{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"stem-branch-relations"},"result":{"entity_type":"calculator","id":"stem-branch-relations","calculator_id":"stem-branch-relations","canonical_url":"https://tttkmbb.com/yijing/stem-branch-relations","name":"Stem and Branch Relations (干支合冲刑害)","title":"Stem and Branch Relations – 五合, 六合, 三合, 三会, 六冲, 六害, 相刑 and 相破 between Ganzhi Characters","category":"yijing","category_name":"I Ching & Five Elements","tool_name":"analyze_stem_branch_relations","featured_mcp_tool":false,"description":"Finds the traditional relations among a set of heavenly stems (天干, tiangan) and earthly branches (地支, dizhi): stem combinations (五合, wuhe) and clashes (相冲, xiangchong), branch six-combinations (六合, liuhe), three-harmony frames (三合局, sanheju, incl. 半合 banhe), directional combinations (三会, sanhui), clashes (六冲, liuchong), harms (六害, liuhai), punishments (相刑 xiangxing, 自刑 zixing) and destructions (相破, xiangpo).","use_when":"You have stems or branches from a Bazi chart, a date or a Liu Yao chart and need to list which of them combine, clash, harm or punish each other.","do_not_use_when":"You need the abstract five-element relation between two elements (use five-elements) or the stems and branches of a date (use sexagenary-cycle or bazi-four-pillars).","inputs":[{"name":"characters","label":"Stems and branches","type":"string_list","required":true,"description":"2–8 stems or branches: Chinese characters (甲 … 癸, 子 … 亥; a pair such as 甲子 is split into both), pinyin (jia, zi …; wu is ambiguous, write 戊/午 or stem_wu/branch_wu) or zodiac animals (rat, ox …).","example":["甲","己","子","午"]}],"outputs":[{"name":"items","label":"Characters","type":"list","decimals":4,"description":"One row per character: character, pinyin, type (stem/branch), element, yin/yang and zodiac animal (branches)."},{"name":"relations","label":"Relations","type":"list","decimals":4,"description":"One row per relation: pair_or_group, kind, relation_cn, relation_en and result (element produced or the relation class)."},{"name":"relation_count","label":"Number of relations","type":"integer","decimals":0,"description":"How many relations were found."},{"name":"summary","label":"Summary","type":"string","decimals":4,"description":"Short summary of the relations found."}],"input_schema":{"type":"object","properties":{"characters":{"description":"2–8 stems or branches: Chinese characters (甲 … 癸, 子 … 亥; a pair such as 甲子 is split into both), pinyin (jia, zi …; wu is ambiguous, write 戊/午 or stem_wu/branch_wu) or zodiac animals (rat, ox …).","type":"array","items":{"type":"string"},"examples":[["甲","己","子","午"]]}},"additionalProperties":false,"required":["characters"]},"output_schema":{"type":"object","properties":{"items":{"description":"One row per character: character, pinyin, type (stem/branch), element, yin/yang and zodiac animal (branches).","type":"array"},"relations":{"description":"One row per relation: pair_or_group, kind, relation_cn, relation_en and result (element produced or the relation class).","type":"array"},"relation_count":{"description":"How many relations were found.","type":"integer"},"summary":{"description":"Short summary of the relations found.","type":"string"}}},"formula":"天干五合: 甲己→土, 乙庚→金, 丙辛→水, 丁壬→木, 戊癸→火; 天干相冲: 甲庚, 乙辛, 丙壬, 丁癸; 地支六合: 子丑→土, 寅亥→木, 卯戌→火, 辰酉→金, 巳申→水, 午未→土; 三合: 申子辰水, 亥卯未木, 寅午戌火, 巳酉丑金 (半合 = the peak branch with one other); 三会: 寅卯辰木, 巳午未火, 申酉戌金, 亥子丑水; 六冲: branches 6 apart; 六害: 子未 丑午 寅巳 卯辰 申亥 酉戌; 相刑: 寅巳申, 丑戌未, 子卯, 自刑 辰午酉亥; 相破: 子酉 丑辰 寅亥 卯午 巳申 未戌","method":"Tables follow the standard Ziping (子平) conventions used in Bazi and Liu Yao; 午未合 is reported as Earth. Only relations among the given characters are listed, each once. Traditional cultural reference calculation; not a prediction and not medical, legal or financial advice.","sources":[{"name":"Wikipedia – Sexagenary cycle","url":"https://en.wikipedia.org/wiki/Sexagenary_cycle","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Wuxing (Chinese philosophy)","url":"https://en.wikipedia.org/wiki/Wuxing_(Chinese_philosophy)","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"甲 己 子 午","inputs":{"characters":["甲","己","子","午"]},"expected":{"relation_count":2,"relations":[{"pair_or_group":"甲己","relation_cn":"天干五合（甲己合化土）","result":"Earth (土)"},{"pair_or_group":"子午","relation_cn":"六冲（子午相冲）","result":"clash (冲)"}]},"url":"https://tttkmbb.com/api/v1/calculate/stem-branch-relations?characters=%E7%94%B2%2C%E5%B7%B1%2C%E5%AD%90%2C%E5%8D%88"},{"name":"申 子 辰 (three-harmony Water)","inputs":{"characters":["申","子","辰"]},"expected":{"relation_count":1,"relations":[{"pair_or_group":"申子辰","relation_cn":"三合水局（申子辰）","result":"Water (水)"}]},"url":"https://tttkmbb.com/api/v1/calculate/stem-branch-relations?characters=%E7%94%B3%2C%E5%AD%90%2C%E8%BE%B0"}],"faq":[{"q":"What is a 半合 (half combination)?","a":"A three-harmony frame needs its three branches (e.g. 申子辰 for Water). When only the peak branch (子, 卯, 午 or 酉) and one of the two others are present, the pair is reported as a half combination of that frame."},{"q":"Why is the pinyin wu rejected?","a":"wu is the pinyin of both the stem 戊 and the branch 午; write the character, or stem_wu / branch_wu."}],"tags":["stems and branches","干支","六合","三合","六冲","bazi relations"],"related":[{"calculator_id":"five-elements","reason":"Generating and controlling relation of the resulting elements."},{"calculator_id":"sexagenary-cycle","reason":"Stem and branch of a year, month, day or hour."},{"calculator_id":"bazi-four-pillars","reason":"The four pillars whose characters are analysed here."}],"links":{"html":"https://tttkmbb.com/yijing/stem-branch-relations","markdown":"https://tttkmbb.com/yijing/stem-branch-relations.md","json":"https://tttkmbb.com/yijing/stem-branch-relations.json","api":"https://tttkmbb.com/api/v1/calculate/stem-branch-relations","schema":"https://tttkmbb.com/api/v1/calculators/stem-branch-relations","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T08:31:26Z","next_actions":[{"tool":"run_calculator","calculator_id":"stem-branch-relations","reason":"Run Stem and Branch Relations (干支合冲刑害) with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/yijing/stem-branch-relations.md"}}