This computation took a lot longer time to reach a much better solution than my previously published result.
A Calculus of Variations Solution to the Quantum Mechanical Schrödinger Wave Equation for the Lithium Like Atom (Atomic Number Z = 3) by James Pate Williams, Jr.
Organometallic Chemistry at LaGrange, GA Country’s BBQ on Thursday, November 16, 2023, by James Pate Williams, Jr.
Tonight, I was dining at Country’s BBQ in the first booth. After eating my salad, I noticed a blue-green discoloration on my table near the condiment area of the booth. I assumed the crystals were formed by Copper (II) acetate hydrate (C4H6CuO4)*H2O. I surmised that the copper table-top reacted with vinegar (a good source of acetic acid).


My New Ordnance Pamphlet 770 Calculations by James Pate Williams, Jr. © November 12, 2023
Guitar String and Piano Key Frequencies by James Pate Williams, Jr.

// FrequencyKey.cpp : Defines the entry point for the console application.
// James Pate Willims, Jr. (c) All Applicable Rights Reserved
#include "stdafx.h"
#include <math.h>
#include <iomanip>
#include <iostream>
#include <string>
#include <vector>
using namespace std;
vector<string> pnote;
double a = pow(2.0, 1.0 / 12.0);
double f0 = 440.0, gStrF[6];
double e2, a2, d3, g3, b3, e4;
double pfreq[9 * 12];
int offset = 0;
double fn(int n)
{
return f0 * pow(a, n);
}
void printFrequency(char note, int octave, double frequency)
{
cout << note << "\t" << octave << "\t";
cout << setw(6) << fixed << setprecision(2);
cout << frequency << endl;
}
int main()
{
for (int octave = 0; octave <= 8; octave++)
{
pnote.push_back("C");
pnote.push_back("C#");
pnote.push_back("D");
pnote.push_back("D#");
pnote.push_back("E");
pnote.push_back("F");
pnote.push_back("F#");
pnote.push_back("G");
pnote.push_back("G#");
pnote.push_back("A");
pnote.push_back("A#");
pnote.push_back("B");
}
pfreq[0] = 16.35;
pfreq[1] = 17.32;
pfreq[2] = 18.35;
pfreq[3] = 19.45;
pfreq[4] = 20.6;
pfreq[5] = 21.83;
pfreq[6] = 23.12;
pfreq[7] = 24.5;
pfreq[8] = 25.96;
pfreq[9] = 27.5;
pfreq[10] = 29.14;
pfreq[11] = 30.87;
for (int octave = 1; octave <= 8; octave++)
{
for (int i = 0; i < 12; i++)
{
pfreq[octave * 12 + i] = 2.0 * pfreq[(octave - 1) * 12 + i];
}
}
gStrF[0] = e2 = fn(offset - 29);
gStrF[1] = a2 = fn(offset - 24);
gStrF[2] = d3 = fn(offset - 19);
gStrF[3] = g3 = fn(offset - 14);
gStrF[4] = b3 = fn(offset - 10);
gStrF[5] = e4 = fn(offset - 5);
cout << "Guitar\tOctave\tFrequency (Hz)" << endl;
printFrequency('E', 2, e2);
printFrequency('A', 2, a2);
printFrequency('D', 3, d3);
printFrequency('G', 3, g3);
printFrequency('B', 3, b3);
printFrequency('E', 4, e4);
cout << endl;
cout << "Piano Keys" << endl << endl;
for (int octave = 0; octave <= 8; octave++)
{
for (int i = 0; i < 2; i++)
{
cout << octave << '\t';
for (int j = 0; j < 6; j++)
{
{
cout << pnote[(12 * octave + 6 * i + j) % 12] << '\t';
cout << pfreq[(12 * octave + 6 * i + j)] << '\t';
}
}
cout << endl;
}
}
return 0;
}
Geriatric Memory Test 3 by James Pate Williams, Jr.
Geriatric Memory Test 2 by James Pate Williams, Jr.
Geriatric Memory Test – Fond Remembrances by James Pate Williams, Jr.
The Lockheed Blackbirds by James Pate Williams, Jr.
Pollard-Shor-Williams Factor Method by James Pate Williams, Jr.
This factoring algorithm is based on Pollard’s rho, Shor’s classical, and my modification of the two preceding methods.








