The Solstice Tri-Decimal calendar (Quechua: 13-killakunayuq Intip-kutiypi-tiqsisqa Wata-sinrina), also known as the Standardized Aymara Calendar (Tiqsichasqa Aymara Wata-sinrina), is a calendar "created" (it is more of a standardization than an innovation) by TheDankBoi69 meant to standardize not just the Aymara Calendar, but also every other 13*28 calendar. This calendar, just like the Lunar Aymara Calendar, consisted of thirteen 28-day months, each divided into four 7-day cycles similar to weeks, plus a spare day in the Southern Winter Solstice. It was designed in part to operate along with the Gregorian Calendar, but in so that the Standardized Aymara Calendar depends on astronomical observances rather than a fixed date of the Gregorian Calendar to calculate the New Year, and that both calendars are used for different purposes. The main benefit of this calendar and other 13*28 calendars is their stability, making it easier to plan events and set schedules for years in advance.
"14th of October, 2025" in Gregorian/Revised Julian and the Solstice Tri-Decimal Notation.
This is a preview of how certain dates would look like if written by the notation of this calendar:
14th of October 2007 Gregorian/Revised Julian= 515¤V°₂
14th of October 2025 G/RJ= 533¤V°₃
28th of July 1821 G/RJ= 329¤II′₂
12th of October 1492 Julian (21st of October 1492 G/RJ)= 000¤V′₃
12th of June 1492 Julian (21st of June 1492 G/RJ)= 000¤N
The earlier Aymara Calendar was already used, at least as early as the decade of the 1980's Gregorian/Revised Julian [5488-5497 Aym.], but mainly to celebrate every Southern Winter Solstice as their New Year (Aymara: Machaq Mara). However, due to the lack of standardization and an instiution to regulate and standardize it, it is largely ignored except on that date.
TheDankBoi69, seeing the amount of 13*28 calendars but lacking any consistencies, decided to make a standard in order to address the following questions, that are based on the varying conventions in Tri-Decimal Calendars:
Should the previously uninterrupted week cycle (Monday, Tuesday, Wednesday) be interrupted every "Spare Day" or "Leap Day"?
What are the parameters for the New Year, if it claims to fall on the solstice?
Should the calendar be a reform of the Julianic (Julian [J], Gregorian [G], and Revised Julian [RJ]) calendars, or should be as different and as independent as possible?
What should be the notation of this Tri-Decimal calendar?
What are the parameters of the Leap Day? Should it follow a Straight 4 rule (Julian), a 4-100-400 rule (Gregorian), or Revised Julian, or entirely on astronomy?
Should the Leap Day it fall in the other solstice, or at the end of February, if it's just a mere reform of the Julianic Calendars?
What are the ideological implications behind the invention/standardization of the Calendar?
What should be the epoch of this calendar? Should it be the same as the current Aymara Calendar, which took a similar approach as the Holocene Calendar (taking an already existing notable event and adding a round number to the year)?
The result was a calendar with an unique notation, but built in a synthesis made out of older, existing ideas.
Design[]
[EVEN THOUGH THIS IS AN STANDARDIZATION OF THE AYMARA CALENDAR, MANY TERMS WILL BE IN QUECHUA, AS THEDANKBOI69 KNOWS IT BETTER THAN AYMARA)
Epoch[]
Since the Solstice Tri-Decimal Calendar has its epoch date as the Southern Winter Solstice before October 1492 Julianic, therefore 000¤ indicates the period between 21st of June, 1492 Gregorian (12th of June, 1492). Because of that, "Columbus Day 1492" (12th of October 1492 Julian, which translates to Proleptic Gregorian as 21st of October 1492) becomes 000¤V′₃. (Notation and reading will be explained later).
Structure and the Kalends[]
There are thirteen months (killakuna), each divided into four 7-day weeks called quarters (hunqakuna). This added up to 364 days. The spare day, known as "Day Zero" or "Monthless Day" ("Punchaw 0" icha "Killanaq P'unchaw"). The concept of the Roman kalends (kalintha; ñawpaq-punchaw) is reintroduced to refer to the first day of each 28-day month. Therefore, there are 13 kalends in a year. After the 13th kalends, exactly 28 days later, the "14th kalends" would actually be the Day 0 of the following year, and the day after Day 0 is the First Calends of that new year.
