This post lays out a basis for analysis, considers the music in four-bar groupings, and finally summarizes the analysis.
Underlying harmonic logic
I propose that Tyner isn't playing in a single mode. Because modal harmony divorces itself from major/minor tonality, focusing more on a (scalar) collection of pitches and avoiding triadic tonal functions, Tyner can oscillate between and mix various modes, never fully committing to any of them.
For the purposes of this analysis, I consider that Tyner is moving between Bb Dorian and Db Lydian. I further interpret this in light of Bb minor and Db major being relative modes. So I look at Bb Dorian as being minor in altered form, and Db Lydian as being major in altered form. Thus, the relationship between Bb Dorian and Db Lydian is in this situation viewed as analogous to the relative minor/major relationship.
I also consider that the abstract structural form as:
| I | I | I | I |
| IV | IV | I | I |
| V | V | I | I |
Bars 1-4 (Dorian = "Altered minor")
As indicated in the OP, Tyner begins with a standard Bb - C quartal voicing projecting Bb Dorian (i.e., "altered" minor). I suggest that these are actually "inverted" F - G quartal voicings. Since we're in Dorian, projecting scale degrees ^5 (F) and ^6 (G) defines the characteristic modal sound. And playing a quartal "V" chord (i.e., rooted on F, the V of Bb) where "tonic" harmony would go (Bb minor/dorian), is very Tyner-esque.
The Db-G-C chord in bar 4 is a prolongation of Bb Dorian, using pitches from that scale, but it also can be understood as a shift to Db Lydian (i.e., the "altered" relative major of "altered" Bb minor). Tyner is reinterpreting the "I" chord from being rooted on Bb to being rooted on Db. The function is a quartal/modal "pivot" chord. Note also that the Db could be viewed as V relative to the upcoming Gb chord.
The Gb chord at the end of the fourth bar is an anticipation of bar 5, so will be discussed in the next section.
Bars 5-8 (Lydian = "Altered major")
With bar 4's Db Lydian ("altered major") chord as the new "I" chord, the Gb chord in bars 5 and 6 is the quartal IV chord, which then returns to the quartal "altered" I chord of Db in bar 6, anticipating bars 7 and 8.
To understand the final chord in bar 8, consider that Tyner is about to return to Bb as the "tonic" for the purposes of the upcoming "V" chord in bar 9. The final chord of bar 8 can be re-spelled (and re-voiced) as E-A#-D#-G# -- another quartal harmony -- this time serving as a "leading-tone" chord moving to the "dominant" of Bb minor: i.e., F.
Bars 9-12 (Lydian = "Altered major")
Bar 9 is an prolongation of the "leading-tone" chord anticipated at the end of bar 8. Tyner then arrives on the "dominant", F, of Bb in bar 10. Though obscured by the preceding ambiguities and by the voicing, bar 10 is an F7b13 in literal terms (the F is in the melody), though it's not heard as such.
In fact, given the Eb in the bass, it's reasonably interpreted as a quartal "II" chord, playing a "dominant" role by setting up the return to Db as the final chord.
It's fascinating to observe that the solo line does, in fact, treat Bb as the ending "tonic", whereas the left hand treats Db as the "tonic".
Here is how the chords relate to the abstract 12-bar blues framework. I identify chords by their root.
Legend: | Measure number |
| Chord function |
| Chord root |
| Key/Mode |
| 1 | 2 | 3 | 4 |
| V subst for I | same | same | Pivot III/Bb, I/Db |
| F | same | same | Db |
| Bb Dorian | same | same | Bb Dorian / Db Lydian |
| 5 | 6 | 7 | 8 |
| IV | same | I | same |
| Gb | same | Db | same |
| Db Lydian | same | same | same |
| 9 | 10 | 11 | 12 |
| VII/V | V | I | I |
| E | F7b13 | Bb | Db |
| Bb Dorian | same | same | Db Lydian |