Lunar–Solar synchronisation — Meton, octaeteris, Islamic (§7–§8)
The 19-year lunisolar cycle (Meton) and its cross-cultural echoes. All numbers computed live from SYN = 29.530589 and TROP = 365.24219.
The Metonic 19-year cycle: 7 leap years (13 months, gold = the 7 doubles) + 12 common years (12 months) = 235 lunations ≈ 19 tropical years. 19 = 7 doubles + 12 simples — the SY's own partition is the lunisolar cycle.
| Cycle | Relation | Days (lunar) | Days (solar) | Δ |
|---|---|---|---|---|
| Meton (19a / 235m) | 12×12 + 7×13 = 144 + 91 = 235 | 6939.69 | 6939.60 | 0.087 |
| Octaeteris (8a / 99m) | 8×12 + 3 = 99 | 2923.53 | 2921.94 | 1.591 |
| Islamic 33y (33×12m) | drift of the Hijri year | 11694 | 12053 | -359 |
- Meton: 19 tropical years ≈ 235 synodic months (Δ ≈ 0.09 d). 235 = 12×12 + 7×13 — the 12² appears here too (cf. 144 in the Revelation tab).
- Octaeteris: 8 years ≈ 99 months (the older, rougher cycle; Δ ≈ 1.59 d).
- Islamic: a 33-year cycle brings the lunar calendar back near the solar year (drift ≈ -359 d over 33 y ≈ 11 d/y).
- China: the 章 (zhāng) = 19 years = 235 months = Meton, discovered independently.
- Draconic month 27.212221 d · anomalistic 27.55455 d · eclipse year 346.62 d → saros 223×SYN = 6585.32 d (see the Saros tab).