Continuity/Roulean Calendar and Portal Years: Difference between revisions

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In early 2003, Turbine released a timeline called [[The History of Auberean]]. We are presented with several events, and the year the occurred on both the Portal Year and Roulean calendars:
In early 2003, Turbine released a timeline called [[The History of Auberean]]. We are presented with several events, and the year they occurred on both the Portal Year and Roulean calendars:


{|class="wikitable"
{|class="wikitable"
|bgcolor=#d0d0d0 width=90| '''Portal Year'''
|width=90| '''Portal Year'''
|bgcolor=#d0d0d0 width=90| '''Roulean Year'''
|width=90| '''Roulean Year'''
|bgcolor=#d0d0d0| '''Event'''
| '''Event'''
|-
|-
| -1441 PY || 324 RC || Jojiism founded.<ref name=HistoryOfAubereanVol3>2003/03 [[The History of Auberean/Volume III: The Fall From Grace (-1,804 to -891)]]</ref>
| -1441 PY || 324 RC || Jojiism founded.<ref name=HistoryOfAubereanVol3>2003/03 [[The History of Auberean/Volume III: The Fall From Grace (-1,804 to -891)]]</ref>
Line 23: Line 23:


{|class="wikitable"
{|class="wikitable"
|bgcolor=#d0d0d0 width=90| '''Point A'''
|width=90| '''Point A'''
|bgcolor=#d0d0d0 width=90| '''Point B'''
|width=90| '''Point B'''
|bgcolor=#d0d0d0| '''Equation'''
| '''Equation'''
|-
|-
| (-1441, 324) || (-869, 704) || RC = (95/143) * PY + (16657/13)
| 324, -1441 || 704, -869 || PY = (143/95) * RC - (183227/95)
|-
|-
| (-1441, 324) || (779, 765) || RC = (441/662) * PY + (849969/662)
| | 324, -1441 || 765, -779 || PY = (662/441) * RC - (94441/49)
|-
|-
| (-1441, 324) || (-758, 779) || RC = (455/683) * PY + (876947/683)
| 324, -1441 || 779, -758 || PY = (683/455) * RC - (876947/455)
|-
|-
| (-1441, 324) || (-540, 924) || RC = (600/901) * PY + (1156524/901)
| 324, -1441 || 924, -540 || PY = (901/600) * RC - (96377/50)
|-
|-
| (-1441, 324) || (-358, 1046) || RC = (2/3) * PY + (3854/3)
| 324, -1441 || 1046, -358 || PY = (3/2) * RC - (1927)
|-
|-
| (-869, 704) || (779, 765) || RC = (61/90) * PY + (116369/90)
| 704, -869 || 765, -779 || PY = (90/61) * RC - (116369/61)
|-
|-
| (-869, 704) || (-758, 779) || RC = (25/37) * PY + (47773/37)
| 704, -869 || 779, -758 || PY = (37/25) * RC - (47773/25)
|-
|-
| (-869, 704) || (-540, 924) || RC = (220/329) * PY + (422796/329)
| 704, -869 || 924, -540 || PY = (329/220) * RC - (9609/5)
|-
|-
| (-869, 704) || (-358, 1046) || RC = (342/511) * PY + (656942/511)
| 704, -869 || 1046, -358 || PY = (511/342) * RC - (328471/171)
|-
|-
| (-779, 765) || (-758, 779) || RC = (2/3) * PY + (3853/3)
| 765, -779 || 779, -758 || PY = (3/2) * RC - (3853/2)
|-
|-
| (-779, 765) || (-540, 924) || RC = (159/239) * PY + (306696/239)
| 765, -779 || 924, -540 || PY = (239/159) * RC - (102232/53)
|-
|-
| (-779, 765) || (-358, 1046) || RC = (281/421) * PY + (540964/421)
| 765, -779 || 1046, -358 || PY = (421/281) * RC - (540964/281)
|-
|-
| (-758, 779) || (-540, 924) || RC = (145/218) * PY + (139866/109)
| 779, -758 || 924, -540 || PY = (218/145) * RC - (279732/145)
|-
|-
| (-758, 779) || (-358, 1046) || RC = (267/400) * PY + (256993/200)
| 779, -758 || 1046, -358 || PY = (400/267) * RC - (513986/267)
|-
|-
| (-540, 924) || (-358, 1046) || RC = (61/91) * PY + (117024/91)
| 924, -540 || 1046, -358 || PY = (91/61) * RC - (117024/61)
|-
|-
|}
|}
Line 62: Line 62:


