Dual cycle system

The dual cycle system is a just-intonation tuning system formed from two finite Pythagorean cycles related by the syntonic comma (80:81), producing 5-limit harmonic relationships through cross-cycle interaction. The system yields an Eight-Pitch Collection that preserves diatonic ordering with a single duplicated degree, enabling pure 5-limit triads and practical modulation.

Dual-cycle system

Music: Also Singt Harmonie — composition demonstrating the dual-cycle system. https://youtu.be/PsVhas-P-OM?si=X0IA0ILjOuerAVoS

Reference: Talebi, Siavash. “Dual-Cycle System: Pure 5-Limit Harmony Within a 3-Limit Framework.” Zenodo, 2025. https://doi.org/10.5281/zenodo.17846833