What is there to even play on a drum set?

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.
 

MrInsanePolack

Platinum Member
2^16 multiplied by 2^16 = 4.29 billion patterns. At least every other person alive today could have a pattern named after them.
Your math here is wrong. 2^16 is 65,536, and squared is approximately 4.29 billion. That's not what you want.

Screenshot_20201231-095446_Calculator.jpg

You need to factor in that if both the left hand and right hand are playing 16ths simultaneously with 2 options (stroke or rest), you are now actually playing 32nds with 4 options (2 per hand). 4^32 = 1.8446741E+19 combinations if each hand is playing in a 16ths framework.

Screenshot_20201231-100248_Calculator.jpg

Interesting post though.

EDIT: After further thought this may be wrong still. I'll keep working on it.
 
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C.M. Jones

Well-known member
While percussive possibilities are almost endless -- daunting, even, in the fury of their immensity -- the practical parameters that govern them are far less overwhelming. Most pop/rock/country applications call for minor variations of three or four patterns. Jazz and fusion might lend themselves to a busyness that promotes nuanced complexity, but that label, too, can be misleading. Even the most intricate series of notes can be tamed and made manageable through tasteful simplification. Quite often, subtraction carries more currency than addition.

We drummers should never dread beats or fear fills; instead, we should take charge of them. We don't need to execute every chop in existence to be well-rounded players. With the proper acumen, we can conquer any template (in our own way) and make it more than fitting for the music at hand. Drumming should be all about music. It's a one-dimensional pursuit in the absence of other instruments.
 

GetAgrippa

Platinum Member
But do you need to play all possibilities playing Mustang Sally. LOL .It is about music and rather than see all possibilities we often see similar patterns- whereas the actual possibilities would be far larger than the simple drum model we have. All the AI generated music I’ve heard sounds familiar so nothing novel yet. It’s interesting the music that gains popularity with humans-seems we use a limited tool box so create genres, etc. it’s really like languages .
 

MrInsanePolack

Platinum Member
EDIT: After further thought this may be wrong still. I'll keep working on it.
There are too many parameters to consider with 16th notes. Are they in total (8ths each hand), or per hand? Alternating, unison, or both (32nd notes)? If 32nds, can each hand play any space or only the 16ths?

Even just 4 spaces has 16 options with 1 hand. 0=rest, 1=stroke
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

Now give each option a left and right option, an alternating option, a unison option, and both options together. That's just too much to think about.
 

Bozozoid

Well-known member
Vinnie mmmmight say good question mmaybe but I still get excited when I learn some new fill possibility while going through stick control thinking I've got something to show the world!
 

Odd-Arne Oseberg

Platinum Member
Even if able it wouldn't do much for you as a musician, so I'll stick with the possibilities I find useful within each of the framworks I find myself playing in. That's already more than what's possible to stay on top of continuously.
 

GetAgrippa

Platinum Member
So are you saying to reach drumming enlightenment we really are all wrong practicing and playing the same when even if we never play same thing twice we’ll never reach all possibilities? I bet hundreds of thousands of years ago primitive drummers did that and it annoyed everyone so they were stoned to death and by a process of natural selection drummers learned to do as they do now. I guess their trial snd error was a trial by fire - or stone.
 
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Your math here is wrong. 2^16 is 65,536, and squared is approximately 4.29 billion. That's not what you want.
No, my math is correct for what I’m describing. Each hand can only play at a 1/16th note resolution, such that if the hands are playing 16ths simultaneously then they’re playing in unison and not alternating. You could say four options per 16 locations like you said…4^16, which is the same as one hand that can do 2^16 multiplied by the same possibilities from the other hand. Glad you find this thought experiment interesting too.

But do you need to play all possibilities playing Mustang Sally. LOL .
No, but then again I never play Mustang Sally, lol. A lot of people spend their time playing crossword puzzles or watching tv for enjoyment, which also don’t help your skills playing Mustang Sally. Drumming is my crossword puzzle, I enjoy the different coordination puzzles and my ears like the results too. Plus I'm a big advocate of gaining as much overhead as possible so that if you get thrown a solo during Mustang Sally, you can play a four bar solo that has never been played before. Playing for an audience or listeners is only one of the many reason why I play the drums.

But even for performance I like to be as dexterous and be able to play as full sounding as possible. You can play busy patterns with lots of unisons or contrasting syncopation, if you can play them at low dynamics. I love a lot of Afro-Cuban, Brazilian, African, and 2nd Line Bands, and I try in ways to cop their feels. These are styles where you already have several percussionists creating soundscapes and making them sound good. Those groups are certainly playing music. I even love trying to replicate a marching band walking through city streets with all of it's reverb and echos. This is a fat sound that doesn't have to be jarring. Electric guitar players use tons of effects to create a bigger tone than what an acoustic guitar is capable. I like thickening up my notes sometimes.

