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Certainly 同调代数 means the mathematical subject of homological algebra. But different sources disagree as to whether the first two characters in that sense of the term are pronounced tóngtiáo or tóngdiào.

In fact I have mostly seen the characters with no pinyin, including on zh.wikipedia, and I have not spoken with Chinese mathematicians about it. The term is not in my paper dictionaries. Google translate and perapera both give tóngdiào. But Wenlin (using the ABC dictionary) gives tóngtiáo for "homology" without specifying the mathematical sense.

Which is it? Since seeing the comments below, I take the Baidu entry with pinyin as authoritative for tóngdiào.

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    Homology is always tong2 diao4. Where did you see tong2 tiao2? – user58955 Jan 19 '16 at 5:01
  • tóngdiào – songyuanyao Jan 19 '16 at 5:17
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    Know nothing about that subject. But tiao2 means "adjust", diao4 means "tone" – which meaning is closer to the contents of homology? – Stan Jan 19 '16 at 5:55
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    baike.baidu.com/view/1370558.htm [tóng diào] 定义 编辑 数学上(特别是代数拓扑和抽象代数),同调 (homology,在希腊语中homos = 同)是一类将一个可换群或者模的序列和特定数学对象(例如拓扑空间或者群)联系起来的过程。背景知识请参看同调论。etc. – user6065 Jan 19 '16 at 6:23
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同调 pronounces as: tóng diào, see reference.

(1) [same tone]∶音调相同

(2) [person with same common purpose or taste]∶比喻志趣或主张相同的人

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    The reference doesn't support the conclusion – because it doesn't include an entry for the mathematical sense. – Stan Jan 20 '16 at 0:58
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    Ah, I should have said it more clearly. I tried to find who was the first mathematician (probably Chinese, possibly Prof. 江泽涵 (zh.wikipedia.org/wiki/%E6%B1%9F%E6%B3%BD%E6%B6%B5) or Prof. 曾炯 (en.wikipedia.org/wiki/Zeng_Jiongzhi)) that translates "Homological algebra" as “同调代数”, but I failed. In fact, there is only one way to pronounce “同调” in modern mandarin Chinese, and that's what I found above. Therefore, because of the uniqueness, the “同调” in “同调代数” must be pronounced as "tóng diào". : ) – Wang Zong'an Jan 20 '16 at 1:32
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I will pronounce it as 同tong2 調diao4 代dai4 數shu4.

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