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My question relates to our capacity (trained or untrained) of detecting differences between two frequencies. In harmony, the analogue to our capacity of detecting the difference between two tones/pitches, which is an obviously trained ability: a non-musician won't tell a note out of pitch, whereas a trained musician will immediately recognize two different notes.. down to a certain point: Likely very few people (if any) can recognize the difference between a 440 Hz and a 439 Hz tone. (notice this is not having perfect pitch, which would mean recognizing -without a reference- that a tone around 440Hz is an A)

Analogue to this, can we really detect the difference between a, say, 140 bpm track and a 141 bpm track? This has two consequences in my experience:

  1. Speeding up or slowing down! If we can't tell the difference of the change of a 141/140 bpm, what prevents us to slow-down/speed-up when playing a groove over a long time period? This is a major problem in my experience, when micro-timing is fine, but over several minutes of playing I notice I am suddendly down by a couple BPMs, and getting progressively slower/faster over time without any possibility of recognizing this on a short-term scale.
  2. Most bands I have played with have the notion that one BPM difference makes a big change in the song feel. They would ask "what BPM was that?" "Answer: 140 bpm" , "Ok that felt a bit too slow, lets try it again at 141 bpm..." . Is this a real thing? Or are they just being obnoxious?

I understand this measure is not in a linear scale, and the difference between 10 vs 11 bpm isa lot more obvious than between 210 vs 211. There must be a threshold above which it is physically impossible for us to tell the difference. My question is, is this threshold already low enough that is within the ranges of common music timings (60 - 300 bpm), thus making our attempts at having machine-like timing unrealistic?

  • Thought provoking, maybe each of us will have a different 'tolerance' that we're happy with? There are plenty of recordings that wallow timing wise, and playing live there's always the music itself that will make the tempo vary - usually for the better. Whether players are aware of that at the moment of playing is another matter. – Tim Nov 28 '19 at 18:45
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    Based on my experiences, I feel like even an average-but-experienced group of marchers will notice if they're being driven just slightly faster or slower than 120 steps per minute, but I can't back that up with anything objective. Might be an avenue of investigation though. – Roger Nov 28 '19 at 20:24
  • Closely related to music.stackexchange.com/q/39683/9426 – Brian THOMAS Nov 29 '19 at 12:56
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    This is a field of academic study. See also journals.plos.org/plosone/article?id=10.1371/… – Brian THOMAS Nov 29 '19 at 13:07
  • define "a couple of BPM." I notice a difference around 4 BPM - probably within a moderate rate of tempos like 65-135 BPM. – Michael Curtis Dec 23 '19 at 16:56
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There are a number of different possible ways of measuring the threshold of tempo perception. It's one type of task to say to someone: "Play me a tempo of 120bpm" out of thin air with no context, and then to measure how accurate they are. It's a completely different task to say: "We'll start you off playing at Tempo A. Maintain a consistent tempo for a minute, and we'll measure you." It's yet another task to say: "Here's an excerpt at tempo A. Now here's a short excerpt at tempo B. Are they different (faster/slower) or the same?" And it's even potentially different to say: "Here's a piece at tempo A. Tell me whether this gradually speeds up or slows down or stays at a constant speed."

All of these kinds of things (and more) have been studied in music perception studies. There are somewhat conflicting results, but here are a few useful datapoints:

  • When subjects (including non-musicians) are asked to reproduce songs they know well, most are able to perform a tempo within +/-8% of the actual tempo of the source recording, and around half are able to get within +/-4% (which would be roughly a range of 115-125bpm for a nominal 120bpm tempo).
  • When asked to continue tapping a tempo with a given beat, the range of accuracy was measured at 7-11% and within 3-4% accuracy when subjects tap along with a continuing beat.
  • Another type of task looks at otherwise steady rhythmic pattern of beats with one beat (or more) potentially "off" by a bit. Depending on the task, accuracy can be a bit better, averaging around a 3% displacement where a beat is noticed as "out of tempo," with sensitivity going down to around 2% or lower.
  • An empirical study of jazz recordings found tempo during performances of groups stayed within 5% variation even when involving significant improvisation. Accuracy between takes or when resuming a previous tempo showed a similar level of accuracy. However, these are actual recordings where presumably the highest priority was not always tempo accuracy.
  • Finally, there's a question of ability to detect tempo "drift" brought up in the question. Some studies have shown that it takes a difference of around 6-8% for listeners to detect a clear alteration in tempo, in agreement with some of the other data above. However, when a different paradigm for testing tempo shifts was used to allow listeners to gradually move toward increasingly small changes around a given tempo, the "just noticeable difference" was measured to be significantly smaller, on the order of 0.27% on average for the subjects in that study. Note in that last study, however, that most subjects have some sort of "internal drift" in over the course of the study in their continuous changes in tempo, so total discrimination capability in the best of circumstances was probably on the order of within 1% or so, or within the the 1 bpm threshold for reasonable tempos that OP asked about.
  • This last finding accords with measurements of professional drummers asked to maintain tempos for 20 seconds, showing that on average they could maintain accuracy within a tempo drift of within 0.2%, though some variance up to around 1% was observed. However, it's important to note that these were only measured for internal consistency -- some of these drummers, for whatever reason, began at a significantly different tempo from the reference tempo they were provided by a metronome (in one case, close to 10% off).

