How accurately can a trained drummer keep time?
December 27, 2010 9:18 PM Subscribe
How accurately can a trained drummer keep time? Could trained drummers be used to keep time accurately enough to determine longitude?
So, I've heard about how it was a big deal to invent a clock that was accurate enough to carry on a ship and be used to determine longitude. But enough about mechanical clocks -- what if you just had a drummer pounding out a rhythm, and other drummers to come and take shifts with them. Maybe someone else who isn't drumming is just counting out the number of measures. So if you want to figure out how much time has passed since the start of your journey, you see how many measures have been played. Compare that with astronomical observations and BAM, longitude.
But, are trained human drummers more or less accurate than mechanical clocks? Would it help or hurt to have two or more drummers playing at the same time? How bad would the clock drift be? So bad as to be useless to longitude calculations?
So, I've heard about how it was a big deal to invent a clock that was accurate enough to carry on a ship and be used to determine longitude. But enough about mechanical clocks -- what if you just had a drummer pounding out a rhythm, and other drummers to come and take shifts with them. Maybe someone else who isn't drumming is just counting out the number of measures. So if you want to figure out how much time has passed since the start of your journey, you see how many measures have been played. Compare that with astronomical observations and BAM, longitude.
But, are trained human drummers more or less accurate than mechanical clocks? Would it help or hurt to have two or more drummers playing at the same time? How bad would the clock drift be? So bad as to be useless to longitude calculations?
are trained human drummers more or less accurate than mechanical clocks?
less.
posted by sanko at 9:30 PM on December 27, 2010 [2 favorites]
less.
posted by sanko at 9:30 PM on December 27, 2010 [2 favorites]
Drummers don't "keep time" in the sense that a clock does.
They are steady, but not accurate. In other words, they are good at putting the same amount of time between each beat, but not so good at making the amount of time equal to X seconds of time.
And even small errors in the short run add up to big errors in the long run.
posted by mikeand1 at 9:33 PM on December 27, 2010 [1 favorite]
They are steady, but not accurate. In other words, they are good at putting the same amount of time between each beat, but not so good at making the amount of time equal to X seconds of time.
And even small errors in the short run add up to big errors in the long run.
posted by mikeand1 at 9:33 PM on December 27, 2010 [1 favorite]
Old joke: How do you know when there's a drummer at the door? A: The knocking keeps getting faster.
In fairness, they're only human. The sort of precision you're talking about is why machines exist.
posted by Gilbert at 9:37 PM on December 27, 2010
In fairness, they're only human. The sort of precision you're talking about is why machines exist.
posted by Gilbert at 9:37 PM on December 27, 2010
Best answer: This question can actually be answered empirically. I once came across a website (that I can't find now) which ran a beat detection algorithm on popular rock songs and plotted the average frequency over time. One of the outcomes was that it was possible to see who was playing to a click track, because the frequency was a flat line with a bit of noise. Other drummers, even good drummers from good bands, had all kinds of short-term variation in tempo - easily 10 to 20% at times - and sometimes long-term drift as well.
As a reasonably trained drummer I can report that it's actually quite difficult to keep an accurate tempo without an external reference over any period of time. Even fairly sizeable changes in tempo are difficult to detect and correct because they happen slowly, and the threshold below which the drummer can't detect a change is relatively large - I'd guess 5 to 10% at least? Even a perfect drummer with infinite stamina - or a perfect set of drummers who can swap out without introducing any noise - would still be vulnerable to long-term drift.
Interestingly though I do think it would be possible to correct for this with some sort of internal referencing. If for example the drummer were to dance while playing and match the base frequency to the speed of hopping back and forth, he would be able to feel when he slips much easier, and lock back into time much easier, because the hops are governed by the inertia of his body, not his mental clock - thus making him a sort of human pendulum. Drummers actually do this naturally to an extent, using their wrists and hands and sticks as minor pendulums, locking the rhythm into the natural frequency of the system (e.g. by varying the height of the stroke or the speed of the arms) so they can physically feel when the beat starts to slip. In my own playing I recently discovered that I do a lot better if I sort of bob my torso along with the beat, for the same reason. But of course you're still left with the stamina problem.
posted by PercussivePaul at 9:52 PM on December 27, 2010 [9 favorites]
As a reasonably trained drummer I can report that it's actually quite difficult to keep an accurate tempo without an external reference over any period of time. Even fairly sizeable changes in tempo are difficult to detect and correct because they happen slowly, and the threshold below which the drummer can't detect a change is relatively large - I'd guess 5 to 10% at least? Even a perfect drummer with infinite stamina - or a perfect set of drummers who can swap out without introducing any noise - would still be vulnerable to long-term drift.
