Re Cents

[PSLOANE@OCVAXA.CC.OBERLIN.EDU]

                 --- ORIGINAL POST ---

     I've noticed that in Journal articles, etc. tuning discussions refer to
 cents when discussing how much difference there is between where a piano is
when one encounters it, and A440.  I know that 100 cents is the distance
between halfsteps, and that when a piano is a half or whole step flat (or #)
I can roughly say that it is 100 or 200 cents.  But when someone says a piano
is 10 or 12 cents off, I wonder if this is of that great use to me. The exact
cent amounts always seem to be small,  for example, " the piano was 17 cents
low".  Nobody ever seems to say,"The instrument was 92 cents flat".  One may
say that a change of 5 or 10 cents constitutes a pitch raise, but as an aural
tuner I find I understand 440 or 435 or whatever beat per second rate, and I
wonder if there is a calculation to translate cents to bps.  Are exact cent
amounts mainly a tool for those using electronic tuners?  Any responses would
be appreciated.  Thanks

Gordon R. Large, RPT
Mt. Vernon, Maine

                   --- MY REPLY --

If you multiply the frequency of any note by the 100th root of the 12th root of
2 (easy to figure out with a calculator; number is 1.0005778) you will arrive at
a note that has a frequency that is one cent sharper than the original. If you
then multiply that note by the same number (100th root of the 12th root of 2),
you will arrive at a frequncy that is two cents sharper than the original and so
on. If you think about it for a while and use a frequency chart for notes in the
equal tempered tuning system in relation to A440 (such a chart is in the William
Braid White book, "Piano Tuning and Allied Arts") you can easily calculate the
exact beat speed for any cents deviation from 440. However, you will be close
enough in calculating how many cents equal one beat for any given semitone by
finding the difference in frequency between the two notes of the semitone and
then dividing 100 by that number. For example, G# below A440 in the equal
tempered system has a frequency of 415.31. Subtract that from 440 and round off
to the nearest whole number and you get 25. Divide that into 100 and you get 4.
Therefore, in the G# below A440 to A440 semitone, 4 cents equals roughly one
beat, and if you do the same calculation for the semitone above A440, you will
find that you can use that 4 cents equals one beat formula also.

Ken Sloane, Oberlin Conservatory