Dual cycle system

The dual cycle system is a just-intonation tuning system formed from two finite Pythagorean cycles related by the syntonic comma (81/80), 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

Siavash Talebi

• Also Singt Harmonie (2026)

References

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