Spring = March 21
Summer = June 21
Fall = September 23
Winter = December 21
As such, the first day of a year should instead start on March 21st. As this numbering system is clunky and awkward, the numbering system would need to be reworked. Days in each month would change as well.
The layout:
[SPOILER="Spoiler"]January 31
Feburary 28-29
March (31) / 21 -> 31 = 10 days
April 30
May 31
June 30 (21) - 9 days
July 31
August 31
September 30 -23 = 7 days
October = 31
November 30
December 31 -21 = 10 days[/SPOILER]
I figure I will easily denote a system with easy alphabetical representations, so then it will be changed as such:
A = Spring = 1-3
B = Summer = 4-6
C = Fall = 7-9
D = Winter = 10-12
The days in the months would then fall like so...
10 30 31 21 = 92 {A}
9 31 31 23 = 94 {B}
7 31 30 21 = 89 {C}
10 31 28(29) 21 = 90/91 {D}
So the recalculated months would then be...
A-1 = 31
A-2 = 30
A-3 = 31
B-1 = 30
B-2 = 32
B-3 = 32
C-1 = 30
C-2 = 29
C-3 = 30
D-1 = 30
D-2 = 30 (31)
D-3 = 30
And of course, a leap day is every 4 years (adds a day) / 356 -> 366. Of course, the actual amount of days in a year is contested... the two most popular figures being:
mean tropical year (solar days) = 365.2422
veneral equinox year = 365.2424
Small differences, but it adds up over the centuries.
But, the days need revamped anyways. I figure, our time system makes little sense. Why is 7 AM during Spring the same as 7 AM during Winter? The sun rises at different times, this denotes nothing, just some arbitrary number. It's more simple than the reality though.
I figure, days should be divided into two parts... Light / Dark, and the amount of time within these should changed based upon when the sun rises and sets.
So for me for instance, on March 24, the sun should rise at 7:21 am and set at 7:38 pm, "noon" occuring at 1:30 pm and the day (light) length being 12h 17m.
The time of these seems to change quite a bit. Going through from the start of March, we can see it like so...
[SPOILER="Spoiler"]Rise / noon / Set / Length
6:54am / 12:36pm / 6:18pm / 11h 24m / 1
6:53am / 12:36pm / 6:19pm / 11h 26m / 2
6:51am / 12:36pm / 6:20pm / 11h 29m / 3
6:50am / 12:36pm / 6:21pm / 11h 31m / 4
6:49am / 12:35pm / 6:22pm / 11h 33m / 5
6:47am / 12:35pm / 6:23pm / 11h 36m / 6
6:46am / 12:35pm / 6:24pm / 11h 38m / 7
6:44am / 12:34pm / 6:25pm / 11h 40m / 8
6:43am / 12:34pm / 6:25pm / 11h 42m / 9
6:42am / 12:34pm / 6:26pm / 11h 45m / 10
7:40am / 1:34pm / 7:27pm / 11h 47m / 11 (DST beings)
7:39am / 1:33pm / 7:28pm / 11h 49m / 12
7:37am / 1:33pm / 7:29pm / 11h 52m / 13
7:36am / 1:33pm / 7:30pm / 11h 54m / 14
7:35am / 1:33pm / 7:31pm / 11h 56m / 15
7:33am / 1:32pm / 7:32pm / 11h 59m / 16
7:32am / 1:32pm / 7:32pm / 12h 1m / 17
7:30am / 1:32pm / 7:33pm / 12h 3m / 18
7:29am / 1:31pm / 7:34pm / 12h 5m / 19
7:27am / 1:31pm / 7:35pm / 12h 8m / 20
7:26am / 1:31pm / 7:36pm / 12h 10m / 21
7:24am / 1:31pm / 7:37pm / 12h 12m / 22
7:23am / 1:30pm / 7:38pm / 12h 15m / 23
7:21am / 1:30pm / 7:38pm / 12h 17m / 24
7:20am / 1:30pm / 7:39pm / 12h 19m / 25
7:19am / 1:29pm / 7:40pm / 12h 22m / 26
7:17am / 1:29pm / 7:41pm / 12h 24m / 27
7:16am / 1:29pm / 7:42pm / 12h 26m / 28
7:14am / 1:28pm / 7:43pm / 12h 28m / 29
7:13am / 1:28pm / 7:44pm / 12h 31m / 30
7:11am / 1:28pm / 7:44pm / 12h 33m / 31[/SPOILER]
As you can see, our DST correction that we do per the seasons, it's actually quite arbitrary not not truly reflective of the days themselves. It's just to account for the inaccuracy of our current system by adding an hour or subtracting it, due to our flawed system.
The days very clearly have the amount of minutes in them increasing as we get closer to equinoxes and then decrease after solstices.
From an astronomical view, the equinoxes and solstices would be the middle of the respective seasons,[1][2] but a variable seasonal lag means that the meteorological start of the season, which is based on average temperature patterns, occurs several weeks later than the start of the astronomical season.[3] According to meteorologists, summer extends for the whole months of June, July, and August in the northern hemisphere and the whole months of December, January, and February in the southern hemisphere. Under meteorological definitions, all seasons are arbitrarily set to start at the beginning of a calendar month and end at the end of a month.[4] This meteorological definition of summer also aligns with the commonly viewed notion of summer as the season with the longest (and warmest) days of the year (365 days), in which daylight predominates. The meteorological reckoning of seasons is used in Austria, Denmark and the former USSR; it is also used by many in the United Kingdom, where summer is thought of as extending from mid-May to mid-August. In Ireland, the summer months according to the national meteorological service, Met Éireann, are June, July and August. However, according to the Irish Calendar summer begins 1 May and ends 1 August. School textbooks in Ireland follow the cultural norm of summer commencing on 1 May rather than the meteorological definition of 1 June.
From the astronomical perspective, days continue to lengthen from equinox to solstice and summer days progressively shorten after the solstice, so meteorological summer encompasses the build-up to the longest day and a diminishing thereafter, with summer having many more hours of daylight than spring. Solstices and equinoxes are taken to mark the mid-points, not the beginnings, of the seasons. Midsummer takes place over the shortest night of the year, which is the summer solstice, or on a nearby date that varies with tradition.
The Western definition based on solstice to equinox is more frequently used where a temperature lag of up to half a season is common.[5] In North America, summer is often the period from the summer solstice (usually June 20 or 21 in the Northern Hemisphere) to the autumn equinox.[6][7][8][9] Unofficially, the U.S. summer season is commonly regarded as beginning on Memorial Day weekend (the last weekend in May) and ending on Labor Day weekend (the first weekend in September), more closely in line with the meteorological definition.
I figure, instead of some arbitrary number, you might start out like
1 Light (as in, the 1st hour of light of the day), 5 Dark (5th hour of darkness in the day), and so on.
But it seems the problem is that while a day will always start at 1 Light, or I suppose 0:00L (Light), it isn't going to end at #:00D (Dark), instead the days will likely end at various different points depending on the solstice and equinox.
For March, the amount of daylight changes each day like so:
2m, 4m, 2m, 2m, 3m, 2m, 2m, 2m, 3m, 2m, 2m, 3m, 2m, 2m, 4m, 2m, 2m, 2m, 3m, 2m, 2m, 3m, 2m, 2m, 3m, 2m, 2m, 2m, 3m, 2m
Is there a pattern? I don't know if there is a pattern. But if there is, then perhaps someone could calculate a more accurate timing system.
The pattern would be inherited from data we already have available via astronomy, as it is what actually effects the time in the (actual) day.
I hate math. Someone else figure it out, and then we can go about our merry days with time making much more sense!