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why_dominant_gets_altered.md

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Why dominant chords get altered?

  • it contains a tritone which is rotationally symmetric (~ +6 transposition)
  • a diatonic pitch class set consists of a pentatonic and this tritone pair
  • two diatonics within a mirror key pair share exactly this tritone pair
  • a dominant chord in one key and dominant chord in its mirror key also share exactly this tritone pair
    • other diatonic chords do not allow this
  • alteration thus naturally allows visiting the other key in the mirror pair
  • in jazz theory using a dominant chord from the mirror key is called tritone substitution
  • example: IIb7 instead of V7, eg. Db7 instead of G7
  • similar is the Neapolitan chord
    • compared to IIb7 it has fifth instead of seventh
    • eg. - C -> Db ~ Fm6-5