52 weeks + 1 day = 1 year
26 weeks = 1 semester
13 weeks = 1 quarter
4 weeks = 1 month
2 weeks = 1 fortnight
1 week = 7 days
1 fortnight = 14 days
1 month = 28 days (4 weeks)
1 quarter = 91 days (13 weeks)
1 semester = 182 days (26 weeks)
1 year = 364 days (52 weeks) + 1 day
The FRW (aka a Quarter Month) vs. MAW (aka the traditional week cycle)[]
This system uses this cycle as the basis by which to organize the year. In this Calendar, along with other 13*28 calendars, a "Fixed Relative Week" (FRW) is simply each of the 4 quarters that each month is divided. Since each month has 28 days, each quarter is 7 days long. This is distinct from the traditional week, also known as the Movable Absolute Week (MAW) i.e. Sunday (Intichaw), Monday (Killachaw), Tuesday (Atipachaw / Antichaw), Wednesday (Quyllurchaw), Thursday (Illapachaw), Friday (Ch'askachaw), and Saturday (K'uychichaw), The uninterrupted cycle of the MAW has spread from the Jewish Calendar to be used in most of the World. Even countries that don’t use the Julianic calendars (Julian, Gregorian, or Revised Julian) follow the seven days of the MAW. It is decided that the MAW shouldn't be sacrificed (that is, interrupted), unlike most proponents of tridecimal calendars.
So, the FRW refers to a numerical period of days, that don't have to necessarily coincide with the MAW, referring to the Sunday-Saturday Week.
Calendar Preview[]
The symbols will be explained later.
Months II-XIII in non-Leap Years; II-VI; VIII-XIII in Leap Years[]
MONTH
1
2
3
4
5
6
7
°
01
02
03
04
05
06
07
′
08
09
10
11
12
13
14
″
15
16
17
18
19
20
21
‴
22
23
24
25
26
27
28
Month I[]
MONTH
1
2
3
4
5
6
7
N
00
°
01
02
03
04
05
06
07
′
08
09
10
11
12
13
14
″
15
16
17
18
19
20
21
‴
22
23
24
25
26
27
28
Month VII in Leap Years[]
MONTH
₀
1
2
3
4
5
6
7
°
01
02
03
04
05
06
07
′
08
09
10
11
12
13
14
″
W
15
16
17
18
19
20
21
‴
22
23
24
25
26
27
28
Calculation of the "Zeroth Day" and Leap Days[]
Day Zero[]
The spare day that is not part of any month, and it is decided by the timing of the Southern Winter Solstice. Since it's a standardization of the Aymara Calendar, the UTC time of the solstice (assumed to be mean solar time in the Prime Meridian) gets substracted by 2/10. (representing a 200 mitawi difference, geographically equivalent to 80 gradians West, or 72°W, these terms will be explained later). If the solstice occurs between midnight and noon, the day it falls in shall be designated as Day Zero. If it occurs between dusk and midnight, the following day shall be designated as Day Zero There is a noticeable pattern: the MAW of the Zeroth Day advances by one, and sometimes by two. If it advances by one, the year lasts 365 days. If it advances by one, it's because the solstice occurs between noon and dusk and the year lasts 366 days. The following chart (in Spanish) shows both the UTC and 72°W times and dates of each Southern Winter solstice between 1992 and 2029, and the Zeroth Days in Italics with an asterisk indicate that the solstice occurred between noon and dusk.
