Beats vs cycles vs cents

[Sarah Fox]

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Hi Jean-Jacques,

It all depends on what you're listening for.  Piano tuners of course are =
used to listening for beats, and they are quite sensitive to the =
presence of beats, how fast they are, where they are, etc.  Normal =
everyday people, and even musicians, listen for how sharp or flat a note =
is, overall.  Ten cents of sharpness sounds the same (in deviation of =
pitch), whether it is towards the bass or towards the treble.  Those who =
doubt this should consider that *100* cents sharpness (i.e. the next =
half step) also sounds the same, irrespective of octave.

Why does a larger deviation in Hertz in the treble sound similar to a =
smaller deviation in the bass?  That's just the way our sensory systems =
work.  All of our senses see proportional changes as equidistant.  The =
difference between 1 and 2 is the same difference as between 4 and 8.  =
Both are doublings.  This works with taste, hearing, sound, touch, and =
olfaction.  In the case of hearing, the same is true with loudness.  =
Each doubling of amplitude, 6 dB SPL, sounds similar, whether the sound =
is soft or loud.  (Or for you people who prefer dealing in power, each =
doubling of power, 3 dB SPL, sounds similar.)

In the end, we just can't resolve differences of, say, 5 Hz in high =
pitched sounds, while they are incredibly conspicuous in low pitched =
sounds.  Another way of looking at this is that a beat rate of 1 beat =
per second (1 Hz) in the high treble is pretty much meaningless.  The =
same beat rate in the low bass is much more meaningful.

Peace,
Sarah

  ----- Original Message -----=20
  From: Jean-Jacques Granas=20
  To: pianotech@ptg.org=20
  Sent: Tuesday, March 16, 2004 2:51 PM
  Subject: Beats vs cycles vs cents


  Hello one and all,

  Dare I suggest (and perhaps live to regret it) that beats, with all =
their imperfections for tuning purposes, are nevertheless a natural =
acoustic phenomenon that exists whether we are there to hear it (or tune =
the stubborn thing) or not.
  Cents on the other hand aren't something you actually hear, are they? =
When I tune in the deep base (the last 4-6 unisons, depending on the =
piano), I don't listen to beats of course, because otherwise In would be =
there all day. I just find the place where the octave or fifth sound =
most pleasant, with occasional help from friends in the 3rd  octave, but =
is what I am hearing 'cents'?
  After all, 100 beats to half a tone (or thereabouts) it is only a =
scale, like 1000 meters to a kilometer, 12 inches to a foot, or 5, .... =
feet (what was it?)  to a mile.
  Or am I missing something ?


  Peace-Paz-Paix-Pok=F3j
  Jean-Jacques Granas
  Warsaw, Poland
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