中国传统阴历闰法主要科学原理解析及应用

闲时为主

2021-6-27

根据百度百科：《汉书·律历志上》：“并终数为十九，《易》穷则变，故为闰法。” 颜师古注引孟康 曰：“天终数九，地终数十。穷，终也，言闰亦日之穷馀，故取二终之数以为义。” 王先谦补注：“ 李锐曰：并天九地十，得十九为闰法。”

以上为十九年七闰法的哲学原理。塑望月周期为29.5306天，而

太阳视回归年周期为365.24219天。十九年七闰法简单科学验证计算如下：(19*12 7)* 29.5306-19*365.24219=0.0892天/19年=0.469天/百年。十九年七闰法每百年误差0.469天。

唐代郭子仪领导的科学测定太阳视回归年周期为365.25天，与现在科学测定的值误差仅十万分之二，可以说相当精确了。

我国南北朝时期杰出的数学家、天文学家祖冲之提出了391年144闰月的新闰法，验证计算如下：(391*12 144)* 29.5306-391*365.24219=0.2853天/391年=0.073天/百年。每百年误差0.073天（105分钟）。

根据上述两个实例计算，我发现了一个事实，那就是：总设计年数与闰年数之比接近自然对数底数e=2.71828。假定round是四舍五入取整函数，则任意不小于19年周期的闰年数计算公式如下：

y=round(Y/e)（式1）

为方便记忆拟谐音如下：

赞曰：【爱仙】是“山巅一寺一壶酒 爱柳悟善”

咒曰:【愚欲】为“兒癫妻异爸而扒 倚爸而霸”

根据上述公式，计算常用的闰年数如下所示。

当不考虑设置每隔一段时间增加闰天数或减少天数时，经计算发现上表中接近391年周期的行，372年137闰比祖冲之的391年144闰更为理想。验证计算如下：(372*12 137)* 29.5306-372*365.24219=0.1959天/372年=0.053天/百年。每百年误差0.053天（75.8分钟）。

经过进一步筛选，发现315年116闰比上述值还要理想。验证计算如下：(315*12 116)* 29.5306-315*365.24219=-0.07225天/315年=-0.023天/百年。每百年误差-0.023天（-33分钟）。此外353年130闰法，误差也较小，这些都不用考虑增加或减小闰天数。

考虑实际情况，设计闰月的同时也可以设置每隔一段时间增加闰天数或减少某月的天数。这样可以选择到误差更小的闰法。以百年误差不大于0.0417天（60分钟），初步筛选如下表所示的闰法。

