Explain the theoretical basis for the application of the minor pentatonic scale in blues improvisation, including its relationship to the underlying chord progressions.

The minor pentatonic scale is a cornerstone of blues improvisation, providing a framework for creating soulful and expressive melodies and solos over a variety of blues chord progressions. The scale, consisting of five notes—the root, minor third, perfect fourth, perfect fifth, and minor seventh—is effective in blues because its intervals create a sound that aligns perfectly with the blues tonality. Let's look at the notes of the A minor pentatonic scale, for instance: A, C, D, E, and G. These notes fit well over various blues progressions and particularly over A7 chords (A, C#, E, G) because the minor third (C) and the minor 7th (G) create a bluesy tension.

The scale's relationship to underlying chord progressions is what truly makes it effective. Typically, in a 12-bar blues progression, the three main chords are the I chord (tonic), IV chord (subdominant), and V chord (dominant), and these can often be dominant 7th chords. For example in the key of A, these are A7, D7 and E7. If we take our minor pentatonic scale in A, we can see how well it functions with these chords. While A minor pentatonic includes the minor third of A, the scale is not strictly aligned with only the A minor chord. Instead, it can be used quite effectively over the A7 chord, as well as the D7 and E7 chords, because the notes of the scale have strong relationships with these chords in the progression. The use of the minor third creates a bluesy dissonance against the major chord tones of the 7th chords.

The minor pentatonic scale avoids some of the more dissonant intervals found in a full minor scale. For example, the minor scale includes a minor 2nd which is avoided in the pentatonic which removes a strong dissonance. This also makes it more forgiving in improvisation. The lack of a major 2nd or minor 6th in the minor pentatonic scale allows for freer movement without clashing hard against common chord tones in the blues progression and these notes are often called ‘avoid notes’. When the minor pentatonic is used over the dominant 7th chords in blues, it introduces a blend of bluesy grit and tension as the minor third against the major third of the chord creates a characteristic blues dissonance. This tension is what makes blues music so emotionally resonant. For instance, playing an A minor pentatonic lick over an A7 chord can create a slightly melancholic feeling, while over an E7 chord, it can give a powerful bluesy drive.

The minor pentatonic scale is not used exclusively as a scale. It is commonly altered to create other scales, and these small alterations can make it a very versatile scale. For example, when we add a flat 5th to the minor pentatonic scale (for A, we add Eb) we are then playing the "blues scale," a fundamental scale in the blues repertoire. This altered scale is a simple variation of the minor pentatonic that introduces an even more dissonant note that perfectly complements the blues style and helps intensify the feeling when used within improvisations. The scale isn’t just a collection of notes, rather the notes are used as reference points, where bending and sliding into and out of them are very important, which adds further blues characteristics into the improvisation.

The minor pentatonic’s power lies in its simplicity and versatility. It can be used as a starting point for beginners but also lends itself well to the intricate variations and complex solos by more experienced players. The scale provides a roadmap for a blues solo, however the feel is often developed by the articulation, bending and phrasing and is not solely based on the specific notes from the scale itself. Its effectiveness stems from its natural fit over the underlying chord progressions of the blues which allows blues musicians to create very complex expressions and emotional impact. The minor pentatonic’s flexibility, and the ability to change the sound and feeling by a simple alteration, are why it is so deeply ingrained in the language of blues music.