Grammar", "proposition", "meaning" thus figure more often than other words, though investigation concerning the word "meaning" is on the same level as a grammatical investigation of the word "time".
I interpret this to mean that an investigation of the word would be a grammatical one. For example, people might dispute about how many arms God had, and someone might enter the dispute by denying that one could talk about arms of God. This would throw light on the use of the word.
For example, a person who tries to trisect an angle is led to another difficulty, posed by the question "Can it be done?" Proof of the impossibility of a trisection takes the place of the first investigation; the investigation has changed.
If no separate investigation is required, then we only mean by a beautiful face a certain arrangement of colours and shapes.
If no separate investigation is possible, then we mean by "beauty of face" a certain arrangement of colours and spaces.
In the statement that their beauty is what approaches the ideal, the word "ideal" is not used as is the word "water", which stands for something that can be pointed to. And no aesthetic investigation will supply you with a meaning of the word "ideal" which you did not have before.
To see how the ideal comes in, say in making the bass quieter, look at what is being done and at one's being dissatisfied with the music as it is. Can one call this "action" of making the bass quieter an investigation?
No, not in the sense of scientific investigation.
In what sense is aesthetic investigation a matter of psychology?
In aesthetic investigation the thing we are not interested in is causal connections, whereas in psychology we are.