These last couple findings perhaps come closest to answer the OP's question. In ideal circumstances, a trained drummer can probably maintain a tempo to within 1% accuracy, which would be within about 1 bpm for reference tempos around the mid-range of 100bpm. (However, note that's maintaining a starting tempo -- which may not even be the intended starting tempo given from a metronome, just the one the drummer "feels" and begins. And note that in real-world circumstances, drummers are not typically just tasked with "Maintain accuracy in tempo, no matter what.") And under ideal circumstances, listeners may be able to detect differences of tempo on that order too, when they are juxtaposed against each other, and listeners are allowed a long time to practice on listening to that specific tempo.

But such ideal circumstances are unlikely to take into account real-world performance conditions, where the range of somewhere around +/-5% is a more reasonable estimate of when most people (both musicians and non-musicians) begin to feel a distinctly different tempo, as shown by numerous studies.


On a slightly unrelated note, to respond to another point brought up in the question about 440 Hz vs. 439 Hz, it's important to note that human ability to discriminate difference in pitch is actually very fine in ideal circumstances and with certain tasks. Certainly OP is correct that there are very few (if any) humans capable of distinguishing 440 Hz vs. 439 Hz without a reference pitch, using only absolute pitch capabilities. But certainly most professional musicians would be quite capable of noting a difference of 440 Hz vs. 439 Hz when comparing pitches during tuning of instruments, as that's an error about 4 cents, well within the frequency discrimination abilities of professional musicians. (Even if comparing only sine waves, those two pitches would have a noticeable beat frequency, which musicians would notice during tuning and try to correct.)

However, if asked to compare those two frequencies outside of extended tuning against each other, almost no one would be able to hear a difference. Again, as in tempo perception, the nature of the specific task matters.

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  • Wow, I'm floored by the amount of study that's out there. Excellent work! +1 – user45266 Jan 6 at 3:18
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Just as with intonation, the ability to differentiate tempi exists within most musicians to varying degrees.

I've met some drummers who could give you the BPM of a song they'd never heard before down to an error of 1 or 2 BPM. But that's kind of like the "perfect pitch" thing, where it's a cool skill to have (especially for a drummer), but it's not an essential. This is basically an absolute sense of tempo, which few musicians develop because of its limited uses.

Most musicians have a much more developed sense of relative tempo. They spend years learning to play at consistent tempi, and variances in the tempo can often be felt quite clearly to even an amateur musician. As with relative pitch, some are better than others at this. From what I can tell, usually a change of 1 BPM at a reasonable tempo isn't going to be noticed, but 2 or 3 might be noticed by the musicians, and 5-10 or more is going to feel like an intentional deviation even to the non-musicians in the audience. If you wanted to do any sort of empirical analysis of this trend, I suggest using percent change to quantify the amount of deviation from the original tempo (as you noted, the effect of any change varies - going from 1 to 2 BPM is twice as fast, but going from 130 to 131 BPM might not even be noticed).

To answer specifics: I've never played in a band where one beat per minute was seen as bad enough to kill a take of a song. That's just an unreasonable standard to hold most bands to, since a mistake that small is not going to be noticed by anyone outside the band. In certain electronic (or just heavily-produced) genres, tempo doesn't vary at all throughout a song due to quantization and other recording technologies, but even in those genres, any actual musician would never be required to be that accurate, since the studio could fix any slight error.

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Yes, but differentiating between tempos should not be the basis for a good musicianship. A musician is a human so even though he or she keeps a consistent tempo when playing, the tempo is not 100% accurate and should not be. Computers are made for that.

The best grooves come from musicians whose tempo includes those micro-changes (that are existent all the time!) in the tempo. If it weren't for those micro-changes, the playing would be mechanical and robotical (= computer-like).

For your question 2., I think it is not relevant to think about or observe 1-2 unit changes in BPM. Concentrate on the groove instead - it is a much more human-related concept referring to the consistent tempo than those BPM numbers.

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