Editing Openai/67a0ab63-ff68-800d-a7fc-4561743f6a8a (section)

==== Mathematical Framework ====

===== 1. Harmonic Ratios and Frequencies =====

Musical notes are related by frequency ratios:

fn=f0×2(n/12)f_n = f_0 \times 2^{(n/12)}fn=f0×2(n/12)
where:
* fnf_nfn is the frequency of the nth note in an equal-tempered scale,
* f0f_0f0 is the reference frequency (e.g., A4 = 440 Hz),
* nnn is the number of semitones from f0f_0f0.

===== 2. Standing Waves in Musical Instruments and Matter =====

For a vibrating string, the fundamental frequency is:

f=nv2Lf = \frac{n v}{2L}f=2Lnv
where:
* nnn is the harmonic number,
* vvv is the wave velocity,
* LLL is the length of the vibrating string.

This equation applies not only to musical instruments but also to quantum wave functions describing electron orbitals.

===== 3. Keely’s Etheric Force & Pressure from Water Disintegration =====

Keely demonstrated that breaking the molecular bonds of water using vibration released tremendous force:

P=kf2mP = k f^2 mP=kf2m
where:
* PPP is pressure generated,
* kkk is a proportionality constant,
* fff is frequency of applied vibration,
* mmm is mass of water disintegrated.

===== 4. Quantum Harmonics and SVP =====

Keely’s vibratory subdivision corresponds to quantum eigenstates:

ψn(x)=Asin⁡(nπxL)\psi_n (x) = A \sin \left( \frac{n\pi x}{L} \right)ψn(x)=Asin(Lnπx)
This is the wave function for a particle in a box, showing how harmonics define energy levels.