In Dm G C the tritone sub is Dm Db C, but a jazz musician is going to hear that augmented interval because the G7 is implied as standard. I know that that stands in rude contravention to every accepted notion of the sub as a replacement, but my method of working is to emphasise the intervallic relationship that exists. The former is agreed upon by mutual consent while the latter is an intrerpretation to widen the scope. Using the interval of the tritone to create a lydian intervallic relationship or even using it to bring out the augmented fourth/dimminishes fifth. Im talking about the sub in a literal sense. The G7 substituted for Db7 creates several lines of convergence not least the common 3rd and 7th but the Gb parent scale or Blydian both of which have semitonal relationships to the dominant and tonic respectively. I agree that the theory books have it laid out as a means to create tonal convergence through semitonal planing. The gist of our respective arguments is that the tritone sub provides semitonal planing vs the tritonic sub in a more abstract impressionistic sense.
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