List of "Zeroth Days" (1992-2029 G/RJ), compared with Southern Winter Solstice timings. 500¤ - 537¤
Year Number
Gregorian/RJ Date - UTC
UTC Time
Gregorian/RJ Date - Peruvian Longitude (72°W)
Peruvian (72°W) Time
Day Chosen to be Day 0 (in G/RJ)
500
domingo, 21 de Junio de 1992
3:14:00
sábado, 20 de Junio de 1992
22:26:00
domingo, 21 de Junio de 1992
501
lunes, 21 de Junio de 1993
9:00:00
lunes, 21 de Junio de 1993
4:12:00
lunes, 21 de Junio de 1993
502
martes, 21 de Junio de 1994
14:48:00
martes, 21 de Junio de 1994
10:00:00
martes, 21 de Junio de 1994
503
miércoles, 21 de Junio de 1995
20:34:00
miércoles, 21 de Junio de 1995
15:46:00
jueves, 22 de Junio de 1995*
504
viernes, 21 de Junio de 1996
2:24:00
jueves, 20 de Junio de 1996
21:36:00
viernes, 21 de Junio de 1996
505
sábado, 21 de Junio de 1997
8:20:00
sábado, 21 de Junio de 1997
3:32:00
sábado, 21 de Junio de 1997
506
domingo, 21 de Junio de 1998
14:03:00
domingo, 21 de Junio de 1998
9:15:00
domingo, 21 de Junio de 1998
507
lunes, 21 de Junio de 1999
19:49:00
lunes, 21 de Junio de 1999
15:01:00
martes, 22 de Junio de 1999*
508
miércoles, 21 de Junio de 2000
1:48:00
martes, 20 de Junio de 2000
21:00:00
miércoles, 21 de Junio de 2000
509
jueves, 21 de Junio de 2001
7:38:00
jueves, 21 de Junio de 2001
2:50:00
jueves, 21 de Junio de 2001
510
viernes, 21 de Junio de 2002
13:24:00
viernes, 21 de Junio de 2002
8:36:00
viernes, 21 de Junio de 2002
511
sábado, 21 de Junio de 2003
19:10:00
sábado, 21 de Junio de 2003
14:22:00
domingo, 22 de Junio de 2003*
512
lunes, 21 de Junio de 2004
0:57:00
domingo, 20 de Junio de 2004
20:09:00
lunes, 21 de Junio de 2004
513
martes, 21 de Junio de 2005
6:46:00
martes, 21 de Junio de 2005
1:58:00
martes, 21 de Junio de 2005
514
miércoles, 21 de Junio de 2006
12:26:00
miércoles, 21 de Junio de 2006
7:38:00
miércoles, 21 de Junio de 2006
515
jueves, 21 de Junio de 2007
18:06:00
jueves, 21 de Junio de 2007
13:18:00
viernes, 22 de Junio de 2007*
516
viernes, 20 de Junio de 2008
23:59:00
viernes, 20 de Junio de 2008
19:11:00
sábado, 21 de Junio de 2008
517
domingo, 21 de Junio de 2009
5:46:00
domingo, 21 de Junio de 2009
0:58:00
domingo, 21 de Junio de 2009
518
lunes, 21 de Junio de 2010
11:28:00
lunes, 21 de Junio de 2010
6:40:00
lunes, 21 de Junio de 2010
519
martes, 21 de Junio de 2011
17:16:00
martes, 21 de Junio de 2011
12:28:00
miércoles, 22 de Junio de 2011*
520
miércoles, 20 de Junio de 2012
23:09:00
miércoles, 20 de Junio de 2012
18:21:00
jueves, 21 de Junio de 2012
521
viernes, 21 de Junio de 2013
5:04:00
viernes, 21 de Junio de 2013
0:16:00
viernes, 21 de Junio de 2013
522
sábado, 21 de Junio de 2014
10:51:00
sábado, 21 de Junio de 2014
6:03:00
sábado, 21 de Junio de 2014
523
domingo, 21 de Junio de 2015
16:38:00
domingo, 21 de Junio de 2015
11:50:00
domingo, 21 de Junio de 2015
524
lunes, 20 de Junio de 2016
22:34:00
lunes, 20 de Junio de 2016
17:46:00
martes, 21 de Junio de 2016*
525
miércoles, 21 de Junio de 2017
4:24:00
martes, 20 de Junio de 2017
23:36:00
miércoles, 21 de Junio de 2017
526
jueves, 21 de Junio de 2018
10:07:00
jueves, 21 de Junio de 2018
5:19:00
jueves, 21 de Junio de 2018
527
viernes, 21 de Junio de 2019
15:54:00
viernes, 21 de Junio de 2019
11:06:00
viernes, 21 de Junio de 2019
528