{|class="wikitable"
{|class="wikitable"
|bgcolor=#d0d0d0| '''Equation'''
| '''Equation'''
|bgcolor=#d0d0d0| '''is similar to:'''
| '''is similar to:'''
|-
|-
| RC = (95/143) * PY + (16657/13) || RC = (0.6643) * PY + (1281.3077)
| PY = (143/95) * RC - (183227/95) || PY = (1.5053) * RC - (1928.7053)
|-
|-
| RC = (441/662) * PY + (849969/662) || RC = (0.6662) * PY + (1283.9411)
| PY = (662/441) * RC - (94441/49) || PY = (1.5011) * RC - (1927.3673)
|-
|-
| RC = (455/683) * PY + (876947/683) || RC = (0.6662) * PY + (1283.9634)
| PY = (683/455) * RC - (876947/455) || PY = (1.5011) * RC - (1927.3560)
|-
|-
| RC = (600/901) * PY + (1156524/901) || RC = (0.6659) * PY + (1283.6004)
| PY = (901/600) * RC - (96377/50) || PY = (1.5017) * RC - (1927.54)
|-
|-
| RC = (2/3) * PY + (3854/3) || RC = (0.6667) * PY + (1284.6667)
| PY = (3/2) * RC - (1927) || PY = (1.5) * RC - (1927)
|-
|-
| RC = (61/90) * PY + (116369/90) || RC = (0.6778) * PY + (1292.9889)
| PY = (90/61) * RC - (116369/61) || PY = (1.4754) * RC - (1907.6885)
|-
|-
| RC = (25/37) * PY + (47773/37) || RC = (0.6757) * PY + (1291.1622)
| PY = (37/25) * RC - (47773/25) || PY = (1.48) * RC - (1910.92)
|-
|-
| RC = (220/329) * PY + (422796/329) || RC = (0.6687) * PY + (1285.0942)
| PY = (329/220) * RC - (9609/5) || PY = (1.4955) * RC - (1921.8)
|-
|-
| RC = (342/511) * PY + (656942/511) || RC = (0.6693) * PY + (1285.6008)
| PY = (511/342) * RC - (328471/171) || PY = (1.4942) * RC - (1920.8830)
|-
|-
| RC = (2/3) * PY + (3853/3) || RC = (0.6667) * PY + (1284.3333)
| PY = (3/2) * RC - (3853/2) || PY = (1.5) * RC - (1926.5)
|-
|-
| RC = (159/239) * PY + (306696/239) || RC = (0.6653) * PY + (1283.2469)
| PY = (239/159) * RC - (102232/53) || PY = (1.5031) * RC - (1928.9057)
|-
|-
| RC = (281/421) * PY + (540964/421) || RC = (0.6675) * PY + (1284.9501)
| PY = (421/281) * RC - (540964/281) || PY = (1.4982) * RC - (1925.1388)
|-
|-
| RC = (145/218) * PY + (139866/109) || RC = (0.6651) * PY + (1283.1743)
| PY = (218/145) * RC - (279732/145) || PY = (1.5034) * RC - (1929.1862)
|-
|-
| RC = (267/400) * PY + (256993/200) || RC = (0.6675) * PY + (1284.9650)
| PY = (400/267) * RC - (513986/267) || PY = (1.4981) * RC - (1925.0412)
|-
|-
| RC = (61/91) * PY + (117024/91) || RC = (0.6703) * PY + (1285.9780)
| PY = (91/61) * RC - (117024/61) || PY = (1.4918) * RC - (1918.4262)
|-
|-
|}
|}


