(or BPPR for short).
This is my name for the process of combining common polyrhythms, like 4 against 3 or 3 against 2, and blurring them in ways that allow unexpected polyrhythms, like 7 against 5, to work as morphable grooves.
I've written 4 songs that feature Blurred PolyPolyRhythms:
Giant Gippsland Earthworm (5 against 7), Eunice (9 against 13), Peak (8 against 5 (and 3, 13 and 21!) and Make Stuff Up (8 against 11).
When I was little, I used to enjoy singing the 5-to-the-bar classic Everything's Alright (from Jesus Christ Superstar) with the first 4 notes of the title sung as dotted quavers (4 against 3). Then when I was about 13, I realised that if I put crotchet triplets over the last 2 beats of the bar (3 against 2) it made it all pretty close to 7 against 5. This kept me quietly amused for the next 30 years, but I didn't do anything with it. Then my friend Carl Pannuzzo wrote a song, for his acapella trio, the Acapelicans, called Seven. I immediately heard it as being in 5 with 7 against it. It turns out that Carl hadn't intended it. The bass singer, Simon, felt the song in 5 while Carl and Sarah felt it in 7, yet they all happily grooved together.
In 2008, I helped record Penelope Swales' version of Baterz's song Twee, which is in 17 (grouped 6-6-5), but for the final singalong, Penelope squashes a 9 across it and it works! Yeah, that got me thinking! Then in 2014, I incorporated some 7 against 5 into my score for Little Wing Puppets' show, "Spike".
Weirdly, my next foray into BPPR was 9 against 13. I was playing a 13 groove with Linsey Pollak and found myself spontaneously putting 9 against it (as 4 against 6 then 2 against 3 then 3 against 4). The "wonky waltz" nature of got me inspired. In working out the ratios, I realised that saying"4 over 3" is misleading*, as it means dividing 3 beats into 4, so therefore the fraction is actually 3/4 (thus 0.75). So I tend to say "4 against 3" for dotted quavers. Crotchet triplets (3 against 2) are thus 2/3 or 0.66... , which means dotted quavers (0.75) are that little bit slower that crotchet triplets (0.66...). Therefore, to even out the blurred polypolyrhythm, you need the rush the 4 against a little and drag the 3 against 2s a bit. Or play with which beats are going to flam. Eventually, my experiments with 9 against 13 became my song Eunice, which starts in a straight 13, then puts a 9 disco over a two bar cycle. Then for a only a few bars it goes into a 9 waltz before making it an 18 grouped in 3s (shuffle) with the one of the groove displaced 3 beats (subdivisions)* later... such fun! This section has a nod Joe Jackson's "Stepping Out" in the bassline. It then displaces back to the 9 disco before doing the straight 13 to the end (except for the 4 bars where all the above grooves are stacked on eachother).
I soon drew up my BPPR page of possibilities (see below). 8 against 11 is particularly satisfying, due to its symmetricality and having an 8 involved and that eventually became my song, Make Stuff Up , with a rather Bossa Nova vibe for the 11 and a 16thy groove (with the one displaced an 1/8 later) for the 8.
Even though 5 against 3 (thus 0.6) isn't a particularly common polyrhythm, I was drawn to the Fibonacci / Golden Ratio vibe of 5 against 8 and 8 against 13. Here's my 13 against 8 version of the Mission Impossible theme: http://malwebb.com/AimHigh.mp3 . I call this "Aim High", as the morse code for AH is dot dash dot dot dot dot, which is what my 13 rhythm is, and Lalo Schifrin based the 5/4 rhythm of Mission Impossible on the morse code for MI, which is dash dash dot dot. I've also subtly ripped off Baterz's song, Darling, which is a lovely 4 against 3 thang in itself. He would've appreciated the odd timey-ness!
My song Peak goes full Fibonacci, being 8 against 5, but eventually also puts 13 and 21 across the bar in a few spots. It actually begins in 5, with 3 and 4 against it (yes, I know 4 isn't a Fibonacci number, but it sounds good!). It soon settles to a 5 against 8 mbira riff which underpins (well, overpins) the rest of the song. The middle part of the song has a fairly straight 8 beatbox groove against it (with its one displaced a beat later) which fits remarkably well with the 5 beatbox groove.
Then I finally wrote a 5 against 7 song, in Giant Gippsland Earthworm . The choruses are a straight up 7, but the rest of the song is various combinations of the 5 and 7 grooves. For the recording, I actually put the "pivot point" of bar (the 5th beat of the 7 and the 4th beat of the 5) at 41/70s of the bar (halfway between 40/70s and 42/70s), so both grooves were equally compromised (but, to me, imperceptably so). I'm thinking of doing a similar "pivot point of the bar" comprimise when I make a studio recording of "Peak", putting it somewhere between 0.6 (3/5) and 0.666... (2/3) perhaps at 0.6180339... (the inverse of the golden ratio, Phi) which would be appropriate, but only if it sounds good! For more fun with Phi, check out my Irrational number delays.
I'm now playing with 12 against 17 (see on the diagram below). 12 is already rich with polyrhythmic possibility, so to be able to blur it into a 17 could be amazing. It could be fun to group the 12 as 2-3-2-2-3 like the classic west african 12 beat bell pattern, so the 17 would be 3-4-3-3-4. Hmmm. But with this, as with all the songs mentioned above, I'm keen to do it in a way that an unwitting listener can still enjoy it as an inviting piece of music, without tripping over the maths: That's the dream!
The BPPR page of possibilities
Just a note on Polyrhythms in general, the western and Indian approach to polyrhythm is generally quite melodic, in that the polyrhythmic element floats over the groove. Whereas in African music the polyrhythm is intrinsic to the groove. i.e. a 12 beat cycle where the pulse might be 2, 3, 4 or 6 at any moment, depending on the listener and/or how the players and/or dancers are accentuating it. To me this is true polyrhythm. I try to leave all the pulse options open to the listener, and yet still guide the listener through a journey of different accetuations of the polyrhythm, switching between the pulse options and even displacing them (moving which pulse is the "one").
*Note: The fact that western time signatures look like fractions adds to the confusion created by a term like "4 over 3" also seeming like a fraction, where it's actually the inverse. [You might've notice I don't use any time signtures in the above description.] The "8" in 7/8 is fairly arbitary: 7/4, 7/8 and 7/16 could really all represent the same groove. So if a groove is 7-in-the-bar, I'll just call it a 7.
That said, if you treat time signatures as fractions, then they represent the fraction of a 4/4 bar (i.e. 7/8 is seven eights of a 4/4 bar). I feel like this is part of why 4/4 is so dominant, to the point where it's known as "common time"! Sure, a 4 groove is very appealing, but maybe it wouldn't be so dominant if our western system of notation didn't default to it so much. Hmmm.
I feel like this page will continue to evolve over the years... stay tuned!