# Why is 奇数 pronounced jīshù and not qíshù?

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".

「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).

• "「奇」(jī) and 「奇」(qí) are different words." Do you happen to have the unicode of these two characters? Jul 27, 2022 at 10:19
• @joehua They are two words written using the same character, just like the verb "lead" and the metal "lead" are written using the same letters, so the Unicode values are the same. Jul 27, 2022 at 11:53
• @joehua (I'm a beginner, so take this with the requisite grain of salt…) The Unicode is the same (`grep ' 奇 ' cedict_1_0_ts_utf-8_mdbg.txt` locates both entries). About 5% of monosyllabic words in CEDICT are heteronyms. Take 和, for instance, which can be pronounced hé, hú, huó, hè and huò, with wildly different meanings. In every case in a straw poll I conducted, the phonetic variance is slight (ji/qi for 奇 and 荠, he/hu/hou for 和, shi/zhi for 氏, etc). The craziest one I found was liao/miao/miu/mou/mu for 缪. Jul 27, 2022 at 11:53

• So, 「畸零地」 should actually be 「奇零地」? Jul 27, 2022 at 10:21

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 .
• 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 .

(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 feels an outlier, but as we see from the reconstructions, it is actually the more basic word. It is 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.

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.

「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.

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. ()(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​)