Integer-Ratio Harmonic Modulation: Mathematical Justification of Base-12 for Precision Direct Digital Synthesis in Cyclic Processes

Integer-Ratio Harmonic Modulation: Base-12 DDS Engine This repository contains the source code for a conceptually new Direct Digital Synthesis (DDS) core. The algorithm utilizes a base-12 phase accumulator, grounded in the properties of the smallest highly composite numbers, to generate waves with absolute phase precision and zero computational jitter. 🚀 The Problem: Limitations of Binary DDS Standard wave generation systems use binary phase accumulators (e.g., 32-bit registers). While convenient for computer architecture, the binary system is mathematically incapable of generating rational phase shifts without errors. Most resonant phenomena are described by fractions (1/3, 1/6, 2/3). Attempting to calculate 1/3 of a period in a binary system (e.g., 1024 / 3 = 341.333...) leads to: Rounding Error (Phase Jitter): Constant shifting of wave nodal points by ±0.5 LSB. FPU Delays: The necessity of using floating-point math destroys the determinism of the hardware response time. 💡 The Solution: Base-12 (Highly Composite Number) The number 12 possesses unique divis