Tempered Calendars
A one-dimensional count of days, such as the Julian Day Number, has no inherent periodicity. Divide it up into 7-day weeks, however, and you get a calendar which is seven days wide and infinitely tall (usually clipped to display a single month’s days).
The periodicity of astronomical phenomena such as the rotation of the Earth around the Sun and the rotation of the Moon around the Earth are used as the basis of many calendar systems, such as the Buddhist, Chinese, Gregorian, Hebrew, Islamic, Korean, Mayan, or Persian. However, these astronomical phenomena can’t be captured perfectly in any calendar system because they are mutually indivisible. For example, it takes 365.2424 days (i.e., 365 days, 5 hours, 49 minutes and 12 seconds) for the Earth to orbit the Sun, and 29.530589 days (29 d 12 h 44 min 2.9 s) for the Moon to orbit the Earth – numbers which are not mutually divisible.
Each calendar system is a set of rules which defines the relationships among its various periodic intervals. Because the intervals are mutually indivisible, the rules of any given calendar system must favor one intervals over another. Therefore, these calendar systems can be viewed as temperaments. They compromise some intervals to capture the purity of others.
For example, the Islamic calendar compromises the purity of the solar interval in order to have an absolutely pure lunar interval, with months that precisely match the rising and setting of the Moon, but with years that drift relative to the Earth’s orbit around the Sun. On the other hand, the Gregorian calendar has a pure solar interval, but its months start and end with no relationship whatsoever to the rising and setting of the Moon. Other calendars temper their intervals differently, but they’re all temperaments, one way or another.
No such tempering would be necessary if the Earth orbited the Sun in exactly 336 days, and the Moon orbited the Earth in exactly 28 days. Then, every year would have 12 months of 4 weeks of 7 days. The new moon would rise on the first of each month; solstices and equinoxes would fall on the same dates (and days of the week) every year.
Unfortunately, we can’t temper the planets to conform to our calendrical needs. ;-)
The periodicity of astronomical phenomena such as the rotation of the Earth around the Sun and the rotation of the Moon around the Earth are used as the basis of many calendar systems, such as the Buddhist, Chinese, Gregorian, Hebrew, Islamic, Korean, Mayan, or Persian. However, these astronomical phenomena can’t be captured perfectly in any calendar system because they are mutually indivisible. For example, it takes 365.2424 days (i.e., 365 days, 5 hours, 49 minutes and 12 seconds) for the Earth to orbit the Sun, and 29.530589 days (29 d 12 h 44 min 2.9 s) for the Moon to orbit the Earth – numbers which are not mutually divisible.
Each calendar system is a set of rules which defines the relationships among its various periodic intervals. Because the intervals are mutually indivisible, the rules of any given calendar system must favor one intervals over another. Therefore, these calendar systems can be viewed as temperaments. They compromise some intervals to capture the purity of others.
For example, the Islamic calendar compromises the purity of the solar interval in order to have an absolutely pure lunar interval, with months that precisely match the rising and setting of the Moon, but with years that drift relative to the Earth’s orbit around the Sun. On the other hand, the Gregorian calendar has a pure solar interval, but its months start and end with no relationship whatsoever to the rising and setting of the Moon. Other calendars temper their intervals differently, but they’re all temperaments, one way or another.
No such tempering would be necessary if the Earth orbited the Sun in exactly 336 days, and the Moon orbited the Earth in exactly 28 days. Then, every year would have 12 months of 4 weeks of 7 days. The new moon would rise on the first of each month; solstices and equinoxes would fall on the same dates (and days of the week) every year.
Unfortunately, we can’t temper the planets to conform to our calendrical needs. ;-)
posted by ThumMeister | 9:07 PM
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