Beats vs cycles vs cents

[Sarah Fox]

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Hi Don et al.,

What you write is of course true.  A cent is a cent is a cent -- same =
difference in pitch, no matter whether treble, tenor, or bass.  I wonder =
if this isn't one point in favor of electronic tuning.  After all, aural =
tuning relies on counting beats, and beat rate would vary with overall =
pitch.  However, beats are irrelevant to electronic tuning.  I can't =
really speak from experience, as I only tune electronically.  Any =
thoughts from you aural tuners?

Peace,
Sarah

  ----- Original Message -----=20
  From: Don Gilmore=20
  To: Pianotech=20
  Sent: Tuesday, March 16, 2004 10:21 AM
  Subject: Re: Beats vs cycles vs cents


  Sure you do, Ric.  Cents are what it's all about.  Cents ARE what you =
perceive in pitch.  Being off 100 cents takes you to the next note.  50 =
cents takes you half way there, no matter what note you're on.  Ten =
cents out of tune sounds like ten cents out of tune, no matter what your =
beat frequency is.  As you said, there are minor discrepancies when =
tuning, but you are pedantically missing the point. =20

  Using beats to tune a string is just a convenient crutch.  It wouldn't =
do you much good when tuning a solo clarinet, would it?  To tune an A0 =
(27.5 Hz) to a beat frequency of one cycle per second in comparison to =
another A0 string would require it to be at 27.5 + 1 =3D 28.5 Hz.  This =
is 62 cents sharp!  That's wayyyyy off.  It's closer to Bb!  And 62 =
cents sharp sounds just as bad for A0 as it would for C7, or A-440, or =
any other note. =20

  For comparison, a beat frequency of 1 Hz for C7 only means it's less =
than half a cent off!

  Beats are a phenomenon related to the *difference* in frequency =
(subtraction); cents are a phenomenon related to the *ratio* of =
frequencies (division), which is what music itself is based on.  Sure, =
you can hear beats, but as you can see it really has no relationship to =
what you hear pitch-wise at all.

  Don A. Gilmore
  Mechanical Engineer
  Kansas City=20


  > I really have to take issue with this. No one <<percieves>> cents at =

  > all.  Our perceptions of out of tuneness have far more to do with =
how=20
  > "clean" any given interval relationship sounds, or how close any=20
  > interval is to what we expect of it. This is exactly beat related.=20
  > Cents is an idealization, a mathmatical representation or modeling =
of=20
  > musical pitch. There is no musical way of defining <<in tuneness>> =
based=20
  > on cents to begin with. Only close approximations.  Beats are used =
both=20
  > individually and whollistically to create a musical effect... the =
very=20
  > best tuners know exactly what kind of vibrational effects they want =
a=20
  > piano to send out through the air for each interval and are very =
good at=20
  > achieving these. Many tuners I know speak of a the overall <<tone>> =
of a=20
  > tuning.... in kind of voicing sense. <<Voicing>> through tuning is a =

  > mulitpartial prospect to begin with, which removes it from a simple=20
  > cents perspective from the get go.
  >=20
  > 100 cents is not always a half step in real piano frequencies.... it =
is=20
  > at best only a half step for one partial at a time.  Pitch =
perception is=20
  > a conglomerate of all partials, their relative loudness, and a good =
deal=20
  > more.
  >=20
  > Cheers
  > RicB
  > _______________________________________________
  > pianotech list info: https://www.moypiano.com/resources/#archives
  > 
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