根据上表，我们考虑每三年或二年闰一次，不考虑增闰天数时，1-2000年（序号）的对应闰年数设置可参考下列数据[基于某个初始年的年序号差]：

[3, 5, 8, 10, 13, 15, 18, 21, 24, 26, 29, 31, 34, 37, 40, 42, 45, 48, 51, 53, 56, 59, 62, 64, 67, 69, 72, 75, 78, 80, 83, 86, 89, 91, 94, 97, 100, 102, 105, 108, 111, 113, 116, 118, 121, 124, 127, 129, 132, 135, 138, 140, 143, 146, 149, 151, 154, 156, 159, 162, 165, 167, 170, 173, 176, 178, 181, 184, 187, 189, 192, 194, 197, 200, 203, 205, 208, 211, 214, 216, 219, 222, 225, 227, 230, 233, 236, 238, 241, 243, 246, 249, 252, 254, 257, 260, 263, 265, 268, 271, 274, 276, 279, 281, 284, 287, 290, 292, 295, 298, 301, 303, 306, 309, 312, 314, 317, 320, 323, 325, 328, 330, 333, 336, 339, 341, 344, 347, 350, 352, 355, 358, 361, 363, 366, 368, 371, 374, 377, 379, 382, 385, 388, 390, 393, 396, 399, 401, 404, 407, 410, 412, 415, 417, 420, 423, 426, 428, 431, 434, 437, 439, 442, 445, 448, 450, 453, 455, 458, 461, 464, 466, 469, 472, 475, 477, 480, 483, 486, 488, 491, 494, 497, 499, 502, 504, 507, 510, 513, 515, 518, 521, 524, 526, 529, 532, 535, 537, 540, 542, 545, 548, 551, 553, 556, 559, 562, 564, 567, 570, 573, 575, 578, 580, 583, 586, 589, 591, 594, 597, 600, 602, 605, 608, 611, 613, 616, 619, 622, 624, 627, 629, 632, 635, 638, 640, 643, 646, 649, 651, 654, 657, 660, 662, 665, 667, 670, 673, 676, 678, 681, 684, 687, 689, 692, 695, 698, 700, 703, 706, 709, 711, 714, 716, 719, 722, 725, 727, 730, 733, 736, 738, 741, 744, 747, 749, 752, 754, 757, 760, 763, 765, 768, 771, 774, 776, 779, 782, 785, 787, 790, 793, 796, 798, 801, 803, 806, 809, 812, 814, 817, 820, 823, 825, 828, 831, 834, 836, 839, 841, 844, 847, 850, 852, 855, 858, 861, 863, 866, 869, 872, 874, 877, 880, 883, 885, 888, 890, 893, 896, 899, 901, 904, 907, 910, 912, 915, 918, 921, 923, 926, 928, 931, 934, 937, 939, 942, 945, 948, 950, 953, 956, 959, 961, 964, 966, 969, 972, 975, 977, 980, 983, 986, 988, 991, 994, 997, 999, 1002, 1005, 1008, 1010, 1013, 1015, 1018, 1021, 1024, 1026, 1029, 1032, 1035, 1037, 1040, 1043, 1046, 1048, 1051, 1053, 1056, 1059, 1062, 1064, 1067, 1070, 1073, 1075, 1078, 1081, 1084, 1086, 1089, 1092, 1095, 1097, 1100, 1102, 1105, 1108, 1111, 1113, 1116, 1119, 1122, 1124, 1127, 1130, 1133, 1135, 1138, 1140, 1143, 1146, 1149, 1151, 1154, 1157, 1160, 1162, 1165, 1168, 1171, 1173, 1176, 1179, 1182, 1184, 1187, 1189, 1192, 1195, 1198, 1200, 1203, 1206, 1209, 1211, 1214, 1217, 1220, 1222, 1225, 1227, 1230, 1233, 1236, 1238, 1241, 1244, 1247, 1249, 1252, 1255, 1258, 1260, 1263, 1266, 1269, 1271, 1274, 1276, 1279, 1282, 1285, 1287, 1290, 1293, 1296, 1298, 1301, 1304, 1307, 1309, 1312, 1314, 1317, 1320, 1323, 1325, 1328, 1331, 1334, 1336, 1339, 1342, 1345, 1347, 1350, 1352, 1355, 1358, 1361, 1363, 1366, 1369, 1372, 1374, 1377, 1380, 1383, 1385, 1388, 1391, 1394, 1396, 1399, 1401, 1404, 1407, 1410, 1412, 1415, 1418, 1421, 1423, 1426, 1429, 1432, 1434, 1437, 1439, 1442, 1445, 1448, 1450, 1453, 1456, 1459, 1461, 1464, 1467, 1470, 1472, 1475, 1478, 1481, 1483, 1486, 1488, 1491, 1494, 1497, 1499, 1502, 1505, 1508, 1510, 1513, 1516, 1519, 1521, 1524, 1526, 1529, 1532, 1535, 1537, 1540, 1543, 1546, 1548, 1551, 1554, 1557, 1559, 1562, 1565, 1568, 1570, 1573, 1575, 1578, 1581, 1584, 1586, 1589, 1592, 1595, 1597, 1600, 1603, 1606, 1608, 1611, 1613, 1616, 1619, 1622, 1624, 1627, 1630, 1633, 1635, 1638, 1641, 1644, 1646, 1649, 1651, 1654, 1657, 1660, 1662, 1665, 1668, 1671, 1673, 1676, 1679, 1682, 1684, 1687, 1690, 1693, 1695, 1698, 1700, 1703, 1706, 1709, 1711, 1714, 1717, 1720, 1722, 1725, 1728, 1731, 1733, 1736, 1738, 1741, 1744, 1747, 1749, 1752, 1755, 1758, 1760, 1763, 1766, 1769, 1771, 1774, 1777, 1780, 1782, 1785, 1787, 1790, 1793, 1796, 1798, 1801, 1804, 1807, 1809, 1812, 1815, 1818, 1820, 1823, 1825, 1828, 1831, 1834, 1836, 1839, 1842, 1845, 1847, 1850, 1853, 1856, 1858, 1861, 1864, 1867, 1869, 1872, 1874, 1877, 1880, 1883, 1885, 1888, 1891, 1894, 1896, 1899, 1902, 1905, 1907, 1910, 1912, 1915, 1918, 1921, 1923, 1926, 1929, 1932, 1934, 1937, 1940, 1943, 1945, 1948, 1951, 1954, 1956, 1959, 1961, 1964, 1967, 1970, 1972, 1975, 1978, 1981, 1983, 1986, 1989, 1992, 1994, 1997, 1999]