Interestingly though I do think it would be possible to correct for this with some sort of internal referencing. If for example the drummer were to dance while playing and match the base frequency to the speed of hopping back and forth, he would be able to feel when he slips much easier, and lock back into time much easier, because the hops are governed by the inertia of his body, not his mental clock - thus making him a sort of human pendulum. Drummers actually do this naturally to an extent, using their wrists and hands and sticks as minor pendulums, locking the rhythm into the natural frequency of the system (e.g. by varying the height of the stroke or the speed of the arms) so they can physically feel when the beat starts to slip. In my own playing I recently discovered that I do a lot better if I sort of bob my torso along with the beat, for the same reason. But of course you're still left with the stamina problem.
posted by PercussivePaul at 9:52 PM on December 27, 2010 [9 favorites]
Here's a relevant blog post that shows very clearly the difference between live drummers and click tracks.
Humans don't really perceive time as clock time. We do okay with ratios (e.g. x is twice as long as y), which form the basis of rhythm. But our granular perception of time breaks down for very long or very short spans of time (i.e. we can count seconds, but not minutes, or nanoseconds). You can use something physical as a reference as PercussivePaul points out, and many people do this instinctively. There's some evidence we have pretty good tempo recall, which probably has a lot to do with muscle memory. But this is still dependent on a lot of factors e.g. how much adrenaline is going through your body (one reason why nervous musicians tend to rush). So keeping a dead steady tempo for even just an hour when your body is in a state of constant flux is, I'm guessing, next to impossible.
posted by speicus at 10:16 PM on December 27, 2010
Humans don't really perceive time as clock time. We do okay with ratios (e.g. x is twice as long as y), which form the basis of rhythm. But our granular perception of time breaks down for very long or very short spans of time (i.e. we can count seconds, but not minutes, or nanoseconds). You can use something physical as a reference as PercussivePaul points out, and many people do this instinctively. There's some evidence we have pretty good tempo recall, which probably has a lot to do with muscle memory. But this is still dependent on a lot of factors e.g. how much adrenaline is going through your body (one reason why nervous musicians tend to rush). So keeping a dead steady tempo for even just an hour when your body is in a state of constant flux is, I'm guessing, next to impossible.
posted by speicus at 10:16 PM on December 27, 2010
"But this is still dependent on a lot of factors e.g. how much adrenaline is going through your body (one reason why nervous musicians tend to rush)."
As a guitarist, this used to drive me nuts. Our band played quite a few songs that were demanding for the guitarist (me). I could pull them off in practice no problem, but when we played live, the drummer was a good 20-30% faster b/c of the adrenaline -- making me much more prone to errors!
But you can't exactly stop the song in the middle and tell the drummer to start again. more slowly this time... Once he starts the song a high speed, you're pretty much stuck with it!
posted by mikeand1 at 10:25 PM on December 27, 2010
As a guitarist, this used to drive me nuts. Our band played quite a few songs that were demanding for the guitarist (me). I could pull them off in practice no problem, but when we played live, the drummer was a good 20-30% faster b/c of the adrenaline -- making me much more prone to errors!
But you can't exactly stop the song in the middle and tell the drummer to start again. more slowly this time... Once he starts the song a high speed, you're pretty much stuck with it!
posted by mikeand1 at 10:25 PM on December 27, 2010
Best answer: Let's say you're sailing directly east-west along the equator, and for some reason, your drummers lose .25 seconds off every minute. Every four minutes, you're off by one second. Every day, your "clock" is off by 6 minutes.
After 10 days of this, of course, you're off by an hour. For simplicity's sake, let's just say that every 20 days, your clock has lost two hours. Your drummers get bored or tired, and over time they deviate even further...
Now, the sun travels across the sky at 15 degrees per hour. Being two hours off translates to being 30 degrees "off" in longitude. At the equator, that's about about 2,000 miles.
So, yeah, having an accurate timepiece was a pretty big deal back in the day.
posted by Cool Papa Bell at 11:13 PM on December 27, 2010 [1 favorite]
After 10 days of this, of course, you're off by an hour. For simplicity's sake, let's just say that every 20 days, your clock has lost two hours. Your drummers get bored or tired, and over time they deviate even further...
Now, the sun travels across the sky at 15 degrees per hour. Being two hours off translates to being 30 degrees "off" in longitude. At the equator, that's about about 2,000 miles.
So, yeah, having an accurate timepiece was a pretty big deal back in the day.
posted by Cool Papa Bell at 11:13 PM on December 27, 2010 [1 favorite]
Oh, and by the way ... it's about 3000 miles from London to New York, and your sailing ship will be lucky to average 5 knots per hour. That's about a 3-week trip. Plenty of time for your drummers to get you completely bugshit lost.