Just get a copy of "Future Sounds" by David Garibaldi. Enuff said.
Yep, my takeaway from Future Sounds was what I take away from a lot of great books, they are a launching pad for you to discover way more beats than can be printed. There is a much larger world of viable Garibaldi-esque beats than what's printed in his book. Consider that in a fusion band you might already have a guitar, bass, keys, and horn player all playing busy 16th note patterns that are sometimes juxtaposed, sometimes in unison with each other. There is already more rhythmic nuance and possibilities created by the rest of the band than what I layed out in my conservative estimates of musical possibilities.

Speaking of books, even in the first part of New Breed we are meant to practice 39 ostinatos over 10 pages each with 36 bars of phrasing. That’s 14,040 measures of pretty basic 3 limb ostinatos + a lead voicing. In the composite systems section he then opens our eyes to the idea that any of these measures we’ve just built can be followed by a mix of 3 of any of the other measures. And playing four bar phrases is certainly more interesting than just my single bar example. So that provides 14,040^4 = 3.88 E+12 ways to use the music written in New Breed.

If I had gone Chester with my numerical examples, it would take 123,214 years to play all these combinations keeping a constant 240 bpm.
 

MrInsanePolack

Platinum Member
No, my math is correct for what I’m describing. Each hand can only play at a 1/16th note resolution, such that if the hands are playing 16ths simultaneously then they’re playing in unison and not alternating. You could say four options per 16 locations like you said…4^16, which is the same as one hand that can do 2^16 multiplied by the same possibilities from the other hand. Glad you find this thought experiment interesting too.
Okay, that makes a bit more sense. I was thinking too far into it. It is interesting. I dont have nearly enough time left to get even remotely close.
 

Odd-Arne Oseberg

Platinum Member
So are you saying to reach drumming enlightenment we really are all wrong practicing and playing the same when even if we never play same thing twice we’ll never reach all possibilities? I bet hundreds of thousands of years ago primitive drummers did that and it annoyed everyone so they were stoned to death and by a process of natural selection drummers learned to do as they do now. I guess their trial snd error was a trial by fire - or stone.
Well, it did take a few beheadings, but they did eventually get the tritone through.
 

GetAgrippa

Platinum Member
I think it's more interesting we don't play all permutations but you can find a paradiddle or six stroke roll used in different ways and context in all kinds of music. Like language I'm sure musicologist try to dissect music to common roots and evolving-so a lil something old and lil something new. But whatever the combinations it has to be attractive and have some meaning to other humans. Sometimes it's space and time related-like old rock I loved back in 60-70s I'm not to fond of today-some I can't believe I ever liked it and other music I like but then never gave a listen. I've read links with genre of music and intellectual abilities -so jazz intellectual others not. I'm sure it's completely made up horse manure. I'm not addressing the statistical analysis with my New Year's resolution to be more concise and less mental masterbatory diarrhea and streaming, rabbit holes, worm holes, and the like. I need to clean up my act for 2021-so getting rid of crap.
 
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So are you saying to reach drumming enlightenment we really are all wrong practicing and playing the same when even if we never play same thing twice we’ll never reach all possibilities? I bet hundreds of thousands of years ago primitive drummers did that and it annoyed everyone so they were stoned to death and by a process of natural selection drummers learned to do as they do now. I guess their trial snd error was a trial by fire - or stone.
Ha! Of course not. I think you're joking and not saying my obsession with over thinking is worthy of a stoning on DW. I tried to make clear that this wasn't intended for anyone to think this is a method or goal that should be used, but just food for thought. I'm also one to think that you could spend a life-time just practicing just a few of the beats out there to truly master them at all reasonable dynamic levels and tempos.😃

[QUOTE="opentune, post: 1766631, member: 44891"
What does any of this say about playing for the song?
In my view the best things to do with drums is make music, not exhausting all the permutations and combinations.
[/QUOTE]

Not much. Notice I never said anything about music or playing for the song. There are plenty of other threads for that. This was just food for thought that I thought some with a similar proclivity for critical thinking would enjoy, and just like posting pictures of gear online or spending time researching what heads to buy it isn't meant to necessarily improve one's musicianship. However like I said, thinking about this has had a number of practical implications for my drumming, both in how I can serve the music, and how I simply enjoy all the benefits that playing drums for me provides. It takes a computer to calculate all of these possibilities but it takes a human to know how to figure out which ones of them might make sense to learn.
 
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