sábado, 20 de Junio de 2020
21:44:00
sábado, 20 de Junio de 2020
16:56:00
domingo, 21 de Junio de 2020*
529
lunes, 21 de Junio de 2021
3:32:00
domingo, 20 de Junio de 2021
22:44:00
lunes, 21 de Junio de 2021
530
martes, 21 de Junio de 2022
9:14:00
martes, 21 de Junio de 2022
4:26:00
martes, 21 de Junio de 2022
531
miércoles, 21 de Junio de 2023
14:58:00
miércoles, 21 de Junio de 2023
10:10:00
miércoles, 21 de Junio de 2023
532
jueves, 20 de Junio de 2024
20:51:00
jueves, 20 de Junio de 2024
16:03:00
viernes, 21 de Junio de 2024*
533
sábado, 21 de Junio de 2025
2:42:00
viernes, 20 de Junio de 2025
21:54:00
sábado, 21 de Junio de 2025
534
domingo, 21 de Junio de 2026
8:24:00
domingo, 21 de Junio de 2026
3:36:00
domingo, 21 de Junio de 2026
535
lunes, 21 de Junio de 2027
14:11:00
lunes, 21 de Junio de 2027
9:23:00
lunes, 21 de Junio de 2027
536
martes, 20 de Junio de 2028
20:02:00
martes, 20 de Junio de 2028
15:14:00
miércoles, 21 de Junio de 2028*
537
jueves, 21 de Junio de 2029
1:48:00
miércoles, 20 de Junio de 2029
21:00:00
jueves, 21 de Junio de 2029
These are the Months II-XIII in non-Leap Years; II-VI; VIII-XIII in Leap Years:
As stated before, the Leap Days are in the Middle of the Year, to coincide with the Southern Summer Solstice, with the days chosen to "fill the gaps" caused by the 366-day years that skipped a weekday. The Leap Years are 502¤; 506¤; 510¤; 514¤; 518¤; 523¤; 527¤; 531¤; 535¤. As you can notice, there is a 5-year period between 518¤ and 523¤. This is the explanation for the slightly complex rules for Gregorian and RJ calendars, which the Julian calendar missed.
List of Leap Days (1994-2028 G/RJ), compared with Southern Summer Solstice timings. 502¤ - 536¤
Year Number
Gregorian/RJ Date - UTC
UTC Time
Gregorian/RJ Date - Peruvian Longitude (72°W)
Peruvian (72°W) Time
Day Chosen to be Day 0 (in G/RJ)
502
jueves, 22 de Diciembre de 1994
2:23:00
miércoles, 21 de Diciembre de 1994
21:35:00
miércoles, 21 de Diciembre de 1994
503
viernes, 22 de Diciembre de 1995
8:17:00
viernes, 22 de Diciembre de 1995
3:29:00
506
martes, 22 de Diciembre de 1998
1:57:00
lunes, 21 de Diciembre de 1998
21:09:00
lunes, 21 de Diciembre de 1998
507
miércoles, 22 de Diciembre de 1999
7:44:00
miércoles, 22 de Diciembre de 1999
2:56:00
510
domingo, 22 de Diciembre de 2002
1:15:00
sábado, 21 de Diciembre de 2002
20:27:00
sábado, 21 de Diciembre de 2002
511
lunes, 22 de Diciembre de 2003
7:04:00
lunes, 22 de Diciembre de 2003
2:16:00
514
viernes, 22 de Diciembre de 2006
0:22:00
jueves, 21 de Diciembre de 2006
19:34:00
jueves, 21 de Diciembre de 2006
515
sábado, 22 de Diciembre de 2007
6:08:00
sábado, 22 de Diciembre de 2007
1:20:00
518
martes, 21 de Diciembre de 2010
23:39:00
martes, 21 de Diciembre de 2010
18:51:00
martes, 21 de Diciembre de 2010
519
jueves, 22 de Diciembre de 2011
5:30:00
jueves, 22 de Diciembre de 2011
0:42:00
523
martes, 22 de Diciembre de 2015
4:48:00
martes, 22 de Diciembre de 2015
0:00:00
lunes, 21 de Diciembre de 2015
524
miércoles, 21 de Diciembre de 2016
10:44:00
miércoles, 21 de Diciembre de 2016
5:56:00
527
domingo, 22 de Diciembre de 2019
4:19:00
sábado, 21 de Diciembre de 2019
23:31:00
sábado, 21 de Diciembre de 2019
528
lunes, 21 de Diciembre de 2020
10:02:00
