Dibalo Jonze
Member
A lot, as most of us have learned. I'm always thinking about permutations on or off the drums. If you don't like math or long posts you should either skip this thread or just read the bolded sentence lower down for a fun fact.
I remember being young and very naive in middle school and thinking that I had played let's say ~80% of what there was to play on drums. One day about 10 years later and after having played with about a dozen stylistically different bands I realized that I had barely scratched the surface of ~1% of what one can do on the drums. After learning some basic probability and statistics I quickly realized that even the ~1% was a very gross underestimate of what there is to do on drums.
Take a basic set-up of ride, snare, kick, and high hat. To start, consider all the different patterns of single strokes that you can play in one bar of a 1/16 note grid with just the right hand. We can use binary numbers to realize the possibilities. Just like the various combinations of computer bits available in 2 bytes worth of memory, we can represent a single measure of sticking patterns using a '1' for notes played and a ‘0’ for the 16ths not played. Just playing every quarter note looks like this:
1000100010001000
The equation to figure out all the combinations of 0s and 1s, aka rests and notes, is "two to the power of 16". SIXTEEN different locations for one of TWO possibilities.
2^16 = 65,536 one handed possible ways to split up a bar of 4/4.
For EACH of those 65,536 patterns, the left hand is also capable of playing any 16th note pattern.
2^16 multiplied by 2^16 = 4.29 billion patterns. At least every other person alive today could have a pattern named after them.
Now some say variety is the spice of life and dynamics are certainly one of the spices of drumming and it takes time and practice to play the combinations of notes & rests we already know with all of their unique accenting possibilities (otherwise the drum book industry wouldn't be as big of a customer to the paper industry). Since each note in the 16th note grid can technically be played as either a rest or a note or an accented note, that means the right hand now has over 43 million possibilities (= 3^16). But since my calculator is about to get overloaded let's pretend that for each one handed 16th note pattern of ‘0’s and ‘1’s, you can only play up to one of those ‘1’s as an accented note per bar. That alone still doubles the possible patterns for one hand.
Let's not totally neglect orchestration. We're often playing on more than just one drum/cymbal with each hand in a bar which makes these equations quite tricky. But again, my calculator. So let's be conservative again and say that despite all the ways we can move around the drums, we are limited to playing just one of the notes in the 16th note grid on a different sound source. No mambos, no rolling down the toms, just a single optional crash cymbal at some point in the measure. Nonetheless, this again doubles the combinations for each hand.
So far we have all the 16th note possibilities of one hand multiplied by two for limited accents per hand multiplied by two again for orchestrating on up to just one note. Now multiply this by the same possibilities of the other hand:
(2 x 2 x 2^16) x (2 x 2 x 2^16) = more than 68 billion hand combinations.
Oh, but those damn feet. If you just add a single kick note on the downbeat you've again doubled all the possibilities. Let's simplify the possibilities again as we consider the legs and say that the left foot and right foot can only play notes in an 1/8th note grid, and they cannot accent notes. So now each lower body limb adds "two to the power of 8" times as many possibilities (2^8 per leg).
~68 billion hand combinations x 2^8 bass patterns x 2^8 high hat patterns = 4.5 quadrillion four limbed combinations.
Okay, even though we've already been conservative with the actual combinations that are technically possible, I'll admit that tons of these drums beats/patterns will sound like junk or just redundant. So let's say that of these 4.5 quadrillion patterns, only one out of every million of them sound good or interesting to play.
Great so now we're down to just a measly 4.5 billion combinations.
Now let's pretend that we are superhumans and can read, practice, then play each of these combinations in ONE SECOND then immediately move on to the next one. We never take a break to eat or sleep, let along take time to read this lengthy absurd post on drummerworld dot com. Oh, and never mind that in order to play one new measure per second every second your average tempo must be at least 240 bpm. No problem, we’re superhumans after all.
So we divide 4.5 billion beats by 60 sec/min, 60 min/hour, 24 hrs/day, and 365 days/year to find out how long it would take us to play these...
**Using VERY conservative estimates it would take 142 years to play all of the possible four-limb, one-measure patterns in a 16th note grid assuming you were somehow able to play a new pattern every single second of every year**
-------------------
For the full scope, keep in mind we already cut this down to playing only one out of a million possible patterns, in a world where you can only play one accented (or one ghosted) note per measure, where you must keep your hand playing the same sound source except for crashing once if you choose, and where your feet haven't yet learned about 16th notes.
What haven't we considered? Eternity, practically speaking.
These calculations do not account for all the other things you can do on drums in addition to just accenting more notes or orchestrating on more than one sound source per limb:
All the of the different time signatures we play, subdivisions that are possible (these calculations don't even account for playing blues, jazz, or basic polyrhythms with a triplet meter), playing some of the notes in unison as flams, using buzz strokes, 32nd note doubles, and the whole spectrum of dynamics that we're accountable for. Okay, now we've got our homework cut out. Oh, one last thing. Don't forget to practice everything at a range of different tempos.
This understandably can seem like daunting information - to hear that in order to play all the possible decent sounding Garibaldi-esque beats in a lifetime you'll not only never sleep or eat again, but you'll have to simultaneously set the Guinness book of world records for longest living human by about three decades.
But for me it's really inspiring to think about all these possibilities, and humbling whenever I start to think “what’s next?” There are so many things we can do on drums that it really is hard to get bored if you're being creative. I find it inspiring, challenging, and a useful method for me to always be expanding my drumming.
