Risset Rhythms

In the 90s, cognitive scientist Roger Shepard came up with the idea of making endlessly rising (or falling) loops by having overlapping notes of rising pitch with the low notes fading in and the high notes fading out (or vice versa for falling). They became known as "Shepard Tones" https://en.wikipedia.org/wiki/Shepard_tone . French composer Jean-Claude Risset then extended this idea to rhythm, creating the Risset Rhythm that endlessly rises in tempo and pitch (there's a recording on https://en.wikipedia.org/wiki/Jean-Claude_Risset ). His original can be quite baffling, and I've read many very unhelpful descriptions of it. So now that I understand it, let me try to explain:
It's a short drum sample (with a highish note in it) that over a period of about 30 seconds doubles in playback rate (hence tempo and frequency/pitch), but at the same time, a double rate version of itself is fading out and a half rate layer is fading in underneath to become the middle layer when it all repeats (and the middle layer becomes the top layer). You can check this by listening to the note in the sample as it slides up an octave over the 30 seconds. About half way through (depending on your ear/focus), the bottom layer takes over as the dominant groove and the process continues. Risset pushes the effect even further, as over the course of the almost 5 minutes, the bottom layer (fading in underneath) is gradually increasingly delayed, making it seem more and more sluggish and making the double tempo version on top of it seem rushier. By the end it's quite a mess (no offense, Mr. Risset!)

I convergently "discovered" Shepard Tones back when I first started looping in the early 90s (using the "Loop of Silence" https://youtu.be/vgXZKNiEGR0 ) and used them a few years ago when using irrational numbers as delays http://malwebb.com/irrational.html . And I also got into looping the harmonic series http://malwebb.com/triangle.html like a kind of musical Fourier Transform, which I turned into a song http://malwebb.com/HarmonicsMalKyDemo.mp3 for my nerdy show Notey and Noisy: A Sound Science Mathemusical http://malwebb.com/notnoi.html .
But in 2019, I was first shown the Risset Rhythm and quickly realised I could use it to create another angle on my harmonic series triangle, which I called Risset/Shepard/Harmonic https://youtu.be/2otKFo79Je0 .
 
It's a three layer beatbox loop that gradually doubles in tempo every 10.5 seconds. The bottom layer (2 bars) is half the tempo of the middle layer (4 bars) and it slowly fades in and becomes the middle layer when it all repeats, at which point the middle layer becomes the top layer (8 bars), which slowly fades out (and is thus double the tempo of the middle layer). As the tempo increases, the frequency (pitch) of the notes correspondingly increases (i.e. a doubling of tempo results in an octave rise), creating the harmonic series across the three layers. The brass lines (in equal temperament) create rising "Shepard tone" lines, giving the whole affair a certain chordal jauntiness! This creates the basis of my song, "Home Sweet Homeostasis" http://malwebb.com/homeo.html , about homeostasis and the illusion of perpetual growth, of course! Hear its premiere here: https://youtu.be/k21TLzKz3Ms&t=1662s (with the loop build).

I also used the reverse of the beatbox part with a guitar part for a breakdown section playing | G | Em | D | G/B Am | (a descending pentonic). If you consider the G/B as the start of the loop, it's 5 bars slowing down. This works because (referring back to the forwards/upwards version) it can be any number of bars speeding up, depending on which harmonic you start on. i.e., if you start on the 5th harmonic, it's 5 bars long, from the 6th harmonic is 6 bars long, and if the double tempo part hung on for longer, from the 7th harmonic would be 7 bars long. Making the whole thing longer would facilitate this. When I was first started playing with it on my Headrush looper, I confused myself several times by hearing the wrong bar as the first bar and thinking, "What? how is it now 5 bars long?!!!"
I made the finished version this length it is so that the tempos were easy powers of 2, and also, being 10.5 seconds long, it fits on my Akai Headrush looper. Bonus!

The version in the video was made in Reaper ( http://reaper.fm ), rate shifting a single bar of beatbox (cut into beats to make the speed up smooth) and a single vocal "dng" rate shifted in parallel. I made sure the speed up corresponded to whole number multiples per note, thus creating the harmonic series. I then rendered out the beat and the notes separately, re-imported them into Reaper and cut each into the three layers, fading in the bottom layer and fading out the top one for the best possible effect. For the rhythm, it's the balance of the ploddy and the frantic. For the notes, I aimed to have not too much of the tonic (harmonics 1, 2 and 4) that it became too defined as being the downbeat, and not too much of high harmonics after the 19th, where it gets less that chromatic ...but enough to be fun! When I perform it, I loop it all live (on my Boomerang III and Akai Headrush loopers), imitating the pitch shift of the beatbox and the note progression with my face.

Having done that, I had the idea of a Triplet Risset, tripling the rate over the cycle. Using a bar of 9/8 would allow this to work and Jesu Joy of Man's Desiring by J.S. Bach was the most famous 9/8 piece I could think of, hence: https://youtu.be/nZoiLMRqUgE . For this one, I'd realised I could automate the playback rate in Reaper, which makes it all significantly easier. And I made the original sample rate half way through the middle layer (by halving its sample rate and adjusting the other layers accordingly: See the graphic).


I even tried a quintupling version, with a bar of Paul Desmond's Take Five https://malwebb.com/TakeRisset.mp3 , but it's way too spread out for the illusion to work.

  I then tried another angle on the tripling one, using one trombone note rate shifted, with the layers being 3 notes, 9 notes and 27 notes. The result is a little reminiscent of Aphex Twin’s Bucephalus Bouncing Ball https://youtu.be/tLjwJijT7gQ&t=183s . Similarly (although very differently!) I found a groove that worked across it (6 pulses in my case) and found chords that kind of fitted it, and thus: https://youtu.be/NQKnpXALuPc ...kinda groovy!