One thing is very clear, the slope of all of these equations is very close to .67. This means we can express the slope as (2/3). Its only the y-intercept that varies. If we round the y-intercept to the nearest whole number, third, or quarter, we are left the following equations (duplicates removed):
One thing is very clear, the slope of all of these equations is very close to 1.5, which we will express as (3/2). Its only the y-intercept that varies. We have determined that the y-intercept is somewhere between around -1,907 and -1,930. One way to further narrow this down is to find the equation that best works for each point, given that the slope is (3/2). If we do so, we get the following equations:
* RC = (2/3) * PY + (1281.3334)
* RC = (2/3) * PY + (1283.25)
* RC = (2/3) * PY + (1283.6667)
* RC = (2/3) * PY + (1284)
* RC = (2/3) * PY + (1284.3334)
* RC = (2/3) * PY + (1284.6667)
* RC = (2/3) * PY + (1285)
* RC = (2/3) * PY + (1285.6667)
* RC = (2/3) * PY + (1286)
* RC = (2/3) * PY + (1291)
* RC = (2/3) * PY + (1293)
 
To determine which equation works best, we can input the PY dates we have, and see how the RC output compares to expected value. Below is a table for each equation, and all of its inputs and outputs:


{|class="wikitable"
{|class="wikitable"
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
| '''Input (RC)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
| '''Best Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
| '''Expected Output (PY)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
| '''Actual Output (PY)'''
|-
|-
| -1441 || RC = (2/3) * PY + (1281.3334) || 324 || <span style="color:red">320.6667</span>
| 324 || PY = (3/2) * RC - 1927 || -1441 || -1,441
|-
|-
| -869 || RC = (2/3) * PY + (1281.3334) || 704 || <span style="color:red">702</span>
| 704 || PY = (3/2) * RC - 1925 || -869 || -869
|-
|-
| -779 || RC = (2/3) * PY + (1281.3334) || 765 || <span style="color:red">762</span>
| 765 || PY = (3/2) * RC - 1926.5 || -779 || -779
|-
|-
| -758 || RC = (2/3) * PY + (1281.3334) || 779 || <span style="color:red">776</span>
| 779 || PY = (3/2) * RC - 1926.5 || -758 || -758
|-
|-
| -540 || RC = (2/3) * PY + (1281.3334) || 924 || <span style="color:red">921.3334</span>
| 924 || PY = (3/2) * RC - 1926 || -540 || -540
|-
| -358 || RC = (2/3) * PY + (1281.3334) || 1046 || <span style="color:red">1042.6667</span>
|-
|-
| 1046 || PY = (3/2) * RC - 1927 || -358 || -358
|}
|}


With this method, we can narrow the y-intercept to between -1925 and -1927. However, this is not perfect, because we are only using whole numbers. In actuality, an event could occur at any point in the year, not just the new year's day. So for example, the event that occurred in 324 RC could have occurred anywhere between 324 and 325 RC. And it's corresponding PY could be anywhere between -1440 and -1441 PY.
<br /><br />
That expands the possible equations to the following:
{|class="wikitable"
{|class="wikitable"
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
| '''Input (RC)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
| '''Output (PY)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1283.25) || 324 || <span style="color:red">322.5833</span>
|-
| -869 || RC = (2/3) * PY + (1283.25) || 704 || <span style="color:red">703.9167</span>
|-
|-
| -779 || RC = (2/3) * PY + (1283.25) || 765 || <span style="color:red">763.9167</span>
| 324 || PY = (3/2) * RC - 1926 || -1440
|-
|-
| -758 || RC = (2/3) * PY + (1283.25) || 779 || <span style="color:red">777.9167</span>
| 325 || PY = (3/2) * RC - 1928.5 || -1441
|-
|-
| -540 || RC = (2/3) * PY + (1283.25) || 924 || <span style="color:red">923.25</span>
|-
| -358 || RC = (2/3) * PY + (1283.25) || 1046 || <span style="color:red">1044.5833</span>
|-
|}


