View source for Dual cycle system

The '''dual cycle system''' is a [[just intonation|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.

[[File:Dual Cycle System.png|thumb|right|Dual-cycle system]]

== Music ==
; [[Siavash Talebi]]
* [https://www.youtube.com/watch?v=PsVhas-P-OM ''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

[[Category:5-limit]]