Roots, Cents and Herz and ETD's

[Meyer Carl]

Picky! Picky! Picky!

Carl Meyer


----- Original Message -----
From: "Robert Scott" <rscott@wwnet.net>
To: <pianotech@ptg.org>
Sent: Sunday, March 11, 2001 2:15 PM
Subject: Re: Roots, Cents and Herz and ETD's


> Duncan,
>
> I think I have your answer.  As Richard Brekne pointed out,
> 1.0005782715387 is not the 1200-th root of 2.  But your
> spreadsheet seemed to say that it was.  So I got to thinking,
> what is 1.0005782715387 and why did it seem to work out for you?
> It turns out that 1.0005782715387 is exactly the 1199-th root of 2.
> So I guess that your spreadsheet program has a counting error.
> You may have left off the first or the last of the 1200 multiplications,
> so that after 1199 multiplications you have exactly 2.0000.  Of
> course the 100-th, 200-th, etc. multiplications will not match
> the 12-note scale under this scenario.
>
> Although you did not seem to suffer from any cumulative error in
> the many multiplications, it would be more reliable to calculate
> these very high powers of numbers near 1 by using logarithms:
>
>     y          (y * log(x))
> x     =   10
>
> -Robert Scott
>   Ypsilanti, Michigan
>
>
> Duncan asked:
>
>  >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.
>   ....
>  >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
>  >
>    ...
>  >My question is: Why don't these two rows exactly match ?
>