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{| class="wikitable"
 
{| class="wikitable"
|+Trical units of time, provisional names
+
|+Trical units of time
 
|-
 
|-
 
! Unit
 
! Unit
! Definition !! Seconds !! Equivalence !! SI equivalence
+
! Definition !! Conds !! Equivalence !! SI equivalence
 
|-
 
|-
  +
! {{dim|se}}cond (c)
! second
 
 
| || 3<sup>0</sup> || || 86400/59049 = ca. 1.463 SI seconds
 
| || 3<sup>0</sup> || || 86400/59049 = ca. 1.463 SI seconds
 
|-
 
|-
  +
! {{dim|mo}}ment
! moment
 
| 3 seconds || 3<sup>1</sup> || ||
+
| 3 conds || 3<sup>1</sup> || ||
 
|-
 
|-
  +
! {{dim|ins}}tant
! instant
 
| 3 moments || 3<sup>2</sup> || 9 s ||
+
| 3 ments || 3<sup>2</sup> || 9 c ||
 
|-
 
|-
  +
! {{dim|mi}}nute (n)
! minute
 
| 3 instants || 3<sup>3</sup> || 27 s || ca. 40 s
+
| 3 tants || 3<sup>3</sup> || 27 c || ca. 40 s
 
|-
 
|-
! dim
+
! dim{{dim|inute}}
| 3 minutes || 3<sup>4</sup> || 81 s || ca. 2 min
+
| 3 mins || 3<sup>4</sup> || 81 c || ca. 2 min
 
|-
 
|-
 
! egg
 
! egg
| 3 dims || 3<sup>5</sup> || 9 min ||ca. 6 min
+
| 3 dims || 3<sup>5</sup> || 9 n ||ca. 6 min
 
|-
 
|-
 
! tertian
 
! tertian
| 3 eggs || 3<sup>6</sup> || 27 min ||ca. 18 min
+
| 3 eggs || 3<sup>6</sup> || 27 n ||ca. 18 min
 
|-
 
|-
  +
! t{{dim|trical h}}our (t)
! hour
 
| 3 tertians || 3<sup>7</sup> || 81 min || 8/9 h
+
| 3 tertians || 3<sup>7</sup> || 81 n || 8/9 h
 
|-
 
|-
 
! watch
 
! watch
| 3 hours || 3<sup>8</sup> || 243 min || 160 min
+
| 3 tours || 3<sup>8</sup> || 243 n || 160 min
 
|-
 
|-
 
! shift
 
! shift
| 3 watches || 3<sup>9</sup> || 9 h || 8 h
+
| 3 watches || 3<sup>9</sup> || 9 t || 8 h
 
|-
 
|-
! day
+
! day (d)
| 3 shifts || 3<sup>10</sup> || 27 h || 86400 s
+
| 3 shifts || 3<sup>10</sup> || 27 t || 86400 s
 
|-
 
|-
 
! trip
 
! trip
| 3 days || 3<sup>11</sup> || 81 h ||
+
| 3 days || 3<sup>11</sup> || 81 t ||
 
|-
 
|-
  +
! {{dim|rou}}tine
! week
 
 
| 3 trips || 3<sup>12</sup> || 9 d ||> 1 week
 
| 3 trips || 3<sup>12</sup> || 9 d ||> 1 week
 
|-
 
|-
! month
+
! moon
| 3 weeks || 3<sup>13</sup> || 27 d ||< 1 month
+
| 3 tines || 3<sup>13</sup> || 27 d ||< 1 month
 
|-
 
|-
  +
! sea{{dim|so}}n
! season
 
| 3 months || 3<sup>14</sup> || 81 d ||< 1 quarter
+
| 3 moons || 3<sup>14</sup> || 81 d ||< 1 quarter
 
|-
 
|-
 
! triad
 
! triad
| 3 seasons || 3<sup>15</sup> || 243 d ||
+
| 3 seans || 3<sup>15</sup> || 243 d ||
 
|-
 
|-
! jear
+
! jear {{dim|(diyear)}}
 
| 3 triads || 3<sup>16</sup> || 729 d ||ca. 2 years
 
| 3 triads || 3<sup>16</sup> || 729 d ||ca. 2 years
 
|}
 
|}
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==Leap rule==
 
==Leap rule==
   
  +
; Jear (di-year)
: <math>3^6 = 729 = 2\times 364.5 = 364+365</math>
+
: 3<sup>6</sup> = 729 = 2 × 364½ = 364 + 365 = 363 + 366
: <math>\frac{2\times 729+3}{4} = 365.25</math> ([[Julian Calendar|Julian alignment]])
 
: <math>\frac{100\times (2\times 729+3)-3}{400} = 365.2425</math> ([[Gregorian Calendar|Gregorian alignment]])
+
; [[Julian Calendar|Julian alignment]]
  +
: 2 × 729 + 3 = 4 × 365.25 = 4 × 365 + 1
 
