Author: jamespatewilliamsjr

My whole legal name is James Pate Williams, Jr. I was born in LaGrange, Georgia approximately 70 years ago. I barely graduated from LaGrange High School with low marks in June 1971. Later in June 1979, I graduated from LaGrange College with a Bachelor of Arts in Chemistry with a little over a 3 out 4 Grade Point Average (GPA). In the Spring Quarter of 1978, I taught myself how to program a Texas Instruments desktop programmable calculator and in the Summer Quarter of 1978 I taught myself Dayton BASIC (Beginner's All-purpose Symbolic Instruction Code) on LaGrange College's Data General Eclipse minicomputer. I took courses in BASIC in the Fall Quarter of 1978 and FORTRAN IV (Formula Translator IV) in the Winter Quarter of 1979. Professor Kenneth Cooper, a genius poly-scientist taught me a course in the Intel 8085 microprocessor architecture and assembly and machine language. We would hand assemble our programs and insert the resulting machine code into our crude wooden box computer which was designed and built by Professor Cooper. From 1990 to 1994 I earned a Bachelor of Science in Computer Science from LaGrange College. I had a 4 out of 4 GPA in the period 1990 to 1994. I took courses in C, COBOL, and Pascal during my BS work. After graduating from LaGrange College a second time in May 1994, I taught myself C++. In December 1995, I started using the Internet and taught myself client-server programming. I created a website in 1997 which had C and C# implementations of algorithms from the "Handbook of Applied Cryptography" by Alfred J. Menezes, et. al., and some other cryptography and number theory textbooks and treatises.

A New Calculus of Variations Solution of the Schrödinger Equation for the Lithium Like Atom’s Ground State Energy

This computation took a lot longer time to reach a much better solution than my previously published result.

new-variational-solution-for-the-lithiumDownload

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.

variational-solution-for-the-lithiumDownload

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).

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;
}

https://en.wikipedia.org/wiki/Piano_key_frequencies#:~:text=%20Every%20octave%20is%20made%20of%20twelve%20steps,Hz%20and%20the%20sixth%20A%20is%20880%20Hz%29.