Hope you brought enough fresh water ...
posted by Cool Papa Bell at 11:17 PM on December 27, 2010
Hope you brought enough fresh water ...
posted by Cool Papa Bell at 11:17 PM on December 27, 2010
A complicating factor is that the ship is rolling back and forth in the waves, and the waves may be big or small. Along with fluctuations of heat and cold, and fluctuations of humidity, that's what made pendulum clocks useless on a ship.
posted by musofire at 5:27 AM on December 28, 2010
posted by musofire at 5:27 AM on December 28, 2010
Here is a discussion of John Harrison's work on making a watch suitable for determining longitude and the magnitude of errors in his timepieces; in one example an error of 5 seconds on an entire transatlantic voyage (presumably several weeks) translated to a error of 1 nautical mile. 5 seconds over several weeks is certainly far more precise than any human could be expected to perform (and it would take several people working in shifts and at top form at all time to even attempt to duplicate that sort of timing). There is a lot about Harrison and his approach to this problem on the web and there is even a good book about his work.
posted by TedW at 6:06 AM on December 28, 2010
posted by TedW at 6:06 AM on December 28, 2010
There's an old musicians' joke that's hard to reproduce in writing, but it goes like this:
How do you know when a drummer is at your door?
(rapping on the table, speeding up)
knock . . . knock . . . knock . . . knock .. knock .. knock .. knock . knock . knock.knock.knock.knockknockknock
From years of playing in bands where the beat really mattered, I can think of 2 drummers out of dozens I've worked with who had the rhythmic equivalent of nearly absolute pitch, or "perfect time."
They worked a lot.
posted by spitbull at 6:34 AM on December 28, 2010 [1 favorite]
How do you know when a drummer is at your door?
(rapping on the table, speeding up)
knock . . . knock . . . knock . . . knock .. knock .. knock .. knock . knock . knock.knock.knock.knockknockknock
From years of playing in bands where the beat really mattered, I can think of 2 drummers out of dozens I've worked with who had the rhythmic equivalent of nearly absolute pitch, or "perfect time."
They worked a lot.
posted by spitbull at 6:34 AM on December 28, 2010 [1 favorite]
As a guitarist, this used to drive me nuts. Our band played quite a few songs that were demanding for the guitarist (me). I could pull them off in practice no problem, but when we played live, the drummer was a good 20-30% faster b/c of the adrenaline -- making me much more prone to errors!
As both a drummer and guitarist this drives me totally up the wall when I see a drummer doing this live. One of the main reasons I used to play with a click track when I played live back in the day.
posted by playertobenamedlater at 8:09 AM on December 28, 2010
As both a drummer and guitarist this drives me totally up the wall when I see a drummer doing this live. One of the main reasons I used to play with a click track when I played live back in the day.
posted by playertobenamedlater at 8:09 AM on December 28, 2010
From years of playing in bands where the beat really mattered, I can think of 2 drummers out of dozens I've worked with who had the rhythmic equivalent of nearly absolute pitch, or "perfect time."
Is it safe to say they used small drum kits and eschewed poorly executed flashy fills?
posted by playertobenamedlater at 8:10 AM on December 28, 2010
Is it safe to say they used small drum kits and eschewed poorly executed flashy fills?
posted by playertobenamedlater at 8:10 AM on December 28, 2010
Response by poster: Okay, I am convinced that Crazy Plan A is insufficiently crazy to just might work. But I'm still convinced that I can sit here on my armchair and solve a problem that's plagued mariners for millenia.
Which brings us to Crazy Plan B:
You get two bells or tuning forks, designed to have a lot of lasting power per strike. They are juuuust out of tune with each other, such that low-frequency beats are produced. Strike them or bow them, and then have a human count the beats that they hear. Repeatedly strike or bow them to keep them ringing throughout the journey.
How about that?
posted by Galaxor Nebulon at 12:28 PM on December 28, 2010
Which brings us to Crazy Plan B:
You get two bells or tuning forks, designed to have a lot of lasting power per strike. They are juuuust out of tune with each other, such that low-frequency beats are produced. Strike them or bow them, and then have a human count the beats that they hear. Repeatedly strike or bow them to keep them ringing throughout the journey.
