Just now in the chat room we came across a reading of the kanji 閉 that seems
to be either rare or erroneous.

In the [English Wiktionary's entry for
閉](https://en.wiktionary.org/wiki/%E9%96%89#Kanji) there is the following
"Readings section":

  * **On** : へい (hei), へつ (hetsu)
  * **Kun** : とじる (tojiru), しめる (shimeru), とざす (tozasu)

None of us in the chat room at the time could come up with anywhere the へつ is
used?

Is it a correct reading? What is/was it used for?
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kanji readings
In which terms, if any, is へつ used as an On-reading of the character 閉?
The 『デジタル大辞泉』 does not list the reading `へつ`, so I'd call it an error.
<http://dictionary.goo.ne.jp/leaf/jn2/197949/m1u/%e9%96%89/>

The dictionary 学研漢和大辞典 does not list any words with this reading either.
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As others have noted, the reading `へつ` is not listed in other dictionaries,
such as デジタル大辞泉. But that could be a measure of the lexicographer's rigor. So
at this point, maybe it's an error, maybe it's not.

Additional evidence is found in the corresponding Chinese reading of `閉`. The
coda /-tu/ typically corresponds to Middle Chinese coda /-t/, which would be
preserved in modern Cantonese. However, 閉 in Cantonese is /bai3/. So `へつ` is
likely an error.

But looking at [Baxter & Sagart's Old Chinese reconstruction
(2011)](http://en.wiktionary.org/wiki/Appendix:Baxter-
Sagart_Old_Chinese_reconstruction), `閉` has the following forms (bearing in
mind the well-documented /p/ to /h/ lenition in Japanese):

> MC: pejH
>
> OC: *pˁit-s {*pˁi[t]-s}

An important note on time periods: Old Chinese (OC) was around 1200 ~ 300 BC,
which makes for an extremely unlikely candidate for borrowing into Japanese.
(音読み are generally borrowed from around 700 AD and later.)

My e-dictionary lists the commmon 漢音 reading of `へい`, and a rarer (and older)
呉音 reading of `はい`. No 唐音 reading listed.

So we can say with some degree of confidence that `へつ` is unlikely to be an
音読み for `閉`. Although, I guess it's always possible that `閉` was
anachronistically used as ateji for `へつ` in some obscure piece of literature.
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I found this in a kanji dictionary from 1920s.

<http://kindai.ndl.go.jp/info:ndljp/pid/936724> (set コマ番号 to 866 and you see
the page)

It lists four sounds for 閉, but none of the following 熟語 has a sound other
than ヘイ. I guess this kind of description (ヘツ、ヘチ。方結切。屑。) originally originates
in classical Chinese hanzi dictionaries like 廣韻 or 康煕字典.
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This is not an _error_ , as some of the other answers may suggest.

The [Kangxi Dictionary](https://en.wikipedia.org/wiki/Kangxi_Dictionary)
records the following additional definition under「閉」:

> 《廣韻》方結切《集韻》《韻會》必結切《正韻》必列切， **音鼈。義同。**
>
> [_Guangyun_](https://en.wikipedia.org/wiki/Guangyun), [Fanqie
> rime](https://en.wikipedia.org/wiki/Fanqie) [方]{ほう}[結]{けつ};
> [_Jiyun_](https://en.wikipedia.org/wiki/Jiyun) and
> [_Yunhui_](https://ja.wikipedia.org/wiki/%E5%8F%A4%E4%BB%8A%E9%9F%BB%E4%BC%9A%E6%8C%99%E8%A6%81),
> Fanqie rime [必]{ひつ}[結]{けつ};
> [_Zhengyun_](https://ja.wikipedia.org/wiki/%E6%B4%AA%E6%AD%A6%E6%AD%A3%E9%9F%BB),
> Fanqie rime [必]{ひつ}[列]{れつ}. **Same sound and meaning as「[鼈]{へつ}」.**

What's going on here is that「閉」, in some Chinese texts, was used as a phonetic
loan for「[鼈]{へつ}」, and this usage was recorded in [Middle
Chinese](https://en.wikipedia.org/wiki/Middle_Chinese) rime dictionaries like
_Guangyun_ and _Jiyun_. Japanese _on'yomi_ largely corresponds to the
phonology in these dictionaries and thus may inherit these rare
readings/usages.

The readings are there for advanced Chinese literature study if you consult a
dictionary, for completeness purposes. There are a lot of obscure _on'yomi_
that you may find in dictionaries which come from this kind of phonetic
borrowing in characters (this is practically the Chinese version of _ateji_ ),
and most of the time you can safely ignore them.

* * *

_On'yomi_ given are for [_Kan'on_](https://en.wikipedia.org/wiki/Kan-on)
readings.
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