IM LISTENING TO " MY LITTLE BOAT" bossa nova song. it has a descending sequence in the verse: Dmaj7 - Db7 -Cmaj7 -B7 -Bbmaj7 etc... what's the best way to describe this theoretically? (from a jazz perspective)
I have played this song many times and have heard various versions of it. The original by the composer is in the key of F and it is often played in Bb as well but the analysis is the same for any key. I will use your example key of D for my explanation. (FYI I use all capital Roman numerals with chord qualities written in)
This song is a series of two modulations down a whole step for three keys total, D, C, and Bb, then back to D. The maj7 chords are the tonics and the 7th chords are substitute dominants, aka tritone substitutions, dominant chords that are a tritone away from the V, called sub V chords for short. If they were regular V chords it would be D-G7-C-F7-Bb, or a cycle of descending 5ths. The subV chords create a chromatic descending motion instead of a cycle of 5ths. This is fairly common in jazz and Brazilian music, both of which share very similar harmonic elements.
Interestingly, the next chord in the sequence, A7, is used as a regular V, not a sub V in order to return to the original key of D. It is however preceded by a IIIm7-V7/IIm7-IIm7-V7 before arriving at the Dmaj7 chord for the repeat.
Another thing to point out about this song is that in most versions, including the version by the composer Roberto Menescal, the sub V’s actually are preceded by IIm7 chords added to them so Db7 becomes Abm7-Db7, etc. This eliminates the chromatic motion but the analysis is basically the same.
Here is a rough analysis of the version with the IIm7-V7’s. The chords written in blue (IV7 chords) are actually played by the composer but are not used in many other versions. The basic analysis is below on the last line.
The best description would be that it's a chromatically descending sequence of alternating major and dominant seventh chords.
The core of the progression is that the root always descends by half step, while the sevenths come in pairs. For example, The seventh in the CM7 chord is B, and the seventh in the B7 chord that follows is also B.
But even more, the entire triadic part of the chords descends by half step, with the sevenths occuring pair-wise as described above.
D(+C#) Db(+Cb=B) C(+B) B(+A) Bb(+A)