{|class="wikitable"
| 704 || PY = (3/2) * RC - 1924 || -868
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
|-
| -1441 || RC = (2/3) * PY + (1283.6667) || 324 || <span style="color:red">323</span>
| 705 || PY = (3/2) * RC - 1926.5 || -869
|-
|-
| -869 || RC = (2/3) * PY + (1283.6667) || 704 || <span style="color:green">704.3334</span>
|-
| -779 || RC = (2/3) * PY + (1283.6667) || 765 || <span style="color:red">764.3334</span>
|-
| -758 || RC = (2/3) * PY + (1283.6667) || 779 || <span style="color:red">778.3334</span>
|-
| -540 || RC = (2/3) * PY + (1283.6667) || 924 || <span style="color:red">923.6667</span>
|-
| -358 || RC = (2/3) * PY + (1283.6667) || 1046 || <span style="color:red">1045</span>
|-
|}


{|class="wikitable"
| 765 || PY = (3/2) * RC - 1925.5 || -778
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1284) || 324 || <span style="color:red">323.3334</span>
|-
| -869 || RC = (2/3) * PY + (1284) || 704 || <span style="color:green">704.6667</span>
|-
|-
| -779 || RC = (2/3) * PY + (1284) || 765 || <span style="color:red">764.6667</span>
| 766 || PY = (3/2) * RC - 1928 || -779
|-
|-
| -758 || RC = (2/3) * PY + (1284) || 779 || <span style="color:red">778.6667</span>
|-
| -540 || RC = (2/3) * PY + (1284) || 924 || <span style="color:green">924</span>
|-
| -358 || RC = (2/3) * PY + (1284) || 1046 || <span style="color:red">1045.3334</span>
|-
|}


{|class="wikitable"
| 779 || PY = (3/2) * RC - 1925.5 || -757
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1284.3334) || 324 || <span style="color:red">323.6667</span>
|-
| -869 || RC = (2/3) * PY + (1284.3334) || 704 || <span style="color:red">705</span>
|-
| -779 || RC = (2/3) * PY + (1284.3334) || 765 || <span style="color:green">765</span>
|-
| -758 || RC = (2/3) * PY + (1284.3334) || 779 || <span style="color:green">779</span>
|-
| -540 || RC = (2/3) * PY + (1284.3334) || 924 || <span style="color:green">924.3334</span>
|-
|-
| -358 || RC = (2/3) * PY + (1284.3334) || 1046 || <span style="color:red">1045.6667</span>
| 780 || PY = (3/2) * RC - 1928 || -758
|-
|-
|}


{|class="wikitable"
| 924 || PY = (3/2) * RC - 1925 || -539
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1284.6667) || 324 || <span style="color:green">324</span>
|-
| -869 || RC = (2/3) * PY + (1284.6667) || 704 || <span style="color:red">705.3334</span>
|-
| -779 || RC = (2/3) * PY + (1284.6667) || 765 || <span style="color:green">765.3334</span>
|-
|-
| -758 || RC = (2/3) * PY + (1284.6667) || 779 || <span style="color:green">779.3334</span>
| 925 || PY = (3/2) * RC - 1927.5 || -540
|-
|-
| -540 || RC = (2/3) * PY + (1284.6667) || 924 || <span style="color:green">924.6667</span>
|-
| -358 || RC = (2/3) * PY + (1284.6667) || 1046 || <span style="color:green">1046</span>
|-
|}


