Cents vs Hertz, was HT query

[Jim Coleman, Sr.]

Hi James:

Many of us have wondered the same thing. However, it simplifies when you 
think of 2 cents as being a very small interval, just like a half step 
is a small interval (just not so small). Now, 2 cents at the 10th partial
WILL make more difference in Hertz than 2 cents at the fundamental. Just 
like a half step at A440 fundamental makes a difference of a little over
26 Hertz, but a half step 2 octaves higher makes well over 100 Hertz
difference. Remember, the Hertz doubles each octave starting with A0 at
theoretically 27.5, the A1 at 55, then 110 then 220 then 440, then 880,
then 1760, then 3520 for the A7.

Lets just think of A4=440. To get to 441, you must make almost 4 cents
change. Therefore 1 cent equal approx. 1/4 Hertz. At 880 Hertz, if you make
a 1 cent change, it changes to approx. 880.5 or a half Hertz change. That's
twice the Hertz change that 1 cent makes at 440.

Therefore, we get better accuracy listening to higher partials than 
listening to lower partials. We can get better accuracy tuning by 3rds than
by tuning by 5ths which use lower partial numbers. Trying to tune by
pure 2:1 octaves gives the least accuracy, unless one listens only to
fundamentals while tuning unisons (I always suggest listening to the 
highest partials you can hear when tuning unisons). In tuning by higher
partials, you get a micrometer adjustment on the fundamentals. I think
the mud is clearing isn't it?

Jim Coleman, Sr.

On Mon, 22 Jun 1998, pianoman wrote:

> Hi ,
> Just a point.  I read that the directions for setting up an HT over an
> existing tuning is a process of altering the cents values of the calculated
> tuning by +2c, -2c, whatever.  Question is, since you are changing whatever
> partial the device is listening to , is that not changing the fundamentals
> placement more than the amount you are changing the tuning partials.  Is
> this as clear as mud or can you tell what I am saying?
> James Grebe
> R.P.T. of the P.T.G. from St. Louis, MO. USA, Earth
> Piano Service and Piano Periperals
> pianoman@inlink.com            May I listen as well as I hear.
>