direct modulation

• dominant chords function well but can only point to one area clearly and two areas overall
  • I-V/V-V[I]
  • I-V/bVI-bVI[I]
• when connecting with these dominant chords, if there are no common tones, there must be a passing chord
  • this chord should be from the prior or new key
  • it could also be from a closely related one
  • if a chromatic alteration is being made for the passing chord, then it must be in the same voice
    • if we do not follow this rule we get nasty cross-relations
• modulation with chord of the 9th and minor 7
  • they are possible but they are not common because they are fraught with difficulties
• diminished triads have ability to function well
• dominant triads can be used regularly
• minor chords of the 9th and diminished 7th chords
  • these are the most common chords that will be found to lead to either major or minor tonalities
• prolonged cadences ensure that we are in a new tonality
• figured bass notation
  • to sharpen, we often see a line [/] through a figure
  • or a plus sign [+]
• three exercises given in this chapter for mastery of connection of chords
  • these are not completed, so i would say that they are optional, though Tchaikovsky lists them as mandatory