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Tchaikovsky, Guide to the Practical Study of Harmony

Pyotr Ilyich Tchaikovsky · section 23 of 36

Chapter XXI. The enharmonic properties of the chord of the diminished seventh

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§ 61. The diminished seventh chord consists of three minor thirds erected one on the other. In the inversions of the chord, we obtain in place of minor thirds, their enharmonic equivalents—angmented seconds. If we now substitute these augmented seconds by the corresponding minor thirds, each inversion thus enharmonically changed gives us a new diminished seventh chord.

Example 197
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a-minor C-minor e flat-minor g flat-minor

So that every diminished seventh chord is the equivalent of three other diminished seventh chords. Twelve keys, in all, are known to us; consequently we recognize but three diminished seventh chords distinct in sound.

Example 198
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Every diminished seventh chord, then, can, by enharmonically changing its intervals, be resolved into four distinct triads.

Example 199
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Example 200
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We will now endeavour to use this peculiarity of the diminished seventh chord for purposes of modulation.

Example 201
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Exercise. Make modulations from different keys employing in each case all tour resolutions of the diminished seventh chord.