1803edo

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1803edo, or the 100 saros tuning, divides the octave into steps of 665.6 millicents each. 1803 factors as 3 x 601.

Theory

Approximation of odd harmonics in 1803edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) +0.208 -0.290 +0.226 -0.249 -0.236 +0.071 -0.082 +0.203 -0.009 -0.232
relative (%) +31 -44 +34 -37 -36 +11 -12 +30 -1 -35
Steps
(reduced)
2858
(1055)
4186
(580)
5062
(1456)
5715
(306)
6237
(828)
6672
(1263)
7044
(1635)
7370
(158)
7659
(447)
7919
(707)

In the 2.19.23.29 subgroup, 1803edo tempers out 2476099/2475904, and supports the corresponding rank 3 temperament eliminating this comma. In the 13 limit, 1803edo tempers out 2080/2079 and 4225/4224. In the 7-limit, it tempers out 420175/419904.

In real life, 1803 years is 100 times the saros cycle, designed to predict eclipses. In addition, it also makes for both the leap week and the leap day calendars that excellently approximate the March equinox - 22300 lunar months is almost exactly 658532 days or 94076 weeks. Therefore, it creates 3 different calendric scales that can be used as leap cycles - 437-note leap day cycle with a 590\1803 generator (a major third), 320-note leap week cycle with 524\1803 generator (a neutral third), and the lunisolar cycle with the 1078\1803 generator (a slightly sharp fifth).

As such, 100 & 223 & 1803 saros temperament can be defined. In the 2.7.13.19.23.29 subgroup, 4952198/4950967 can be the starting comma.

Scales

  • SolarLeapDay[437]
  • SolarLeapWeek[320]
  • Lunisolar[664]

Links