Dr. Alfred's Partheil's Paper, Page 8

for cadmium A.W. = 64 * 1.75 = 112
and for radium A.W. = 128 * 1.75 = 225

The note of arsenic is d# with i = 1.171, the octave number is 64, so that
A.W. = 64 * 1.71 = 74.944

Mercury has the note g# with i = 1.5625, the octave number is 128, so we calculate
A.W. = 128 * 1.5625 = 200.

I want to explain the meaning of the interval and the octave number with the following table:
(See table page 474 and 475)

While our pianos have besides the notes of the octave c, d, e, f, g, a, b also the five black keys for the half notes, all in all 12 notes to the octave that we can play in all pitches because the tuning of the piano is equal tempered, for the physically exact tuning we get 30 notes. It would go too far to explain the derivation of the intervals of these 30 notes from the intervals of the c major scale. So it will suffice to say that these 30 intervals are arrived at by transposing the scale of c major through all major and minor keys. In practice the 30 notes are not used but replaced by the 12 notes of our piano octave, because an instrument with that many keys would be too cumbersome. In practice the notes are not tuned to a physically exact pitch, but to chamber pitch. For our current reflection it is enough to know that a physically exact tuned octave contains 30 notes with the intervals found in the table above.

If the atomic weights are divided by the octave numbers mentioned earlier 1, 2, 4, 8, 16, 32, 64 and 128 and the octave number is chosen as denominator which gives us a fraction between 1 and 2 , we get fractions that for the overwhelming majority of elements correspond so closely with intervals of notes, that we can order the elements according to rising atomic weights into the 8 octaves, as shown in the table. We find for example