lunes, 21 de Diciembre de 2020
5:14:00
531
viernes, 22 de Diciembre de 2023
3:27:00
jueves, 21 de Diciembre de 2023
22:39:00
jueves, 21 de Diciembre de 2023
532
sábado, 21 de Diciembre de 2024
9:20:00
sábado, 21 de Diciembre de 2024
4:32:00
535
miércoles, 22 de Diciembre de 2027
2:42:00
martes, 21 de Diciembre de 2027
21:54:00
martes, 21 de Diciembre de 2027
536
jueves, 21 de Diciembre de 2028
8:20:00
jueves, 21 de Diciembre de 2028
3:32:00
Notations[]
Written Notation[]
Overview[]
There are two main ways to notate the date:
YYY¤M(MMM)WD(Septimal notation , which takes weeks into account)
YYY¤M(MMM)~DD(Weekless notation , which ignores weeks)
Years[]
For consistency, larger units are towards the left and smaller units are towards the right. Therefore, the years are written leftmost in Arabic Numerals, separated from the month with a "currency sign" [¤], which could be interpreted as a rotated quadrate cross (chakana).
526¤ = 21/JUN/2018 - 20/JUN/2019 G/RJ
527¤ = 21/JUN/2018 - 20/JUN/2020 G/RJ
531¤ = 21/JUN/2023 - 19/JUN/2024 G/RJ
532¤ = 20/JUN/2024 - 20/JUN/2025 G/RJ
Years before Columbus Day are written with a minus sign:
Sometimes, a small 5, whether as a subscript of superscript, is written to show the difference between this calendar and the Aymara one.
₅526¤ = 5526 Aym
⁵532¤ = 5532 Aym
However, this only works well between 000¤ (5000 Aym; 1492 Julianic) and 999¤(5999 Aym; 2492 Julianic)
−001¤ = 4999 Aym
1000¤ = 6000 Aym
Months[]
The months are written in Roman Numerals (Rumap-yupaykuna) from 1 to 13, following the years, separated by the "rotated chakana". Although the months are currently nameless due to the disputed namings (as described in the article dedicated to the Aymara calendar), it's believed that once the calendar achieves legal status, the names of the months will arise naturally.
The week notation (only used in the Septimal Notation, the one that takes weeks into account) uses exclusive counting (that is, starts with 0), partially for ease in easy conversion between notations, and to fit with the inclusive counting used in days, mosty primarily used in Kalends counting. (Ring (siwicha) = 0 weeks. 1 to 3 Primes (sut'ukuna) = amount of Weeks passed since the Kalends)
[°](siwicha), the week of the kalends (ñawpaq-hunqa, kalintha-hunqa) (Days 1-7)
[′](1 sut'u) the first week after the kalends (at least 1 week passed since the kalends, (kalinthamanta qhipaman 1-ñiqi hunqa), Days 8-14)
[″](2 sut'ukuna) the second week after the kalends (at least 1 week passed since the kalends, (kalinthamanta qhipaman 2-ñiqi hunqa), Days 15-21)
[‴](3 sut'ukuna) the third week after the kalends (at least 1 week passed since the kalends, (kalinthamanta qhipaman 3-ñiqi hunqa), Days 22-28)
Examples:
533¤V° = 12/OCT/2025 - 18/OCT/2025 G/RJ
532¤XIII‴ = 14/JUN/2025 - 20/JUN/2025 G/RJ
Days[]
Septimal Notation[]
Since the week of the month is already stated, only the day number of the week is enough. (Note that this refers to the FAW, the MAW changes every year). The notation of the number of the day of the FAW uses subscript numbers from 1 to 7, therefore it uses inclusive counting:
[₁]1-ñiqi punchaw, the first day of the week
[₂]2-ñiqi punchaw, the second day of the week.
[₃]3-ñiqi punchaw, the third day of the week.
