Jazz musicians often use different harmonic substitutions to modify the content of diatonicprogressions. The most common harmonic modifications of the Imaj 7 –vi 7 –ii 7 –V 7progression involve the use of secondary dominant chords (V7/X), and tritone substitutions(TR/X 7). Figure 13.5 demonstrates these substitutions using Model III of harmonicrealization.The secondary dominant 7ths A7 and D7 are analyzed with two different Roman numerallabels VI7 and V 7/ii, and II 7 and V 7/V, which can be used interchangeably. The tritonesubstitutions, E≤7 and D≤7, also use two Roman numerals, ≤III7 and TR/VI7, and ≤II7and TR/V7, respectively

The ii7–V7–Imaj7 progression constitutes the perfect vehicle to introduce one of the mostimportant features of jazz harmony: the tritone substitution, notated as TR/X 7. Thetritone substitution has its theoretical origins in the equal or symmetrical division of theoctave. This substitution is associated with the dominant 7th chord and capitalizes oninversional invariance of the tritone inherent to the dominant 7th formation.