Like I said, you had the option of skipping this entire thread. You could have instead practiced 0.000000000000001% of these permutations by now.
I remember being young and very naive in middle school and thinking that I had played let's say ~80% of what there was to play on drums. One day about 10 years later and after having played with about a dozen stylistically different bands I realized that I had barely scratched the surface of ~1% of what one can do on the drums. After learning some basic probability and statistics I quickly realized that even the ~1% was a very gross underestimate of what there is to do on drums.
Take a basic set-up of ride, snare, kick, and high hat. To start, consider all the different patterns of single strokes that you can play in one bar of a 1/16 note grid with just the right hand. We can use binary numbers to realize the possibilities. Just like the various combinations of computer bits available in 2 bytes worth of memory, we can represent a single measure of sticking patterns using a '1' for notes played and a ‘0’ for the 16ths not played. Just playing every quarter note looks like this:
1000100010001000
The equation to figure out all the combinations of 0s and 1s, aka rests and notes, is "two to the power of 16". SIXTEEN different locations for one of TWO possibilities.
2^16 = 65,536 one handed possible ways to split up a bar of 4/4.
For EACH of those 65,536 patterns, the left hand is also capable of playing any 16th note pattern.
2^16 multiplied by 2^16 = 4.29 billion patterns. At least every other person alive today could have a pattern named after them.
Now some say variety is the spice of life and dynamics are certainly one of the spices of drumming and it takes time and practice to play the combinations of notes & rests we already know with all of their unique accenting possibilities (otherwise the drum book industry wouldn't be as big of a customer to the paper industry). Since each note in the 16th note grid can technically be played as either a rest or a note or an accented note, that means the right hand now has over 43 million possibilities (= 3^16). But since my calculator is about to get overloaded let's pretend that for each one handed 16th note pattern of ‘0’s and ‘1’s, you can only play up to one of those ‘1’s as an accented note per bar. That alone still doubles the possible patterns for one hand.
Let's not totally neglect orchestration. We're often playing on more than just one drum/cymbal with each hand in a bar which makes these equations quite tricky. But again, my calculator. So let's be conservative again and say that despite all the ways we can move around the drums, we are limited to playing just one of the notes in the 16th note grid on a different sound source. No mambos, no rolling down the toms, just a single optional crash cymbal at some point in the measure. Nonetheless, this again doubles the combinations for each hand.
So far we have all the 16th note possibilities of one hand multiplied by two for limited accents per hand multiplied by two again for orchestrating on up to just one note. Now multiply this by the same possibilities of the other hand:
(2 x 2 x 2^16) x (2 x 2 x 2^16) = more than 68 billion hand combinations.
Oh, but those damn feet. If you just add a single kick note on the downbeat you've again doubled all the possibilities. Let's simplify the possibilities again as we consider the legs and say that the left foot and right foot can only play notes in an 1/8th note grid, and they cannot accent notes. So now each lower body limb adds "two to the power of 8" times as many possibilities (2^8 per leg).
~68 billion hand combinations x 2^8 bass patterns x 2^8 high hat patterns = 4.5 quadrillion four limbed combinations.
Okay, even though we've already been conservative with the actual combinations that are technically possible, I'll admit that tons of these drums beats/patterns will sound like junk or just redundant. So let's say that of these 4.5 quadrillion patterns, only one out of every million of them sound good or interesting to play.
Great so now we're down to just a measly 4.5 billion combinations.
Now let's pretend that we are superhumans and can read, practice, then play each of these combinations in ONE SECOND then immediately move on to the next one. We never take a break to eat or sleep, let along take time to read this lengthy absurd post on drummerworld dot com. Oh, and never mind that in order to play one new measure per second every second your average tempo must be at least 240 bpm. No problem, we’re superhumans after all.
So we divide 4.5 billion beats by 60 sec/min, 60 min/hour, 24 hrs/day, and 365 days/year to find out how long it would take us to play these...
**Using VERY conservative estimates it would take 142 years to play all of the possible four-limb, one-measure patterns in a 16th note grid assuming you were somehow able to play a new pattern every single second of every year**
-------------------
For the full scope, keep in mind we already cut this down to playing only one out of a million possible patterns, in a world where you can only play one accented (or one ghosted) note per measure, where you must keep your hand playing the same sound source except for crashing once if you choose, and where your feet haven't yet learned about 16th notes.
What haven't we considered? Eternity, practically speaking.
These calculations do not account for all the other things you can do on drums in addition to just accenting more notes or orchestrating on more than one sound source per limb:
All the of the different time signatures we play, subdivisions that are possible (these calculations don't even account for playing blues, jazz, or basic polyrhythms with a triplet meter), playing some of the notes in unison as flams, using buzz strokes, 32nd note doubles, and the whole spectrum of dynamics that we're accountable for. Okay, now we've got our homework cut out. Oh, one last thing. Don't forget to practice everything at a range of different tempos.
This understandably can seem like daunting information - to hear that in order to play all the possible decent sounding Garibaldi-esque beats in a lifetime you'll not only never sleep or eat again, but you'll have to simultaneously set the Guinness book of world records for longest living human by about three decades.
But for me it's really inspiring to think about all these possibilities, and humbling whenever I start to think “what’s next?” There are so many things we can do on drums that it really is hard to get bored if you're being creative. I find it inspiring, challenging, and a useful method for me to always be expanding my drumming.
Like I said, you had the option of skipping this entire thread. You could have instead practiced 0.000000000000001% of these permutations by now.
I would get into the maths but I can only count up to 4...
