I have lines for weekdays and months, but they are trivial (the mont sequence turns 90 degrees right in the middle of June, on 1st September, just before Christmas and on 1st January, forming a rectangle. The weekday line turns right before and after the weekend, so two weeks together make a rectangle.

My lines can also have a fractal substructure - if looking in a detail on a particular region, further turns appear, usually inherited from the general number line or another relevant line or part of it. This may not be compatible with the overall structure: for example, from greater distance the stretch from 1910 to 1920 is a straight line, but in detail, any single year has the "closed rectangle" structure, beginning and ending in the same point.

To help understanding the interplay of cultural bias and synesthesia, this is the hopefully full list of turns in my history line when looked at in detail (the probable cause for the turn - a historical event or other thing - is in parentheses)

1. cca. 220 B.C. uncertain direction, perhaps multiple turns (Punic wars)
2. 40 B.C. right (end of the Roman republic)
3. 30 B.C. - 0 A.D. left 180° curved
4. 0 A.D. or 14 A.D. right (beginning of millenium / death of Augustus; context dependent)
5. during 1st century left curved
6. cca. 70 A.D. uncertain, probably left - right - right (end of Claudian dynasty, destruction of Pompeii)
7. 100 right (end of century)
8. 110/114/120 left (generic number 20 / conquests of Traian)
9. 130 left (generic number 30)
10. 150 - 200 right curved (to return to previous direction?)
11. cca. 330 uncertain (Christianity official in Rome)
12. 476 right (fall of Rome)
13. cca. 500 left (maintaining direction?)
14. 6th-8th century right curved
15. 880 left (generic number 80)
16. 890 left (generic number 90)
17. 900 right (generic number 100)
18. 910 right (generic number 10)
19. 920 left (generic number 20 / assassination of Wenceslaus I)
20. 1000 right (end of millenium)
21. 1300 uncertain
22. 1310 balances the 1300 change
23. cca. 1350 left and then curved right (battle of Crécy)
24. 1410 right (generic number 10)
25. 1415 45° left (execution of John Huss)
26. 1420 45° left (generic number 20)
27. 1420-1435 curved right (Hussite wars)
28. 1492/1500 left, perhaps right-left-left series (discovery of the Americas / end of century; context dependent)
29. 1526 right (battle of Mohács)
30. 1530 left (restoring direction / generic number 30)
31. cca. 1580 right
32. 1618 / 1620 left (Thirty Years' War)
33. 1700 right (end of century)
34. 1789/1790 right (French revolution)
35. 1800 left (end of century)
36. around 1810 left-left (for uncertain reasons the generic number 20 and 30 turns are placed here; perhaps the second turn is 1813 because that's when the oldest surviving locomotive was built, but certainly it is before Waterloo)
37. around 1830 curved right
38. 1846-1850 curved left - right - right - curved left (revolutions of 1848)
39. 1890 left, maybe preceded by right - left (generic number 90)
40. 1900 right (end of century)
41. 1910 right (generic number 10)
42. 1914 left-right (World War I)
43. 1918/1920 left (end of WWI / generic number 20)
44. 1930 left (Great Depression)
45. 1933 right (Nazis come to power)
46. 1938-1940 curved left (WWII / generic number 30 moved here)
47. 1945 uncertain (end of WWII, usually a month line is put here when looked at in a greater detail)
48. 1956-1968 curved left - curved 180° right
49. 1968/1970 left (Soviet occupation of Czechoslovakia)
50. 1990 uncertain (end of Cold War)
51. 2000 right (end of millenium)