The Inversions of the Diminished and Augmented Triads

• first inversion of the diminished triad is very important
  • it is more commonly used than any of the other chords inversions
  • it is the more common than the root position of this chord
    • the reason for this is – the chord is essentially a consonant one
      • from the bass, it forms a third and a sixth
        • with the root position of this chord containing a diminished fifth, it simply cannot be employed in consonant harmony [therefore making a dissonant chord]
          • the second inversion of the diminished chord is harsh – it is really only used in three part writing
  • how to connect the first inversion of the diminished chord to other chords in a key have two special cases
    1. when it precedes tonic
       • in a diminished chord, the fundamental tone is also the leading tone – which must be lead upward
         • thus, the leading tone cannot be doubled in four part writing
           • the best alternative is to double the 5th, though sometimes the 3rd is doubled
             • if the doubled 5th is above the leading tone in four part writing, then it must be lead downward to avoid forbidden progressions
               • for this reason, we cannot voice a chord with two 5ths above the leading tone
    2. when it precedes another triad of the scale
       • diminished chords in first inversion before chords that are not the tonic can easily double the fundamental, as it no longer acts as the leading tone
         • this is not how I understand harmony as the fundamental tone always is just that
           • Tchaikovsky obviously views it differently in the context of a diminished chord in the first inversion
             • what is more strange is that only one of his examples shows this

• when a diminished chord is in first inversion from the minor – the chord and the rules governing it fall into the general category of rules
• augmented chords
  • in minor they are much too difficult to deal with at present – so they will be left for a later time
  • in major they will be treated at present as a passing chord