determing Cents flat or sharp

[Richard Moody]

> 
> 
> Any of you brave souls care to try and explain to this newbe tuner how
you
> determine that a piano is 16 cents flat or 44 cents flat etc. aurally?
> 
> I have looked in every book I have and can't seem to find
> it.................
> 
> Terry Jack

You can't determine cents by ear.  It must be calculated. One beat either
way of 440 is 3.9 or 4 cents.   Cents is the measure of the difference as
a ratio of two frequencies.  440 does not have a cents value.  The cents
between 440 and 220 (an octave) is 1200 cents. The cents difference
between 220 and 110 also an octave is 1200 cents.  Now for a quizz. 
  The cents difference (roundedoff) between 220 and 221 is......... 
	a. 4 cents
	b. 8 cents
	c.  2 cents
	d. none of the above...... 

The answer is   B.   8 cents,   7.8 actually.  Is that surprising? It was
to me...Just remember that cents is an expression of the ratio of an
interval.  221/220 is a larger interval than  441/440.  It is twice as
large, actually (as cents indicate)  The beat rate though is the same.  

So If you miss 440 by 1 bps you are off 4 cents.  If you miss 220 by 1 bps
you are off nearly 8 cents. On the other hand if you miss A 1760 by one
beat you are only off 1 cent.  
If you want to see if this trend continues get your calculator and enter
110/109 hit  = press  log and multiply by 3986.
 
In words, the log of the ratio of a musical interval times 3986 gives
cents.

In math  log(F/f)/log(2)*1200.
 
=log(2/1)/log(2)*1200  This can  be pasted into spread sheets.  This
should give a result of 1200.  You might need an @ before log.  Hmm
Quatropro supplies it.   Of course in place of 2/1 you put your own ratio,
or two frequencies you want to know the cents difference of.   

If you need to know what the frequency  is 4 cents sharper,
use...F*2^(cents/1200) 
This pastes into a spread sheet.   On a calculator do 4/1200 and store it.
 then clear and enter  2 ,  press [x^y],  press MR,  hit *,  enter 440, 
and you should get 441.01..if you press  =  If you want the cents down,
use the negative value of 4/1200---ric