{|class="wikitable"
| 1046 || PY = (3/2) * RC - 1926 || -357
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1285) || 324 || <span style="color:green">324.3334</span>
|-
| -869 || RC = (2/3) * PY + (1285) || 704 || <span style="color:red">705.6667</span>
|-
| -779 || RC = (2/3) * PY + (1285) || 765 || <span style="color:green">765.6667</span>
|-
| -758 || RC = (2/3) * PY + (1285) || 779 || <span style="color:green">779.6667</span>
|-
| -540 || RC = (2/3) * PY + (1285) || 924 || <span style="color:red">925</span>
|-
| -358 || RC = (2/3) * PY + (1285) || 1046 || <span style="color:green">1046.3334</span>
|-
|}
 
{|class="wikitable"
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1285.6667) || 324 || <span style="color:red">325</span>
|-
| -869 || RC = (2/3) * PY + (1285.6667) || 704 || <span style="color:red">706.3334</span>
|-
| -779 || RC = (2/3) * PY + (1285.6667) || 765 || <span style="color:red">766.3334</span>
|-
| -758 || RC = (2/3) * PY + (1285.6667) || 779 || <span style="color:red">780.3334</span>
|-
| -540 || RC = (2/3) * PY + (1285.6667) || 924 || <span style="color:red">925.6667</span>
|-
| -358 || RC = (2/3) * PY + (1285.6667) || 1046 || <span style="color:red">1047</span>
|-
|}
 
{|class="wikitable"
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1286) || 324 || <span style="color:red">325.3334</span>
|-
| -869 || RC = (2/3) * PY + (1286) || 704 || <span style="color:red">706.6667</span>
|-
| -779 || RC = (2/3) * PY + (1286) || 765 || <span style="color:red">766.6667</span>
|-
| -758 || RC = (2/3) * PY + (1286) || 779 || <span style="color:red">780.6667</span>
|-
| -540 || RC = (2/3) * PY + (1286) || 924 || <span style="color:red">926</span>
|-
| -358 || RC = (2/3) * PY + (1286) || 1046 || <span style="color:red">1047.3334</span>
|-
|}
 
{|class="wikitable"
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1291) || 324 || <span style="color:red">330.33334</span>
|-
| -869 || RC = (2/3) * PY + (1291) || 704 || <span style="color:red">711.6667</span>
|-
| -779 || RC = (2/3) * PY + (1291) || 765 || <span style="color:red">771.6667</span>
|-
| -758 || RC = (2/3) * PY + (1291) || 779 || <span style="color:red">785.6667</span>
|-
| -540 || RC = (2/3) * PY + (1291) || 924 || <span style="color:red">931</span>
|-
| -358 || RC = (2/3) * PY + (1291) || 1046 || <span style="color:red">1052.3334</span>
|-
|}
 
{|class="wikitable"
|bgcolor=#d0d0d0 width=90px| '''Input (PY)'''
|bgcolor=#d0d0d0 width=180px| '''Equation'''
|bgcolor=#d0d0d0 width=140px| '''Expected Output (RC)'''
|bgcolor=#d0d0d0 width=120px| '''Actual Output (RC)'''
|-
| -1441 || RC = (2/3) * PY + (1293) || 324 || <span style="color:red">332.3334</span>
|-
| -869 || RC = (2/3) * PY + (1293) || 704 || <span style="color:red">713.6667</span>
|-
| -779 || RC = (2/3) * PY + (1293) || 765 || <span style="color:red">773.6667</span>
|-
| -758 || RC = (2/3) * PY + (1293) || 779 || <span style="color:red">787.6667</span>
|-
| -540 || RC = (2/3) * PY + (1293) || 924 || <span style="color:red">933</span>
|-
|-
| -358 || RC = (2/3) * PY + (1293) || 1046 || <span style="color:red">1054.3334</span>
| 1047 || PY = (3/2) * RC - 1928.5 || -358
|-
|-
|}
|}


