Since no brave soul has come forward yet to give answers, here they are:
This is the Adoration of the Magi, the second movement of Respighi's Botticelli Triptych. Good Italian that he was, Respighi depicts the Magi's coming to the Holy Family with a Siciliana rhythm:
Like many ancient rhythms it has become part of the rhetoric of musical style. Undoubtedly this rhythm existed in melodies long before our current notation system was adopted. Therefore, any interpretation of this rhythm must be undertaken with the understanding that the notation on the page is just an approximation of what the rhythm should feel like when performed effectively.
After the performer can accurately execute the rhythm exactly as printed on the page, he must recognize the rhythm is code for a particular style -- in this case, the Siciliana. Then the execution must be altered slightly.
The characteristics of a Siciliana are a moderate or slow tempo and a lilting feeling. These can be accomplished by showing the flow of quarter/eighth, quarter/eighth, etc., with the eighth acting as a pick up note to each successive quarter.
The sixteenth note in the middle is just a gentle addendum to the eighth note. It should not be emphasized or given much weight. The weight in the phrase goes from quarter to quarter with the eighth acting as an uptake of energy and the quarter as a release of that energy.
Here would be my way of grouping the three notes. As you can see, the notation system used doesn't allow for this to be made explicit. So often the beaming and bar lines in music simply function as a mathematical accounting system and can get in the way of good phrasing and musical style.
Sometimes the execution of this rhythm is taken a step further by delaying and lightening up on the sixteenth so that it becomes close to a 32nd note.
Here is an effective way of performing this passage from the Hindemith Sonate:
Here is another dotted rhythm, this time articulated and in a fast tempo. This is a Fanfare or Signal rhythm. You could trace its roots back to ancient times when brass instruments were used to signal in hunting or to present royalty.
Practice evolved over time -- perhaps in order to make the announcement or call more stirring -- to put a space or lift between the dotted note and the short note. Used by Mozart in the last movement of his "Jupiter" Symphony it adds a royal flourish to the motives of the movement. In conjunction with the use of trumpets and timpani in the orchestration the audience at the time would have at least subconsciously felt the allusion to royalty.
There are echoes of this style in the Bassoon Concerto, especially if the performer chooses to articulate the first dotted rhythm:
3. Implied meter. In these examples the composers stray from the printed meter for a short time. They leave it up to the performers to find these hidden codes.
Mozart Symphony #40, mvt. 3
Saint Saëns Sonate, mvt. 2