Special Birthdays

60還暦かんれき "return calendar"Returning to the sign under which you were born (see below)
70古希こき "ancient rare"The Chinese poet Tu Fu wrote in By The Winding River: "Since ancient times, it has been rare to live to 70."
77喜寿きじゅ "rejoice longevity"喜 has an abbreviated form consisting of three 七 (7s).
80傘寿さんじゅ "umbrella longevity"傘 has an abbreviated form 仐; 八十 = 80.
88米寿べいじゅ "rice longevity"米 has a (modified) 八 on top, then 十, and then a 八 below; 八十八 = 88.
90卒寿そつじゅ "graduate longevity"卒 has an abbreviated form 卆; 九十 = 90.
99白寿はくじゅ "white longevity"白 is 百 (100) minus the 一 (1) = 99.
100百寿ひゃくじゅ"100 longevity"百 = 100.
100百賀ひゃくが "100 celebration"百 = 100.
100上寿じょうじゅ"upper longevity"?
108茶寿ちゃじゅ "tea longevity"The top of 茶 can be written like 十十 (10, 10). The bottom part is 八十八 = 88. 88 + 10 + 10 = 108.
111皇寿こうじゅ "emperor longevity"皇 is 白 (99) with 王 below. 王 is 一 (1), 十 (10), and 一 (1). 99 + 1 + 10 + 1 = 111.

Sexagenary Calendar

There are 12 earthly branches, associated with the zodiac. In order:

1.Rat ネズミ(usually kana)
2.Ox うし ウシ
3.Tiger とら トラ (usually kana? (name only))
4.Rabbit / Hare う/ぼう ウサギ(usually kana)
5.Dragon たつ 竜/龍 リュウ(usually first kanji)
6.Snake / Serpentヘビ
7.Horse うま ウマ
8.Sheep / Ram ひつじ ヒツジ
9.Monkey さる サル (usually kana?)
10.Rooster とり 鳥/鶏 トリ (probably only first kanji)
11.Dog いぬ 犬/狗 イヌ (only first kanji)
12.Pig / Boar い/いのしし 豚/猪 ブタ (usually first kanji? (second is name only))

There are 10 heavenly branches, associated with the 5 elements; one older, and one younger. The older stands for yang and the younger for yin. In order:

1.Wood, older こう木の兄きのえ
2.Wood, younger おつ木の弟きのと
3.Fire, older へい火の兄ひのえ
4.Fire, younger てい火の弟ひのと
5.Earth, older 土の兄つちのえ
6.Earth, younger土の弟つちのと
7.Metal, older こう金の兄かのえ
8.Metal, youngerしん金の弟かのと
9.Water, older じん水の兄みずのえ
10.Water, younger水の弟みずのと

These combine to make a 60 year cycle. The cycles align in such a way that all 120 combinations are not used (mathematical note: the least common multiple of 12 and 10 is 60). As it so happens, an even zodiac will match up with the older elements, and an odd zodiac with the younger elements; each zodiac matches up with each element. Each earthly branch/zodiac lasts one years and recurs every twelve years. Each heavenly branch lasts one year and recurs every ten years, but due to the older/younger pairing, each element lasts two years.

Zodiac Wood 木Fire 火Earth 土 Metal 金Water 水
Yang 甲Yin 乙Yang 丙Yin 丁Yang 戊 Yin 己Yang 庚Yin 辛Yang 壬Yin 癸
Rat 1 13 25 37 49
Ox 2 14 26 38 50
Tiger 51 3 15 27 39
Rabbit / Hare 52 4 16 28 40
Dragon 41 53 5 17 29
Snake / Serpent 42 54 6 18 30
Horse 31 43 55 7 19
Sheep / Ram 32 44 56 8 20
Monkey 21 33 45 57 9
Rooster 22 34 46 58 10
Dog 11 23 35 47 59
Pig / Boar 12 24 36 48 60

1984 is a 甲子 "Wood (yang) Rat" year. 2007 is a 丁亥 "Fire (yin) Boar" year.