: After every two jears there is a leap trip (3 days).
  +
; [[Gregorian Calendar|Gregorian alignment]]
  +
: 100 × (2 × 729 + 3) - 3 = 400 × 365.2425 = 400 × 365 + 97
  +
: After every two jears there is a leap trip (3 days), but every hundredth leap trip is omitted.
  +
; [[Symmetry454 Calendar|Symmetrian alignment]]
  +
: 73 × (2 × 729 + 3) + 363 = 293 × 365 + 71 = 293 × 364 + 52 × 7
  +
: After every two jears there is a leap trip (3 days), and after 73 such sub-cycles there is an extra short year.
   
After every two jears there is a leap trip (3 days), but every hundredth leap trip is omitted.
 
 
==Year calendar==
 
==Year calendar==
 
A jear may be subdivided into 2 years, a '''long year''' of 122 trips or 366 days followed by a '''short year''' of 121 trips or 363 days. Leap trips turn a short year into a long year.
 
A jear may be subdivided into 2 years, a '''long year''' of 122 trips or 366 days followed by a '''short year''' of 121 trips or 363 days. Leap trips turn a short year into a long year.
   
 
Years may be subdivided into 12 months of either 10 trips ('''short month''') or 11 trips ('''long month'''), i.e. 30 or 33 days. The sixth and, in long years, the twelfth month would be long months.
 
Years may be subdivided into 12 months of either 10 trips ('''short month''') or 11 trips ('''long month'''), i.e. 30 or 33 days. The sixth and, in long years, the twelfth month would be long months.
  +
  +
An even '''lunar year''' usually consists of 13 moons (351 days), whereas an odd one always has 14 moons (378 days). Every 40th lunar year (or every 20th even one) also has 14 moons, but every 400th lunar year has an extraordinary 15 moons. Thus, there are 211 extra moons (i.e. 14th and 15th) in every 400-year cycle.
  +
==See also==
  +
*[[Kalentris]], a very similar calendar
 
[[Category:3-day week]]
 
[[Category:3-day week]]
 
[[Category:9-day week]]
 
[[Category:9-day week]]
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[[Category:Radical designs]]
 
[[Category:Radical designs]]
 
[[Category:30-33-day month calendars]]
 
[[Category:30-33-day month calendars]]
  +
[[Category:Christoph Päper]]

Revision as of 08:23, 20 April 2021

Trical is a calendar based on powers of three.

Trical units of time
Unit Definition Conds Equivalence SI equivalence
second (c) 30 86400/59049 = ca. 1.463 SI seconds
moment 3 conds 31
instant 3 ments 32 9 c
minute (n) 3 tants  33 27 c ca. 40 s
diminute 3 mins 34 81 c ca. 2 min
egg 3 dims  35 9 n ca. 6 min
tertian 3 eggs  36 27 n ca. 18 min
ttrical hour (t) 3 tertians 37 81 n 8/9 h
watch 3 tours 38 243 n 160 min
shift 3 watches 39 9 t 8 h
day (d) 3 shifts 310 27 t 86400 s
trip 3 days 311 81 t
routine 3 trips 312 9 d > 1 week
moon 3 tines 313 27 d < 1 month
season 3 moons 314 81 d < 1 quarter
triad 3 seans 315 243 d
jear (diyear) 3 triads 316 729 d ca. 2 years

Leap rule

Jear (di-year)
36 = 729 = 2 × 364½ = 364 + 365 = 363 + 366
Julian alignment
2 × 729 + 3 = 4 × 365.25 = 4 × 365 + 1
After every two jears there is a leap trip (3 days).
Gregorian alignment
100 × (2 × 729 + 3) - 3 = 400 × 365.2425 = 400 × 365 + 97
After every two jears there is a leap trip (3 days), but every hundredth leap trip is omitted.
Symmetrian alignment
73 × (2 × 729 + 3) + 363 = 293 × 365 + 71 = 293 × 364 + 52 × 7
After every two jears there is a leap trip (3 days), and after 73 such sub-cycles there is an extra short year.

Year calendar

A jear may be subdivided into 2 years, a long year of 122 trips or 366 days followed by a short year of 121 trips or 363 days. Leap trips turn a short year into a long year.

Years may be subdivided into 12 months of either 10 trips (short month) or 11 trips (long month), i.e. 30 or 33 days. The sixth and, in long years, the twelfth month would be long months.

An even lunar year usually consists of 13 moons (351 days), whereas an odd one always has 14 moons (378 days). Every 40th lunar year (or every 20th even one) also has 14 moons, but every 400th lunar year has an extraordinary 15 moons. Thus, there are 211 extra moons (i.e. 14th and 15th) in every 400-year cycle.

See also