping of the notes gives the kind of time signature you are looking at. You may ask why not just write it as 3/4 if they both contain the same amount of musical "time"... well, the feel of a bar in 6/8 is actually a feeling of 2 "beats" in a bar (2 groups of 3 quavers each: One-and-a Two-and-a); the bar is divided equally into 2 halfs. In 3/4 time, the bar is divided into 3 beats (3 groups of just 2 quavers: One-and Two-and Three-and)
Now a polyrhythm is basically more than one rhythm being played at once to create a new rhythm.
Rhythm 1: 2 equal quavers
Rhythm 2: 3 triplet quavers
Rhythm1: One -and
Each rhthym lasts for one beat which in the example abouve is a crotchet beat. Clap the first rhythm at a speed of crotchet=60 (one beat per second) Even quavers... not hard!
Now clap rhythm 2 to the same beat. Triplet quavers, so you're fitting 3 notes evenly into the same beat.
Now for the polyrhythm... you have to do both together! This isn't as hard as it sounds. we're going to tap rhythm1 on your right knee with your right hand and tap rhythm2 on your left knee with your left hand. The easy way to get the correct rhythm is this: Use the phrase "nice cup of tea" to the rhythm of "One Two-And Three" with One Two and Three being the triplet quavers from rhythm 2 (whilst the One and And are from rhythm 1). So in the Nice Cup Of Tea rhythm, it goes (with your hands!) Together left right left. That new rhythm which is what you hear when you play the 2 old rhythms at the same time is a polyrhythm (but bear in mind it's a simple one!)
Technically speaking, what you have just constructed isn't in actual fact a polyrhythm - musical purists like to state that if there are only 2 rhythms and one rhythm can be contained as natural subdivisions of the other rhythm, then it is not a true polyrhythm. However, the above demonstrates the idea and would be classed as a polyrhythm by all but the most nit-picking of musicians! Also, if the two rhythms are notated as one then it obviously is still only 1 rhyhtm and also not a polyrhythm.
(Edited by Spagbol at 4:22 pm on Dec. 29, 2001)