Roots, Cents and Herz and ETD's

[D.Martens]

Hi,  apparently I wasn't clear enough in my last post,
I'll rephrase the problem :

Suppose you want to divide an octave in 1200 steps (cents), 100 for each,
note, what should be the correct number if the first note is 110 Hz, and the
last 220 Hz ? (the last ofcourse, is exactly double the amount of the first)

Suppose you want to divide an octave in 12 steps, 1 for each  note, what
should be the correct number if the first note is 110 Hz, and the last 220
Hz ? (the last ofcourse, is exactly double the amount of the first)

I filled this in in a spreadsheet, and had the 110 Hz multiplied 1200 times
by the number 1.0005782715387   in 1200 cells in a row.
220 came out to be the answer in the 1200th cell, NOT rounded off.

I did the same for the twelfth root of two.
again no surprise , the answer is 220 Hz in 12th cell in the other row,
again NOT rounded off.

I figured that if both numbers are exactly correct, they must have 12 places
that exactly match: the 100th, the 200th,......the 12hunredth cell of the
first row vs. the cells in the second row.

1200 row                 12row
A    110                   110
A#  116.4791983  116.5409404
B    123.4113571  123.4708253
C    130.7560774  130.8127827
C#  138.5379123  138.5913155
D    146.7828764  146.832384
D#  155.5185324  155.5634919
E     164.7740834  164.8137785
F     174.5804706  174.6141157
F#   184.9704764  184.9972114
G     195.9788344  195.997718
G#   207.6423453  207.6523488
A      220                   220

As you can see in  the above table, differences are between 0.06 Hz and 0.01
Hz, which is too much.

1.05946309436       for the 12
1.0005782715387   for the 1200

My question is: Why don't these two rows exactly match ?
Did I overlook something, or is it the computer's processor,

Does anyone have a clue ?


Duncan.