The Tropical Year: 31.6888 nHz
One of the most important cycles we live by is the tropical year, measured from equinox to corresponding equinox (or solstice to corresponding solstice). The tropical year lasts, on average, 365.2422 days (365 days, 5 hours, 48 minutes, 45 seconds), which means that it is an oscillation with a frequency of 31.6888 nanohertz (nHz). This is the cycle of the seasons.
Spring, summer, autumn, and winter are the conventional seasons, but the tropical year may be split up into more than or less than four seasons, and these need not be of equal length. In northern Australia, a frequent division is “the dry” (May to September), “the build up” (September to December), and “the wet” (December to April). Local Aboriginal people, however, may recognise as many as six seasons.
The Sidereal Year: 31.6875 nHz
A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the stars. This is the time that it takes for the sun to move through the “signs of the zodiac.” Because of the precession of the equinoxes, the sidereal year is 365.2564 days, which is about 20.4 minutes longer than the tropical year. As a result, ancient rules assigning dates to the signs of the zodiac are now completely wrong. The sidereal year corresponds to an oscillation of 31.6875 nanohertz.
The Synodic Month: 391.935 nHz
A synodic month is a cycle from new moon to new moon or full moon to full moon. This period actually varies by several hours, but it averages out to 29.530588 days (29 days, 12 hours, 44 minutes, 3 seconds).
In 432 BC, Meton of Athens noted that 235 synodic months (6939.7 days) is almost exactly equal to 19 years (6939.6 days). This period is called the Metonic cycle, and is used for predicting solilunar events such as the date of Easter.
The synodic month is also strangely similar to the average menstrual cycle (28 days), and this is reflected in the word (“menstrual” derives from the Latin mēnsis = month).
The Week: 1.65344 µHz
The week has an origin among the ancient Hebrews. It also has a Babylonian origin (the relationship between the two origins is unclear). The Babylonians related the 7 days of the week to the sun, moon, and 5 visible planets. They also related them to various gods. Our days of the week derive from the Babylonian week, via Greece and Rome: Sunday (Sun), Monday (Moon), Tuesday (Tiw, god of war = Mars), Wednesday (Woden = Mercury), Thursday (Thor = Jupiter), Friday (Frigg = Venus), and Saturday (Saturn).
Early Christians related the two week concepts together, pointing out that the day of the Resurrection (the day after the Jewish Sabbath) corresponded to the day of the Sun in the Roman system. The week corresponds to an oscillation of 1.65344 microherz.
The Sidereal Day: 11.6058 µHz
A sidereal day is the time that it takes the earth to rotate once around its axis. It often surprises people to discover that this time is 23 hours, 56 minutes, 4.1 seconds. It can be measured by the time to go from a star being overhead to the same star being overhead again.
The Solar Day: 11.5741 µHz
A solar day (24 hours, give or take some seconds) is the time from noon to noon. It is longer than a sidereal day because, while the earth is rotating around its axis, it is also moving around the sun. To put it another way, the sun is not a fixed reference point for the earth’s rotation. The difference between the sidereal and solar days mean that the stars seem to rise about 3 minutes and 56 seconds earlier every night.