The only equations which will work will be somewhere between the following:
* PY = (3/2) * RC - 1926
* PY = (3/2) * RC - 1926.5


We can repeat this entire process with the points in reverse order (e.g. 324, -1441 becomes -1441, 324) to find the equation for converting PY to RC. When all is done, the only equations which will work will be somewhere between the following:
* RC = (2/3) * PY + 1284
* RC = (2/3) * PY + (1284 + (1/3))


== Conclusion ==
== Conclusion ==
We don't have more information to help narrow down the range, and it would make equal sense for the y-intercept to be a whole number or a decimal. However, with noting else to go on, the simplest path seems like the best choice. Therefore, when calculating dates between the Roulean and Portal Year calendars, use the following equations:
* PY = (3/2) * RC - 1926
* RC = (2/3) * PY + 1284


== References ==
== References ==
<references />
<references />

Latest revision as of 07:29, 2 October 2018

In early 2003, Turbine released a timeline called The History of Auberean. We are presented with several events, and the year they occurred on both the Portal Year and Roulean calendars:

Portal Year Roulean Year Event
-1441 PY 324 RC Jojiism founded.<ref name=HistoryOfAubereanVol3>2003/03 The History of Auberean/Volume III: The Fall From Grace (-1,804 to -891)</ref>
-869 PY 704 RC Viamont invades Aluvia. The reign of Pwyll II ends and the reign of Alfric begins.<ref name=HistoryOfAubereanVol4>2003/03 The History of Auberean/Volume IV: Shifting Ways (-888 to -574)</ref>
-779 PY 765 RC Reign of Alfrega begins. Harlune stays behind on Ispar during an expedition.<ref name=HistoryOfAubereanVol4 />
-758 PY 779 RC Reign of Osric begins.<ref name=HistoryOfAubereanVol4 />
-540 PY 924 RC Gharu'n armies seige the Roulean capital of Tirethas.<ref name=HistoryOfAubereanVol5>2003/03 The History of Auberean/Volume V: New Arrivals (-540 to 13)</ref>
-358 PY 1046 RC Emperor Kou unites the Sho under his rule.<ref name=HistoryOfAubereanVol5 />

With multiple matching pairs of dates, we can determine the equation to convert between calendars. All we have to do is treat the pairs of dates as coordinates of points, and find the equation for the line that intersects those points. We will determine the equation for each set of points:

Point A Point B Equation
324, -1441 704, -869 PY = (143/95) * RC - (183227/95)
324, -1441 765, -779 PY = (662/441) * RC - (94441/49)
324, -1441 779, -758 PY = (683/455) * RC - (876947/455)
324, -1441 924, -540 PY = (901/600) * RC - (96377/50)
324, -1441 1046, -358 PY = (3/2) * RC - (1927)
704, -869 765, -779 PY = (90/61) * RC - (116369/61)
704, -869 779, -758 PY = (37/25) * RC - (47773/25)
704, -869 924, -540 PY = (329/220) * RC - (9609/5)
704, -869 1046, -358 PY = (511/342) * RC - (328471/171)
765, -779 779, -758 PY = (3/2) * RC - (3853/2)
765, -779 924, -540 PY = (239/159) * RC - (102232/53)
765, -779 1046, -358 PY = (421/281) * RC - (540964/281)
779, -758 924, -540 PY = (218/145) * RC - (279732/145)
779, -758 1046, -358 PY = (400/267) * RC - (513986/267)
924, -540 1046, -358 PY = (91/61) * RC - (117024/61)

If we solve the division within the parentheses, we see these equations are all fairly similar. Below is a table with the equations, where the division has been solved to four decimal places:

