Cents making sense

[Richard Moody]

Some Questions:

Not sure why, but someone (had to be a mathematition) decided to divide up
each interval into 100 parts.  Each part is called a cent.  Since there are
12 intervals in an octave there are 1200 cents in an octave.

What is the difference between cents in an interval, and per cent of an
interval?

Is 2 cents the same as 2% of an interval.

If I read that a third is flat by 3.5 cents, how do I translate that to
cycles per second.  Other wise how would one figure the beat rates for
different temperaments?

I know little about logs other than the ones that heat my house.  Can cents
be calculated with out them.? Better yet is there a way to calculate
temperaments without using cents?

Here are some calculations I have tried.  Looking for confirmation or
corrections, or suggestions.


Distance between one interval       100 cents.

Freq of Middle C   (mC)       261.626
Difference between mC and C#  in cps.   277.183 - 261.626=  15.557
Difference between mC and C# in cents
      100

Question:  Does one cent here mean a value of .15557  cycles per second?


If I want to tune mC sharp by 4 cents.  Do I
multiply .15556 by 4 and add it to the freq of mC ?
 261.626 +  0.62224 =  262.24824

I ask this because I have seen some tables that give different temperaments
in cents differing from Equal Temperament.  To tune by ear one needs to
know the beat rates of the intervals, and to figure these the cycles per
second have to be known.  Then the partials must be figured, and then
the beats from them.    OR is there a way to figure beat rates from cents?


Thanks for your consideration

Richard Notoutofthewoodsyet Moody

He went to the woods to learn about logs.