[₄]4-ñiqi punchaw, the fourth day of the week.
[₅]5-ñiqi punchaw, the fifth day of the week.
[₆]6-ñiqi punchaw, the sixth day of the week.
[₇]7-ñiqi punchaw, the seventh day of the week.
Here are some examples of use:
533¤V°₃ = 14/OCT/2025 G/RJ
000¤V′₃ = 12/OCT/1492 J (21/OCT/1492 pG)
532¤XIII‴₇ = 20/JUN/2025 G/RJ
Weekless Notation[]
Unlike the Septimal Notation, this one indicates the day number without taking into account the week, so it is notated with Arabic Numerals (normal size, not subscript) from 01 to 28. They are separated from the month with a tilde (q'inqu siq'i): [~]
533¤V~03 = 14/OCT/2025 G/RJ
000¤V~10 = 12/OCT/1492 J (21/OCT/1492 pG)
532¤XIII~28 = 20/JUN/2025 G/RJ
"Day Zero"[]
Usually it is marked with the letter N, as it was used by medieval scribes to represent the number zero, although this was never used by the original Romans.
533¤N = 21/JUN/2025 G/RJ
Other alternatives include the Arabic Numeral Zero.
533¤0 = 21/JUN/2025 G/RJ
Leap Days[]
The Leap Days may be marked by in the septimal notation by a small zero in the place of the FRW day, to signify that this is like "another day zero" that starts the second half of the year.
531¤VII″₀ = 21/DEC/2023 G/RJ
Although they may also be notated by the letter W, standing for wakllanwata, the Quechua word for "leap", in this sense.
531¤W = 21/DEC/2023 G/RJ
Graphic Notation[]
In addition to the written notation, there is also another type of notation, which is comprised of a rectangle that uses colors to identify the month, notches to identify the week, and dots to identify the day.
MAW Days[]
The number of dots, ranging from one to seven, indicates which day of the Movable Absolute Week is it.
On most of the rectangle, at the lower half, the day of the MAW is indicated via a number of dots, ranging from 1 to 7. They are akin to the subscripts used in written notation.
MAWeeks[]
The amount of notches is akin to the exclusive counting method of weeks.
The amount of weeks passed since the last kalends is represented by the amount of notches on the top half of the rectangle (that's how you sensically explain the exclusive counting of weeks), the same way the same is represented by rings and "primes" on the written notation. No notches represent that a week hasn't yet passed since the last kalends.
Months[]
The color of the rectangle represents the month it indicates. This is a tentative standard and it's unofficial so far. For starters, the Zeroth Day is represented by Gold. The month colors in this tentative standard are the following:
The colors represent the months.
Lime Green
Red
Peach Skin
Teal
Purple
Orange
Brick Bronze
Mustard Yellow
Forest Green
Beige
Chocolate Brown
Black
Grey
Given this 7*4 matrix of rectangular symbols that represent each one of the 28 days of the standard month, this is how the standard month would look like in graphic notation:
This is how the standard 28-day month looks like in graphic notation.
Day Zero[]
The Day Zero is represented differently than other days.
The Day Zero is represented with a quadrate cross, with the color being golden, as aforementioned. It signifies that it's monthless and it announces a new year.
Leap Day[]
The symbol for the Leap Day is colored the same as the Seventh Month.
The Leap Day is represented with a quadrate cross, and also mirrors its written notation: it's part of Month VII, but it acts like another Day Zero, and thus can be considered "part" of the Second Week After The Seventh Kalends.
