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I noticed that in the word 子牛 both "o" and "u" are pronounced while in the
word 格子 there is a long "ō" and they are, respectively, written in rōmaji
(Hepburn romanization) koushi and kōshi. What I'd like to ask you is if: 1) in
Middle Japanese the diphthong "ou" was reduced to "ō" only when the two vowels
were part of the same syllable (like in 格子) 2) the reduction happened only in
kango and waseigo or it happened also in some yamato kotoba
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orthography history phonology
Reduction of the diphthong "ou" to "ō" in Middle and Modern Japanese
# Is coalescence blocked between syllables?

No, coalescence also occurs between syllables, and even involving vowels from
different morphemes. In fact it's not clear whether /ou/ was even a diphthong
to being with; it's quite possible that it only ever existed as a hiatus. In
modern Tokyo Japanese probably only /ai/, /oi/ and /ui/ are actual diphthongs
(every vowel sequence ending in -u needs another syllable for it; they
coalesce nonetheless).

# Was historical coalescence restricted to _kango_ words?

No, it happened throughout the entire lexicon. Primitive Japanese had no
sequential vowels, so _yamato-kotoba_ examples aren't as plentiful as _kango_
; but some vowel sequences did emerge later, and among them, /ou/ did coalesce
into /o:/. For example, * _saso-pu_ → _saso-u_ → _sasō_.

Notice that /au/ also coalesced into /o:/, so that /au/ and /ou/ merged.
Diphthongs in /-i/, by contrast, were resistant and survived to this day. So
_hayau_ → _hayō_ but _hayai_ → _hayai_.

Regarding questions raised in the comment thread:

# Is coalescence blocked between morphemes? What about words?

Consider:

  * Conclusive (終止形) suffix -u: _saso-u_ /saso:/
  * Adjectival suffix -u: _samuk-aro-u_ /samukaro:/
  * 御宇 _gyo-u_ /gyo:/
  * 如雨露 _jo-u-ro_ /Zo:ro/

By contrast:

  * 子牛 _ko-usi_ /kousi/
  * 小唄 _ko-uta_ /kouta/
  * 壇ノ浦 _dan-no-ura_ /daNnoura/
  * 選挙運動 _senkyo-undō_ /seNkjoundo:/
  * 左顧右眄 _sako-uben_ /sakouben/

For the purposes of coalescence, compound words (words made of two free words)
count as "different words". So a word like _usi_ or _uta_ won't lose its _u-_
, but a bound suffix might.

Notice that this is consistent with other forms of coalescence in Japanese. So
_au_ > _ō_ regardless of whether it was found in native Japanese or Sinitic
words, and across morpheme boundaries ( _haya-u → hayō_ ), but not across word
boundaries ( _matu-ga-ura_ ­→ _matu-ga-ura_ ). Even other sound changes behave
similarly; 買ひ → _ka-wi_ → _ka-i_ (cross-morpheme lenition) vs. 朝日 → _asa-hi_
(no cross-word lenition).

# What about words like 降雨 or 堂宇?

The final -u doesn't coalesce: /ko:u/, /do:u/. However, the previous /o:/ is
already long, so they wouldn't coalesce anyway (/o::/ isn't a legal coda).

# Does coalescence behavior differ between _yamato-kotoba_ and _kango_ words?

From the above, it seems like not (except indirectly, insofar as diphthongs
are rare in _yamato-kotoba_ and free-word compounds are plentiful).

**Sources:**

  * Kubozono, _Diphthongs and vowel coalescence_ (in: _The Handbook of Japanese Phonetics and Phonology_ )
  * Kenkyūsha's Japanese-English dictionary, for pronunciation guides.
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> 1) in Middle Japanese the diphthong "ou" was reduced to "ō" only when the
> two vowels were part of the same syllable (like in 格子)

I think what you mean is "the same morpheme", because that's the difference
tells 子牛 from 格子. This is a part of four sound shifts have taken place in
parallel.

  * //au// → //ɔː// → //oː//
  * //iu// → //yuː//
  * //eu// → //yoː//
  * //ou// → //oː//

This sound shift has had effect mostly inside a morpheme with a few
exceptions, but most of those exceptions are eventually reverted in today's
language. Some examples of surviving exceptional outcomes are:

  * the volitional suffix: 行かむ //yuka-mu// → 行こう //ikoː//, 出でむ //ide-mu// → //(i)dyoː// (→ leveled to 出よう //deyoː//) etc.
  * -うと/-うど pseudo-suffix series: 素人 //sira-bito// → //siraudo// → //siroːto//, 玄人 //kuro-bito// → //kuroudo// → //kuroːto// etc.
  * 酔ふ //weɸ-u// → //eu// → //yoː// (→ leveled to 酔う //yo-u//)
  * 言ふ //iɸ-u// → //iu// → //yuː// (deemed non-standard now)

In fact, 格子 has never been pronounced like //kousi// despite its modern
spelling, because its actual historical development is //kakusi// → //kausi//
→ //kɔːsi// → //koːsi//. The reason it's spelled こうし is because the [Modern
Kana Orthography](https://en.wikipedia.org/wiki/Modern_kana_usage) defines
that all historical おう, おふ, あう, あふ that pronounced as //oː// should be
replaced with おう.

> 2) the reduction happened only in kango and waseigo or it happened also in
> some yamato kotoba

This sound change affected all qualified diphthongs regardless of kango or
wago (yamato-kotoba), but since such combinations are rare in native Japanese
words, the great portion of the effect was seemingly exerted on kango.

  * 塔 (kango) //taɸu// → //tau// → //toː//
  * 尊き (wago) //taɸuto-ki// → //tauto-i// → 尊い //toːto-i//

But some wago apparently showed some degree of resistance.

  * 倒るる //taɸur-uru// → //taur-uru// → 倒れる //taore-ru//  
cf. 放る //ɸaɸur-u// → //ɸaur-u// → //hoːr-u//
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