This question has made me think about the class of adjectives, which can function both as イ- and as ナ-adjective, e.g.
大きい 大きな
小さい 小さな
真っ白い 真っ白な (etc.)
細かい 細かな
暖かい 暖かな
四角い 四角な (etc.)
柔らかい 柔らかな
In my (non-)answer to the question, I mentioned that the difference of やわらかい and やわらかな is very subtle at best.
I am wondering, can this maybe explained in more generality? What are the differences in the word pairs above?
After some research, there seems to be little difference in meaning. In some situations, maybe ease of pronunciation is more of a guide than nuance of meaning. For example, in the Balanced Corpus of Contemporary Written Japanese (BCCWJ, 少納言), we have
大きな木 154 results
大きい木 12 results
(But 木 is clearly no abstract concept.)
However, my question stated that 大きい etc. can be used as both イ- and ナ-adjective, which seems to be only half of the truth as 大き shouldn't be considered a ナ-adjective, even though it can modify nouns as 大きな.
For example, 大き cannot be inflected, to form an adverb (cf. 静か → 静かに.)
Rather 大きな belongs to the class of [連体詞]{れんたいし} (Rikaichan calls this pre-noun adjectival or adnominal adjective, a better name would be adnoun).
連体詞 are words which cannot inflect and must modify a noun (or pronoun), e.g.
この、その、あの、……
おかしな、大きな、小さな、……
as in
このやり方は一番よい。
こうするのが一番よい。
or
空におかしな形の雲が浮かんでいる。
空に変な形の雲が浮かんでいる。
These 連体詞 seem to come in 4-5 varieties (depending on the book you read):
「～の」の形・・・この、その、あの、どの、ほんの
「～な」の形・・・大きな、小さな、おかしな、いろんな
「～た、～だ」の形・・・たいした、たった、とんだ、ばかげた
「～る」の形・・・ある、あらゆる、いわゆる、さる、きたる、いかなる、堂々たる
「～が」の形・・・わが
All this information is a summary of this site. I hope someone will find it useful.
This should also shed some grammatical light on this and this question.
In an after-thought as to why 小さい時 cannot be 小さな時 is that 小さな is a 連体詞 and must modify a (pro)noun and thus forces the meaning small time, rather than allowing for the interpretation as a sentence in which the (omitted) subject was small, which is usually translated with a relative clause, i.e. the time, when I was small or just when I was small.
So, the general rule seems to be that one can choose either one of the word pair, but when choosing the one ending in な, one chooses to modify directly the noun which must follow it and disallows constructions with relative clauses.
E.g. compare
山の大きい街 vs. 山の大きな街.
The former can mean a city with a big mountain, whereas the latter is necessarily a big city situated on a mountain. (One can probably come up with better examples.)
To answer part of the question:
For 大きい／大きな and 小さい／小さな I understand the difference is small, but the na-form is often preferred with abstract words
大きな功績 great achievement
大きな進歩 great progress
小さな間違い small mistakes
小さい時 when I was small (i.e. when I was a child).
I use the word "often" because there are exceptions: both 大きい問題 and 大きな問題 are acceptable*.
*Reference: "nihongo notes 10", p. 56
A morphological analysis may help to shed light on the difference between 形容詞 and 形容動詞 (referred to as i- and na-adjective respectively in Japanese grammar books written in English). 形容詞 expresses the appearance, nature, or state of things. 形容動詞 does the same but the structure of it is a noun followed by the conjugated form of the copula だ 「だろ・だっ（で・に）・だ・な・なら・〇」. So, a noun followed by the attributive form of だ (which is な) transfers the attributes of that noun to the described word (noun, pronoun or a noun clause).
In this light, let's compare 小さい and 小さな. 小さい simply means small, but 小さな means having attributes of 小さ. 小さ is an archaic term for a baby. So, 小さい木 is simply a small tree, while 小さな木 is a tree with the attributes of a baby, in other words a baby tree. The meaning of both expressions are almost identical, but the latter uses the technique called personification. This technique gives that artistic and emotional taste mentioned at the end of the dictionary entry for 小さい.
