There are some very interesting portions of that paper, but I really wish the author would focus on the science and omit the jabs at what he considers "music theory".
He's correct that music education doesn't typically start with Pythagoras, but should it? It would be almost impossible from this paper to aurally appreciate his points about intervals, tonal variety and intonation schemes without having a fairly broad knowledge of harmony already.
It's certainly interesting, but it does not provide a framework that can reliably reproduce the characteristics of music he describes, which is the bulk of theory and harmonic analysis.
EDIT: I don't think it needs to be portrayed as competing with existing theory -- it's something that has been extensively studied and dovetails well with the history of scales and harmony.
As far as the fencepost error, it helps to remember that musical intervals are multiplicative, rather than additive. An octave above do is f_Hz(do) • 2. Half an octave (fa#) would be f•sqrt(2). Generalized to a twelve tone scale, each half step is f_0•2^(1/12), dividing the octave into twelve equal multiplicative intervals.
Pretty sure you can't get out of the fact that do appears twice by invoking multiplicative rather than additive logic:
two octaves played together contains 3 dos, 3 octaves contains 4, etc.
The octave interval is stupidly named by counting from 1: CDEFGABC': 8 notes!
For the next octave, the high C' has to be stupidly counted again: C'D'E'F'G'A'B'C".
It's perhaps better to think of it as the number of notes you have to count before you reach the second note, starting with the first. If you start with C, you have to count one note before you get to that same C. You have to count 8 before you get to the second C, and 15 before you get to the third.
"For the rabbit Justin Cetas …"
Some lovely garden-path sentences :-)