: Why do lower instruments speak "slower"? Why do lower instruments, such as double bass and cello in an orchestra or chamber setting, are discerned by the ear slower than higher instruments (violin, flute, etc)? Does it have

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There is a difference between percussive and continuous-tone instruments: percussive instruments (like a piano or a plucked bass or even a bass drum or its more defined cousin kettle drum) start with a rather prominent part of the vibration while continuous-tone instruments have to build up the the energy of their sustained operation first. So bass recorders and wind pipes (organ) are among those with the slowest attack. Reed instruments like bassoons are faster starters.

However, many instruments with a comparatively poignant primary oscillator then feed some resonator, and a resonator still needs to pump up its energy over several oscillations before being in full swing, and in order to resonate, its operation already includes a mechanical delay for one cycle time that retains a significant amount of energy.

So there is a basic slowness for the development of the actual sound. There also is a basic time/frequency unsharpness relation that limits how fast pitch differences can be determined: this is a mathematical rather than a physical limit. And finally the detection in the inner ear again works with a semi-resonant contraption relying on a delay line introducing some frequency-related delay to reliable detection.

This is ameliorated somewhat by the listener not making sense of his hearing in real-time but with some delay of perception that allows reconciling faster and slower detected features.

This particularly helps with percussive instruments where a poignant attack gives a good location in time and the associated pitch can be determined only later. Trills, coloratura, tonally specific fast runs and phrases are still usually not working well for the listener in the lower ranges of bass instruments.

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It takes more energy to get a large instrument resonating than a small one. I'm dubious about the strings example - we hear the 'bite' of the bow on the string as an immediate transient, even if it does take a little time for the body to fully resonate. I'm sure there's some truth in what the viola player has been told though, maybe more applicable to legato passages.

But it's certainly true for the larger brass instruments. The vibration applied at the mouthpiece of a tuba has to kick a 5m air column into vibration. (It's about setting up a wave, not passage of air. Not THAT much air actually travels through the instrument.) So the player compensates by playing a bit early. It's not particularly calculated, he just knows what to do in order to hear the note at the right time.

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Phase-locking-driven instruments, including strings and winds (but not percussion or plucked strings) can be described as a primary†, linear oscillator (the string, or air column) which is coupled to a nonlinear “energy pump” (the bow or mouthpiece, respectively). It is the oscillator that defines the frequency, so the coupling must not be too strong (else you don't get proper tones but only avant-garde overpressed screeching noises etc.). Weak coupling means, the oscillator does largely what it might also do all by itself, and only changes the waveform much more slowly. Much more slowly, relative to the oscillation period, that is – and the oscillation period is obviously shorter if the pitch is higher. So in that sense, e.g. violin is indeed more naturally agile than double bass – at least bowed double bass. (This is certainly one of the reasons why fast bass work such as in Jazz is usually pizzicato.)

Good players on any instruments are actually able to substantially cheat this: they make the coupling much stronger only very briefly for the initial transient (“grabbing the string with the hair”), but this requires ever more skill as the instrument goes lower.

†In acoustic string instruments, this oscillator is also coupled to a resonator and that coupling likewise introduces some delay, but that can actually be much shorter.