Equation is similar to:
PY = (143/95) * RC - (183227/95) PY = (1.5053) * RC - (1928.7053)
PY = (662/441) * RC - (94441/49) PY = (1.5011) * RC - (1927.3673)
PY = (683/455) * RC - (876947/455) PY = (1.5011) * RC - (1927.3560)
PY = (901/600) * RC - (96377/50) PY = (1.5017) * RC - (1927.54)
PY = (3/2) * RC - (1927) PY = (1.5) * RC - (1927)
PY = (90/61) * RC - (116369/61) PY = (1.4754) * RC - (1907.6885)
PY = (37/25) * RC - (47773/25) PY = (1.48) * RC - (1910.92)
PY = (329/220) * RC - (9609/5) PY = (1.4955) * RC - (1921.8)
PY = (511/342) * RC - (328471/171) PY = (1.4942) * RC - (1920.8830)
PY = (3/2) * RC - (3853/2) PY = (1.5) * RC - (1926.5)
PY = (239/159) * RC - (102232/53) PY = (1.5031) * RC - (1928.9057)
PY = (421/281) * RC - (540964/281) PY = (1.4982) * RC - (1925.1388)
PY = (218/145) * RC - (279732/145) PY = (1.5034) * RC - (1929.1862)
PY = (400/267) * RC - (513986/267) PY = (1.4981) * RC - (1925.0412)
PY = (91/61) * RC - (117024/61) PY = (1.4918) * RC - (1918.4262)

One thing is very clear, the slope of all of these equations is very close to 1.5, which we will express as (3/2). Its only the y-intercept that varies. We have determined that the y-intercept is somewhere between around -1,907 and -1,930. One way to further narrow this down is to find the equation that best works for each point, given that the slope is (3/2). If we do so, we get the following equations:

Input (RC) Best Equation Expected Output (PY) Actual Output (PY)
324 PY = (3/2) * RC - 1927 -1441 -1,441
704 PY = (3/2) * RC - 1925 -869 -869
765 PY = (3/2) * RC - 1926.5 -779 -779
779 PY = (3/2) * RC - 1926.5 -758 -758
924 PY = (3/2) * RC - 1926 -540 -540
1046 PY = (3/2) * RC - 1927 -358 -358

With this method, we can narrow the y-intercept to between -1925 and -1927. However, this is not perfect, because we are only using whole numbers. In actuality, an event could occur at any point in the year, not just the new year's day. So for example, the event that occurred in 324 RC could have occurred anywhere between 324 and 325 RC. And it's corresponding PY could be anywhere between -1440 and -1441 PY.

That expands the possible equations to the following:

Input (RC) Equation Output (PY)
324 PY = (3/2) * RC - 1926 -1440
325 PY = (3/2) * RC - 1928.5 -1441
704 PY = (3/2) * RC - 1924 -868
705 PY = (3/2) * RC - 1926.5 -869
765 PY = (3/2) * RC - 1925.5 -778
766 PY = (3/2) * RC - 1928 -779
779 PY = (3/2) * RC - 1925.5 -757
780 PY = (3/2) * RC - 1928 -758
924 PY = (3/2) * RC - 1925 -539
925 PY = (3/2) * RC - 1927.5 -540
1046 PY = (3/2) * RC - 1926 -357
1047 PY = (3/2) * RC - 1928.5 -358

The only equations which will work will be somewhere between the following:

  • PY = (3/2) * RC - 1926
  • PY = (3/2) * RC - 1926.5

We can repeat this entire process with the points in reverse order (e.g. 324, -1441 becomes -1441, 324) to find the equation for converting PY to RC. When all is done, the only equations which will work will be somewhere between the following:

  • RC = (2/3) * PY + 1284
  • RC = (2/3) * PY + (1284 + (1/3))

Conclusion

We don't have more information to help narrow down the range, and it would make equal sense for the y-intercept to be a whole number or a decimal. However, with noting else to go on, the simplest path seems like the best choice. Therefore, when calculating dates between the Roulean and Portal Year calendars, use the following equations:

  • PY = (3/2) * RC - 1926
  • RC = (2/3) * PY + 1284

References

<references />

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