Why is 奇数 pronounced jīshù and not qíshù?

Question

Integers {...,-2,-1,0,1,2,...} split into two types:

CC-CEDICT: 偶数 (ǒu​shù​) even number
CC-CEDICT: 奇数 (jī​shù​) odd number

Oddly, 奇 is pronounced jī and not qí. This leads to the question...

Question: Why is 奇数 pronounced jīshù and not qíshù?

Google gave me this which isn't helpful, and this which just says 奇 is a 多音字, but doesn't explain how it came to be a 多音字. Did some Chinese mathematician start pronouncing 奇数 as jīshù, and it caught on? This video discusses how "singularity" 奇点 (in the mathematical sense, and in the sense of a black hole) should be pronounced qí​diǎn​, despite people saying jī​diǎn​ motivated by 奇数 and 奇函数 = "odd function".

Answer 1

「奇」(jī) and 「奇」(qí) are different words, they have different meanings and are pronounced differently also in most other Chinese languages, e.g. "kî" vs "ki" in Taiwanese. Their reconstructed Old Chinese pronunciation is similar, but different (*kral vs *gral), see Wiktionary.

The meaning of 「奇」(qí) is "odd", "strange", as in 「奇怪」.
The meaning of 「奇」(jī) is listed as "unsmooth", "surplus".

So 「奇数」 does literally mean "number with surplus (after divided by 2)" and it has nothing to do with the "strange" meaning, so it is "jīshù".

Sometimes two related words with similar pronunciation are written with the same character, for example「数」(shù; number) vs 「数」(shǔ; to count). In some cases phonological processes have made the pronunciations very different, for example 「乐」(yùe; music) and 「乐」(lè; joy).

Answer 2

因为「奇点」实际上是「奇异点」的缩写，意思是这个点有「奇怪」的性质。而「奇数」是与「偶数」相对的概念，这个义项的「奇」本意是「余下」，例如「奇羡」：余财，「八分有奇」：（长度）八分多一点。所以表示「单数」时，实际是说两两分组，余者为「奇」。

在术算中，「阳卦奇，阴卦偶」，古人也认为奇数不吉利，所以有「命舛数奇」的说法。

Answer 3

The character 奇 stands for two different, though related, morphemes.

• The first (Old Chinese, in Baxter-Sagart reconstruction, [k](r)aj) 'odd (number)'. This one develops into Early Middle Chinese kje and modern Mandarin jī.
• The second (N-k(r)aj, N- stands for an unknown nasal), 'strange, wonderful'. It develops into Early Middle Chinese gje (with voiced consonant) and modern Mandarin qí.

(The fact that both of the meanings can be expressed by the English word 'odd' is a serendipity of languages and is but an accident.)

Clearly, the second meaning is much more frequent in everyday life, and so jī feels an outlier, but as we see from the reconstructions, it is actually the more basic word. It is qí that is derived with a nasal prefix. The exact meaning of the prefix here is unclear (usually N- derives stative intransitive verbs from transitive ones), but the etymological connection between two seems clear.

Answer 4

Emmm, there are many polyphones in Chinese you just have to remember.

Basically, 奇（ji）means odd, as in mathematically odd only, either for the definition of numbers:奇数 (1,3,5,7,9...),or for functions:奇函数 ( f(-x)=-f(x) ).

where, 奇（qi）means special:奇特; odd as in strange：奇怪.

yes, there are many ppl pronouncing 奇点 as jidian by mistake. This is a common mistake and wildly accepted by the society. It should be qidian meaning 'special point'. In daily life, either is ok.

Answer 5

「奇」(jī) and 「奇」(qí) are same words, but they have different meanings and different prononciation. Many other words in chinese also behave the same, such as「都」(dū) and 「都」(dōu). As you say, it was a「多音字」.

But all「多音字」have usual and unusual usage, all we need to do is remember the unusual usage and combination, then the rest are usual.

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Such as:

「奇」

1. (jī)(unusual), meaning "odd number", most combination are「奇数」(jī​ shù​) and 「奇函数」(jī​ hān shù​)
2. (jī)(unusual), meaning "redundant", most combination are 「奇得」(jī​ dé​): redundant benefit, and 「奇零」(jī​ líng​): the number of unsatisfied integers
3. (qí)(usual), the reset are all pronounced (qí), meaning "strange", "unexpected", "infrequent", the combination are 「奇怪」(qí guaì​), 「奇兵」(qí bīng​), 「奇缺」(qí quē​)