Cents making sense

[Jim]

Hi Richard:

If you think of a cent as a very small interval, it may help you to see
the difference between cents and Hz (cycles per second).  If you have
an IBM type computer, I can send you a program written in BASIC which
will convert cents to beats in relation to a particular note.  Its twin
program will convert beats into cents.  The program does all of the
wrestling with the logs, you can come back in out of the woods (logs)
now.  This offer is for anyone else who will send me a personal request
by email.

When you realize that at the pitch of 440, it takes almost a 4 cent
raise to bring it up to 441. At 880 pitch it only takes 2 cent to
raise to 881. At 1760 pitch it takes almost 1 cent to raize to 1761.
>From this it is easy to see that cents relate to Hz or beats is a way
that is not too simple, yet not too difficult.  That's where logarithms
come in.  On might say "there is a rhythm to logarithms."

Jim Coleman, Sr.


On Wed, 5 Feb 1997, Richard Moody wrote:

>
> 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.
>
>
>
>
>