Dr. Alfred's Partheil's Paper, Page 7

If we multiply with 16 the atomic weight of hydrogen and of uranium, the elements with the lowest and the highest atomic weight respectively, we get 1.008*16=16,128 and 238.5*16=3816, numbers which differ less from the frequencies of subcontra C - 16 and the b''''=3840 than they would in a tempered tuning ( 16.165 and 3906.168 ). In other words, man with his senses is able to perceive an interval of about the same frequency range (8 octaves) as matter as the ear can perceive as musical tones. Through multiplication of the atomic weights of the other elements with 16 we get numbers that for most of the elements match the frequency of certain tones. E.g.:

[table on page 472 of original text, wherein ais=a#, fis=f#,ges=gb,as=ab,dis=d#,gis=g#]

Following this view I was able to develop the following formula for the calculation of the atomic weights A.W.:

A.W. = o * i

in which o is the so called octave number and
i the interval for the pitch associated with the element.

The octave numbers are 1, 2, 4, 8, 16, 32, 64 and 128.
Lithium for example has the note a#, which has the interval 1.75, the octave number of lithium is 4.

A.W. = 4 * 1.75 = 7

Nitrogen has the same note, but the octave number 8 and it is

A.W. = 8 * 1.75 = 14

With cadmium and radium we also have the note a#, but the octave numbers 64 and 128 respectively, and we calculate