Decimal Time Extension[]
In addition to the 13*28 calendar, there are also units smaller than the day, based on the decimal system. TheAbsymal Calendar decided to conform to the 24-Hour system, but not this one. This decimal time system, intended to be a companion to the Solstice Tri-Decimal Calendar, is similar to the Swatch Internet Time:
Units and Notation[]
Instead of 24 hours divided sexagesimally into minutes and seconds, the mean solar day is divided into 1000 equal parts called mitawikuna, meaning each mitawi lasts 86.4 seconds (1.440 minutes) in 24H time, and an hour lasts for approximately 42 mitawikuna. Additionally, a thuyna is the hundredth part of a mitawi, extending the standard for better precision: ·800.00. Thus, with the previously mentioned year and date system, Since the notation of the Solstice Tri-Decimal Calendar is comprised of writing the largest units at the left side and the smallest units at the right, the decimal time notation is separated from the date with an interpunct. [·]: ₅533¤III~″₂·600
YYY¤M(MMM)WD·TTT.TT
YYY¤M(MMM)~DD·TTT.TT
The ideology behind it[]
The time of day always references the amount of time that has passed since midnight (standard time) in Sacsaywaman, Cusco, as the city is nicknamed "The Navel of the World" and a historically important and convenient location as its longitude is a round number if measured in gradians: 80 gradians west (72°W). This time standard therefore shall be named "Sacsaywamán Mean Time". (It should not surprising that Swatch chose Biel for its time standard, as Biel is the city where its headquarters are located, but Biel Mean Time is actually based on the traditional 15° wide time zones, and not really in the actual mean time of Biel.) For example, ·800 indicates a time 800 mitawikuna after solar midnight in SMT, (which is equivalent to solar midnight in London). Because of the decimal nature of the units, it favours gradians over sexagesimal degrees in its calculations. There were ideological reasons behind it: The Incas used the decimal system and organized their people as such (contrary to the Babylonians, who used a sexagesimal system and it's the source of both the minute and second divisions of the hour and the degree). Thus, it would make sense to reference it through the time system, especially if the decimal system is the one we widely use today. One of the goals was to simplify the way people in different time zones communicate about time, mostly by eliminating time zones altogether. It also does away with the division of the day into 12 or 24 parts called "hours" (originally an Egyptian unit, which spread to Greece and then Rome), then dividing them sexagesimally (a Babylonian idea).
Conversion table
24-60-60 units
Decimal units
1 day (punchaw)
1000 mitawikuna
1 hour (hura)
41.6 mitawikuna
1 minute with
26.4 seconds
1 mitawi
1 minute
(minut)
69.4 thuynakuna
1 second
(siquntu)
0.011574 thuynakuna
"Numbering Zones"[]
Instead of 24 time zones, each spanning 15° in longitude, there are 40 "numbering zones" (yupanalla-suyukuna), each spanning 10 gradians (9 degrees) in longitude. That is, the "time number" (chawpi-tuta yupay) is the same everywhere, the time is constant, unlike in time zones, where, because the sun position is different, the time number is also different. A number divisible by 25 is assigned to each of the 40 zones, to be established as the "midnight number" of that zone. The SMT Numbering Zone (SaqsayWaman Awari Mitasuyu), is the zone spanning from 85 to 75 gradians West centered on 80 gradians West (76.5°-67.5°W), it is the Numbering Zone where the midnight number is ·000. As we've said before, unlike Swatch Internet Time, it is independent from the 24h sexagesimal timezones, and based on the actual mean solar time of Cusco.
The amount of 40 zones is not arbitrary if it's measured in decimal units and gradians: The day can be divided into 8 equal parts, with each division coinciding with either the "4 main points of the day", namely midday (noon), dusk, midnight, and dawn; or the intermediate points between each of them. (All 8 point of them shall be named the "8 Key Points of the Day, with half of them being Main Points) Dividing the world into 40 numbering zones will make the numbers of the 8 Key Points align with a number divisible by 25, and not only that, it would make 4 of the 8 numbers end in a 0, and 2 of them end in 00. For example:
Key Point
London /
Greenwhich
SMT
Swiss N.Z.
(where Biel is)
Midnight
·800
·000
·775
(midpoint between midnight and dawn)
·925
·125
·900
Dawn
·050
·250
·025
(midpoint between dawn and midday)
·175
·375
·150
Midday
·300
·500
·275
(midpoint between midday and dusk)
·425
·625
·400
Dusk
·550
·750
·525
(midpoint between dusk and midnight)
·675
·875
·650
To show that the concept of "numbering zones" is the inverse to the timezones, for example: ·800 represents midnight in London, but noon in Fiji, sunrise in Bhutan, and dusk in Guatemala. Likewise, The "midnight numbers" of the Numbering Zones of Guatemala, Fiji, and Bhutan are ·050; ·300 and ·550 respectively. It doesn't observe daylight savings time.
