Roots, Cents and Herz and ETD's

[Joe & Penny Goss]

Or 1 devided by 1=1
Joe Goss
imatunr@primenet.com
http://www.primenet.com/~imatunr/

----- Original Message -----
From: "D.Martens" <cybertuner@planet.nl>
To: <pianotech@ptg.org>
Sent: Sunday, March 11, 2001 4:18 AM
Subject: Roots, Cents and Herz and ETD's


> 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.
>
>
>
>
>