How about that?
posted by Galaxor Nebulon at 12:28 PM on December 28, 2010
Well, a) that would require an around-the-clock shift of people to do the counting and the re-striking, an extremely menial task that I doubt anybody would want to do, so you'd have to hire extra hands and pay them extra. And b) everything mechanical has a temperature coefficient (tempco) which causes drift. In quartz watches and sophisticated mechanical movements you have compensation mechanisms that act to make the tempcos cancel each other out. With just two tuning forks, a linear tempco would cause the beat frequency to vary slightly with temperature, and though it's small, these things add up over long periods. But I think by far the bigger problem is human counting error. Are you seriously suggesting that a team of people count numbers constantly for 24 hours a day for weeks on end without making mistakes? (Have you ever seen The Amazing Race? Some of their events involve counting things and you'd be surprised how many teams fuck it up, and those are like 5 minutes to an hour max of counting.)
posted by Rhomboid at 4:53 PM on December 28, 2010
posted by Rhomboid at 4:53 PM on December 28, 2010
Response by poster: Hey, now. Who said anything about being serious?
Now, with these beats, the important thing isn't the absolute pitches of the forks -- just the difference between them. If the temperature changed, wouldn't the forks deform in the same way, if they were made of the same material? Would their pitches really drift away from each other? If I'm not mistaken, forks at 440Hz and 441Hz will produce a 1Hz beat, and so would forks at 441Hz and 442Hz.
posted by Galaxor Nebulon at 7:51 PM on December 28, 2010
Now, with these beats, the important thing isn't the absolute pitches of the forks -- just the difference between them. If the temperature changed, wouldn't the forks deform in the same way, if they were made of the same material? Would their pitches really drift away from each other? If I'm not mistaken, forks at 440Hz and 441Hz will produce a 1Hz beat, and so would forks at 441Hz and 442Hz.
posted by Galaxor Nebulon at 7:51 PM on December 28, 2010
But they don't increase to 441 and 442 Hz. With a linear tempco, the frequency is a linear function of temperature:
F = F0 * (1 + k(T-T0))
Where F0 and T0 specify the nominal points, e.g. 440 Hz at 25C, and k specifies the tempco. If you had two tuning forks with reference frequencies F0,1 and F0,2 both made of the same material (same k) then the beat frequency is
F0,1 * (1 + k(T-T0)) - F0,2 * (1 + k(T-T0))
or
(F0,1 - F0,2)*(1 + k(T-T0))
The first term is the nominal desired difference, i.e. 441 - 440 or 1 Hz. The second term is the same temperature coefficient correction term -- the difference depends on temperature as well. For example, if k(T-T0) equaled 0.01 then both frequencies would increase by 1 percent, making them 445.41 Hz and 444.4 Hz, and the difference is now 1.01 Hz. The beat frequency depends on temperature too.
You can also have nonlinear tempcos, in which case the numbers are different but the beat frequency is still a function of temperature. What you really need in order to have a temperature-compensated instrument is one fork with a positive tempco and one with a negative tempco. You can achieve this in certain types of electronic circuits using feedback and such, but with physical things that vibrate it's pretty hard to get a negative tempco. You could choose metals with different tempcos (perhaps because they have different moduluses of elasticity), but as long as they're both still positive the beat frequency would still depend on temperature.
posted by Rhomboid at 7:43 AM on December 29, 2010
F = F0 * (1 + k(T-T0))
Where F0 and T0 specify the nominal points, e.g. 440 Hz at 25C, and k specifies the tempco. If you had two tuning forks with reference frequencies F0,1 and F0,2 both made of the same material (same k) then the beat frequency is
F0,1 * (1 + k(T-T0)) - F0,2 * (1 + k(T-T0))
or
(F0,1 - F0,2)*(1 + k(T-T0))
The first term is the nominal desired difference, i.e. 441 - 440 or 1 Hz. The second term is the same temperature coefficient correction term -- the difference depends on temperature as well. For example, if k(T-T0) equaled 0.01 then both frequencies would increase by 1 percent, making them 445.41 Hz and 444.4 Hz, and the difference is now 1.01 Hz. The beat frequency depends on temperature too.
You can also have nonlinear tempcos, in which case the numbers are different but the beat frequency is still a function of temperature. What you really need in order to have a temperature-compensated instrument is one fork with a positive tempco and one with a negative tempco. You can achieve this in certain types of electronic circuits using feedback and such, but with physical things that vibrate it's pretty hard to get a negative tempco. You could choose metals with different tempcos (perhaps because they have different moduluses of elasticity), but as long as they're both still positive the beat frequency would still depend on temperature.
posted by Rhomboid at 7:43 AM on December 29, 2010
Response by poster: Dang. I guess there's a reason this problem plagued mankind for so long.
Thanks!
posted by Galaxor Nebulon at 9:26 AM on December 29, 2010
Thanks!
posted by Galaxor Nebulon at 9:26 AM on December 29, 2010
This thread is closed to new comments.
posted by Chocolate Pickle at 9:26 PM on December 27, 2010