Dual cycle system: Difference between revisions
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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. |
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[[Category:Just intonation]] | [[Category:Just intonation]] | ||
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[[Category:5-limit]] | [[Category:5-limit]] | ||
[[Category:Syntonic comma]] | [[Category:Syntonic comma]] | ||
Revision as of 22:08, 29 September 2026
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.
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