It would be unwise to half the number into 20, because it would be even less precise than our current 24-time zone system.
List of Numbering Zones:
"Midnight number:"
Longitude (in gradians)
Longitude (in degrees)
"Midnight number:"
Longitude (in gradians)
Longitude (in degrees)
·000
−85g - −75g
(nearest to −80g)
nearest to 72°W
·500
+115g - +125g
(nearest to +120g)
nearest to 108°E
·025
−95g - −85g
(nearest to −90g)
nearest to 81°W
·525
+105g - +115g
(nearest to +110g)
nearest to 99°E
·050
−105g - −95g
(nearest to −100g)
nearest to 90°W
·550
+95g - +105g
(nearest to +100g)
nearest to 90°E
(equivalent to UTC+6h)
·075
−115g - −105g
(nearest to −110g)
nearest to 99°W
·575
+85g - +95g
(nearest to +90g)
nearest to 81°E
·100
−125g - −115g
(nearest to −120g)
nearest to 108°W
·600
+75g - +85g
(nearest to +80g)
nearest to 72°E
·125
−135g - −125g
(nearest to −130g)
nearest to 117°W
·625
+65g - +75g
(nearest to +70g)
nearest to 63°E
·150
−145g - −135g
(nearest to −140g)
nearest to 126°W
·650
+55g - +65g
(nearest to +60g)
nearest to 54°E
·175
−155g - −145g
(nearest to −150g)
nearest to 135°W
·675
+45g - +55g
(nearest to +50g)
nearest to 45°E
(equivalent to UTC+3h)
·200
−165g - −155g
(nearest to −160g)
nearest to 144°W
·700
+35g - +45g
(nearest to +40g)
nearest to 36°E
·225
−175g - −165g
(nearest to −170g)
nearest to 153°W
·725
+25g - +35g
(nearest to +30g)
nearest to 27°E
·250
−185g - −175g
(nearest to −180g)
nearest to 162°W
·750
+15g - +25g
(nearest to +20g)
nearest to 18°E
·275
−195g - −185g
(nearest to −190g)
nearest to 171°W
·775
+05g - +15g
(nearest to +10g)
nearest to 09°E
·300
+195g - −195g
(nearest to +200g)
nearest to 180°
(antimeridian)
(equivalent to UTC-12h)
·800
⧿05g - ⧾05g
(nearest to 00g)
nearest to 00°
(Prime Meridian)
(equivalent to UTC)
·325
+185g - +195g
(nearest to +190g)
nearest to 171°E
·825
−15g - −05g
(nearest to −10g)
nearest to 09°W
·350
+175g - +185g
(nearest to +180g)
nearest to 162°E
·850
−25g - −15g
(nearest to −20g)
nearest to 18°W
·375
+165g - +175g
(nearest to +170g)
nearest to 153°E
·875
−35g - −25g
(nearest to −30g)
nearest to 27°W
·400
+155g - +165g
(nearest to +160g)
nearest to 144°E
·900
−45g - −35g
(nearest to −40g)
nearest to 36°W
·425
+145g - +155g
(nearest to +150g)
nearest to 135°E
·925
−55g - −45g
(nearest to −50g)
nearest to 45°W
(equivalent to UTC−3h)
·450
+135g - +145g
(nearest to +140g)
nearest to 126°E
·950
−65g - −55g
(nearest to −60g)
nearest to 54°W
·475
+125g - +135g
(nearest to +130g)
nearest to 117°E
·975
−75g - −65g
(nearest to −70g)
nearest to 63°W
Appendix[]
Here are a bunch of images that display how would the calendar look like with the graphical notation, in non-leap and leap years. In both of them, it is assumed that 21st of June is the Day Zero. Each of the 4 quarters of the year, traditionally associated with the 4 seasons, are easily idenitified, and all four of them have 13 weeks each. The turquoise divisions indicate the comparison with the Julianic months (the golden division separates December from January, as they are from different years) As you can see, the Tri-Decimal months are uniform, while the Julianic ones vary in shape.
[[File:STD year large.png|thumb|910x910px|[[File:STD Leap Year.png|thumb|943x943px|