我设想2020年由于新冠病毒启动了一个新的纪元，今年（2021）农历五月初六之后是新天启元年（年序号为一），则按公历，上述序号需要均应加上2020，需设置闰月的年份如下：

[2023, 2025, 2028, 2030, 2033, 2035, 2038, 2041, 2044, 2046, 2049, 2051, 2054, 2057, 2060, 2062, 2065, 2068, 2071, 2073, 2076, 2079, 2082, 2084, 2087, 2089, 2092, 2095, 2098, 2100, 2103, 2106, 2109, 2111, 2114, 2117, 2120, 2122, 2125, 2128, 2131, 2133, 2136, 2138, 2141, 2144, 2147, 2149, 2152, 2155, 2158, 2160, 2163, 2166, 2169, 2171, 2174, 2176, 2179, 2182, 2185, 2187, 2190, 2193, 2196, 2198, 2201, 2204, 2207, 2209, 2212, 2214, 2217, 2220, 2223, 2225, 2228, 2231, 2234, 2236, 2239, 2242, 2245, 2247, 2250, 2253, 2256, 2258, 2261, 2263, 2266, 2269, 2272, 2274, 2277, 2280, 2283, 2285, 2288, 2291, 2294, 2296, 2299, 2301, 2304, 2307, 2310, 2312, 2315, 2318, 2321, 2323, 2326, 2329, 2332, 2334, 2337, 2340, 2343, 2345, 2348, 2350, 2353, 2356, 2359, 2361, 2364, 2367, 2370, 2372, 2375, 2378, 2381, 2383, 2386, 2388, 2391, 2394, 2397, 2399, 2402, 2405, 2408, 2410, 2413, 2416, 2419, 2421, 2424, 2427, 2430, 2432, 2435, 2437, 2440, 2443, 2446, 2448, 2451, 2454, 2457, 2459, 2462, 2465, 2468, 2470, 2473, 2475, 2478, 2481, 2484, 2486, 2489, 2492, 2495, 2497, 2500, 2503, 2506, 2508, 2511, 2514, 2517, 2519, 2522, 2524, 2527, 2530, 2533, 2535, 2538, 2541, 2544, 2546, 2549, 2552, 2555, 2557, 2560, 2562, 2565, 2568, 2571, 2573, 2576, 2579, 2582, 2584, 2587, 2590, 2593, 2595, 2598, 2600, 2603, 2606, 2609, 2611, 2614, 2617, 2620, 2622, 2625, 2628, 2631, 2633, 2636, 2639, 2642, 2644, 2647, 2649, 2652, 2655, 2658, 2660, 2663, 2666, 2669, 2671, 2674, 2677, 2680, 2682, 2685, 2687, 2690, 2693, 2696, 2698, 2701, 2704, 2707, 2709, 2712, 2715, 2718, 2720, 2723, 2726, 2729, 2731, 2734, 2736, 2739, 2742, 2745, 2747, 2750, 2753, 2756, 2758, 2761, 2764, 2767, 2769, 2772, 2774, 2777, 2780, 2783, 2785, 2788, 2791, 2794, 2796, 2799, 2802, 2805, 2807, 2810, 2813, 2816, 2818, 2821, 2823, 2826, 2829, 2832, 2834, 2837, 2840, 2843, 2845, 2848, 2851, 2854, 2856, 2859, 2861, 2864, 2867, 2870, 2872, 2875, 2878, 2881, 2883, 2886, 2889, 2892, 2894, 2897, 2900, 2903, 2905, 2908, 2910, 2913, 2916, 2919, 2921, 2924, 2927, 2930, 2932, 2935, 2938, 2941, 2943, 2946, 2948, 2951, 2954, 2957, 2959, 2962, 2965, 2968, 2970, 2973, 2976, 2979, 2981, 2984, 2986, 2989, 2992, 2995, 2997, 3000, 3003, 3006, 3008, 3011, 3014, 3017, 3019, 3022, 3025, 3028, 3030, 3033, 3035, 