TAG || AbΔ - - - | DbΔ - - - ||
TAG || IVΔ | bIIIΔ ||
This is a 12-measure through-composed melody—with intentional irregularities employed to control the pacing of the tune's exposition:
Measure 2 is an elongation of m.1 (extra measure). The first 5mm. are stretched out to be twice the melodic rhythm of the rest of the melody.
M.14 is a transitional extension (extra bar), as are m.18 and the last two mms. before the double bar.
The tune is clearly in the primary key of Bb—and it should therefore take its correct key signature of two flats.
With regard to brightness, the tune begins in Bb major, and then progresses to the incrementally brighter keys of C and then G major, before returning to conclude in Bb.
The root progression moves essentially through the cycle of fourths in typical fashion (its guide-tone line is typical as well). What makes this composition both melodically and harmonically significant is its key progression, which moves from the primary key to the key of II (C), and then to the key of VI (G), both of which are not traditionally considered to be strong tonal modulations (that is to say closely-related, such as the keys of IV and V), but instead rather vague (not intended in any way as an aesthetic judgment).
In learning to improvise on this piece, begin by internalizing the reduction through paraphrasing and singing chromatic targeting of these essential melody notes, before addressing the entire form. Once this is accomplished, the specifics of the chord changes become far less of a necessary focus.
Working on this tune ahead of time in this fastidious manner is necessary, because if you want to sound better than you are (at best) just getting through it in a passable, mediocre way, it is a good idea to know how the tune is constructed, and to use that information to inform your preparation on it in the practice room—especially on a sophisticated composition such as this. You also need to be on intimate terms with the melody.
I have heard, for example, many very competent—even great—professional jazz artists fall right on their asses on Dolphin Dance for just that kind of lack of preparation. You just can't jive it and be convincing. At first, even Chet Baker and Frank Vicari played some lame solos in getting used that tune—and also some of Wayne Shorter's compositions, because they don't follow a standard type, and are tonally ambiguous and often contain irregular forms. You cannot rely on your licks on this kind of composition; you have to compose yourself into it.
Analysis isn't essential, and you don't need to do any more of it than you intend to use for writing exercises and etudes on tunes to be learned. It can be done without all of that. One way or another, though, you have to learn a complex tune such as this as a special story in order to be convincing on it, even if it just entails playing it on the piano and singing improvisations.
In creating each and every role I am to play on a given piece, they are most effectively developed from the essential elements of the composition itself. Everything else is merely generic. Since in analyzing complex tunes such as this I always have to start by reducing the melody, I did that in Albert Shanker fashion, a process which is always revealing. I based this on Swallow's lead sheet and posted it here:
Of course, no matter what you do in the practice room, leave it all behind in performance. You don't want to know anything intellectual about it at that point. Often, though, the systematic process points me to vocabulary, approaches, and additional options that might not have occurred to me otherwise. Especially helpful for me on this particular tune would be to first learn the melody in its simplified and reduced form, since that process really liberates.