Describe the function of the tritone substitution and how it can be used to create harmonic tension and resolution in a ii-V-I progression.

The tritone substitution is a fundamental technique in jazz harmony, where the dominant 7th chord (V7) in a progression is replaced by another dominant 7th chord that is a tritone away. The tritone is an interval of six half steps, or three whole steps, and in the context of a dominant 7th chord, this interval exists between the 3rd and 7th notes of the chord. The most common tritone substitution is the flat-five substitute, which is often referred to as bII7. For example, if the dominant chord is G7, its tritone substitution would be Db7. The function of the tritone substitution lies in its ability to maintain the dominant function of the V7 chord while altering its sound, creating harmonic interest and a sense of surprise. This works because both chords share the same tritone interval between their 3rd and 7th, the critical interval that creates the dominant function by resolving inwards to the root and third of the tonic chord.

In a typical ii-V-I progression, the tritone substitution of the V7 chord can dramatically change the harmonic landscape. Let's take a ii-V-I in the key of C major: Dm7 - G7 - CMaj7. The V7 chord, G7, can be replaced with its tritone substitute, Db7. The modified progression then becomes: Dm7 - Db7 - CMaj7. The bII7, in this case, Db7, still functions as a dominant chord. Db7 wants to resolve towards the CMaj7 since Db7’s notes, Db-F-Ab-Cb, contain the same tritone interval between F and Cb (which is enharmonically B), as in G7, which is B and F. The resolution still has the tendency to resolve into C major, but the movement now incorporates a chromatic slide. This technique introduces a new color to the progression, making it sound more complex and sophisticated.

The tritone substitution is used for several reasons, with one of the most prominent being its ability to create harmonic tension. The Db7 chord in the above example, sitting between Dm7 and CMaj7, creates a higher level of dissonance compared to the standard G7 chord. This added tension leads to a richer resolution when moving to the CMaj7. Also, the descending root movement from the Db to C adds a smoother voice leading, further enhancing the resolution. This is due to the half step movement in the bass, which is often perceived as a stronger and more elegant way of moving through chords.

Another way the tritone substitution is used in a ii-V-I is by substituting a chord a half step below the root of the V7. Using the Dm7-G7-CMaj7 example, a chord a half step below G would be Gb. The tritone substitute of Gb is Cb, but it can also be seen as a B major dominant 7th chord (B7). The progression then becomes Dm7-B7-CMaj7. Here, B7 would act as a substitute for G7. Another way the V7 can be used in a ii-V-I with a tritone substitution would be if the Dm7 is substituted with a Dm7b5, the V7 would then become an altered dominant, like G7alt (a G7 chord with alterations), and the tritone sub would become a Db7 with alterations like Db7alt. These types of alterations can be more suited for fast bebop tempos.

The tritone substitution isn't just a theoretical concept; it’s a practical tool widely used in jazz improvisation and arranging. Improvisers use the tritone substitution to create unexpected melodic lines, and arrangers use it to add depth to their arrangements. For example, in a blues tune, the use of tritone substitution can bring a modern sound to a traditional structure. The substitution adds a twist that keeps the traditional chord progression and resolution intact but expands the harmonic palette, creating greater interest and musical depth, allowing improvisers to play different melodic ideas using altered or related scales.