3038, 3041, 3044, 3046, 3049, 3052, 3055, 3057, 3060, 3063, 3066, 3068, 3071, 3073, 3076, 3079, 3082, 3084, 3087, 3090, 3093, 3095, 3098, 3101, 3104, 3106, 3109, 3112, 3115, 3117, 3120, 3122, 3125, 3128, 3131, 3133, 3136, 3139, 3142, 3144, 3147, 3150, 3153, 3155, 3158, 3160, 3163, 3166, 3169, 3171, 3174, 3177, 3180, 3182, 3185, 3188, 3191, 3193, 3196, 3199, 3202, 3204, 3207, 3209, 3212, 3215, 3218, 3220, 3223, 3226, 3229, 3231, 3234, 3237, 3240, 3242, 3245, 3247, 3250, 3253, 3256, 3258, 3261, 3264, 3267, 3269, 3272, 3275, 3278, 3280, 3283, 3286, 3289, 3291, 3294, 3296, 3299, 3302, 3305, 3307, 3310, 3313, 3316, 3318, 3321, 3324, 3327, 3329, 3332, 3334, 3337, 3340, 3343, 3345, 3348, 3351, 3354, 3356, 3359, 3362, 3365, 3367, 3370, 3372, 3375, 3378, 3381, 3383, 3386, 3389, 3392, 3394, 3397, 3400, 3403, 3405, 3408, 3411, 3414, 3416, 3419, 3421, 3424, 3427, 3430, 3432, 3435, 3438, 3441, 3443, 3446, 3449, 3452, 3454, 3457, 3459, 3462, 3465, 3468, 3470, 3473, 3476, 3479, 3481, 3484, 3487, 3490, 3492, 3495, 3498, 3501, 3503, 3506, 3508, 3511, 3514, 3517, 3519, 3522, 3525, 3528, 3530, 3533, 3536, 3539, 3541, 3544, 3546, 3549, 3552, 3555, 3557, 3560, 3563, 3566, 3568, 3571, 3574, 3577, 3579, 3582, 3585, 3588, 3590, 3593, 3595, 3598, 3601, 3604, 3606, 3609, 3612, 3615, 3617, 3620, 3623, 3626, 3628, 3631, 3633, 3636, 3639, 3642, 3644, 3647, 3650, 3653, 3655, 3658, 3661, 3664, 3666, 3669, 3671, 3674, 3677, 3680, 3682, 3685, 3688, 3691, 3693, 3696, 3699, 3702, 3704, 3707, 3710, 3713, 3715, 3718, 3720, 3723, 3726, 3729, 3731, 3734, 3737, 3740, 3742, 3745, 3748, 3751, 3753, 3756, 3758, 3761, 3764, 3767, 3769, 3772, 3775, 3778, 3780, 3783, 3786, 3789, 3791, 3794, 3797, 3800, 3802, 3805, 3807, 3810, 3813, 3816, 3818, 3821, 3824, 3827, 3829, 3832, 3835, 3838, 3840, 3843, 3845, 3848, 3851, 3854, 3856, 3859, 3862, 3865, 3867, 3870, 3873, 3876, 3878, 3881, 3884, 3887, 3889, 3892, 3894, 3897, 3900, 3903, 3905, 3908, 3911, 3914, 3916, 3919, 3922, 3925, 3927, 3930, 3932, 3935, 3938, 3941, 3943, 3946, 3949, 3952, 3954, 3957, 3960, 3963, 3965, 3968, 3971, 3974, 3976, 3979, 3981, 3984, 3987, 3990, 3992, 3995, 3998, 4001, 4003, 4006, 4009, 4012, 4014, 4017, 4019]

本文暂推荐125年46闰法，这样可以结合政府5年换届周期分为5*5=25年一个五行结构，125*4=500年一个四季结构，历史的波动性记录将有法可依。每125年阴历仅需要减闰1天，月球的阴晴圆缺与古法19年7闰均大致相同。

以上数据为概略计算，仅供我国政府制定阴历的新历法时参考，具体算法规律可联系作者获取相关资料。