Cents to Hertz Conversion Chart

[Stephen Bellieu]

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If an aural tuner can ask a stupid question:  does this mean that a one =
cent mistake in the top of the piano is much bigger than a one cent =
mistake in the bottom of the piano?  By bigger I mean more likely to be =
percieved aurally.

Steve B
  ----- Original Message -----=20
  From: Wimblees@aol.com=20
  To: pianotech@ptg.org=20
  Sent: Monday, December 23, 2002 12:04 PM
  Subject: Re: Cents to Hertz Conversion Chart


  In a message dated 12/23/02 12:25:08 PM Central Standard Time, =
joegarrett@earthlink.net writes:


    Alan,
    Thanks for the link! Nice to have. One thing struck me: As this is a =
chart
    to convert Cents TO Hertz,(CPS), there is nothing that shows the =
exact cents
    to achieve frequencies such as 435cps or 425cps. I wonder if there =
is a
    reverse of this chart somewhere?
    Oh, as an aside, on the bottom of the chart is the statement that =
this chart
    is copyrighted by "International Piano Suppy". Who/what is that?
    Best Regards,
    Joe Garrett, RPT, (Oregon)




  Joe

  Technically, the chart doesn't convert cents to Hertz. You cannot =
convert cents to Hertz, because cents are not a frequency. What this =
chart is showing is at what frequency, (or Hertz), a particular note is =
beating a certain number of cents above or below that particular note. =
If you look at A, and zero cents, it shows the frequency, or Hertz, is =
440.00. (It is presumed that A on this chart is A4.) Then for every =
cents below A, it give the frequency.  =20

  Cents are the measurement between intervals, and there are 100 cents =
between each interval. There are 100 cents between A0 and A#0 and =
between B7 and C8, and between every interval all the way up and down =
the piano. The higher you go up the scale, the difference in the number =
of Htz between notes gets greater and greater. The greater the =
difference, the fewer cents there will be between beats. And the =
opposite, there are fewer beats difference between intervals as you go =
down the scale, so there will be more cents between beats.=20

  That is what this chart illustrates. A 440 is at 440.000 Htz. A# is at =
a frequency of 466.164. That mean A# beats 26.164 faster than A. There =
are 100 cents between A and A#. That means the difference between each =
beat is about 3.82 cents. G# beats at 415.305 beats per second, which is =
24.95 beats less than A. There also 100 cents between G# and A. But =
because it is lower, there are more cents between beats. (4.01 to be =
exact).  =20

  So if you want tune a piano to A435, considering there are about 4 =
cents difference between beats at A4, you multiply 5 beats times 4 =
cents, and you get 20 cents. If you want to go down to A425, you =
multiply 4 cents time 15 beats, or 45 cents.=20

  According to the chart, the closest you can get to A 435 is 435.197 at =
19 cents below A or 434.916 at 20 cents below A.  So if you want to get =
super accurate, you'll have to off set your machine to 19.5. But I don't =
think any one will hear the difference if you play it safe at 19 or 20 =
cents below A.=20

  Quite frankly, someone spent a lot of time on a chart that is =
virtually useless. Why would any one want to know the frequency of D#  =
50 cents below pitch? Whoever put this together at the International =
Piano Supply Company either had too much time on their hands, or is =
trying to impress piano tuners that they know something others don't. =
But as far as I'm concerned, this is useless information.=20

  Wim=20

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