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I know that progressions based on the chords E7,A7 and B7 form the basic rhythm guitar section of a blues song. These chords dont seem to strictly lie on the blues scale. Why do these chords harmonize well with the blues scale. How are they constructed from the scale?

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I think these two questions answer your question: music.stackexchange.com/q/5991/104 and music.stackexchange.com/q/1024/104 –  Dr Mayhem Jul 29 '13 at 18:34

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The Blues is interesting in that there is no one scale for the whole progression. Each chord within the progression will use a blues scale starting on its root. So E7 would be and E major blues, A7 would be A major blues etc. All the notes in a dominant 7 chord can be found in a major blues scale, 1,3,5, and b7 (in E: E,G#,B, D). The strangest part of the scale is the addition of the note b3/#9 (in E: G natural). b3 Would be used in a minor chord and would usually not have a place in a major chord. This distinctive tone is often referred to as the "Blue Note". The strangest part about the style of music is that a dominant chord is your tonic. This sounds weird because traditionally a dominant chord is used to get back to tonic. Similarly, since all the chords are dominant all of your progression/resolution brings you to another dissonant place. Blues probably would have driven Bach crazy waiting for "proper" resolution. I find that blues doesn't seem so strange now as it was when they first started because there is much less emphasis on traditional resolutions in modern music.

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Blue Note: there are three possible blue notes: b3, #4/b5 aka tritone, and b7. You have the idea though, but in blues we have to pay tribute to the string instruments (traditionally guitar, banjo, and fiddle) that can bend notes in addition to the blue notes, also the horns, trombones, harmonicas, vocals, sax too that can bend notes. Bending notes by more and less than a half step too. –  filzilla Jul 31 '13 at 0:00
Absolutely agree. I tried to answer specific to the progression and found myself wanting to add more about minor blues. –  Basstickler Jul 31 '13 at 0:07

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