. Harmony : a course of study . C-F#(Gb)-C. Db-G-Db. D-Ab-D. Eb-A-Eb. E-Bb-E. F-B-F. These may be combined in turn with the modulations upward anddownward a semitone, viz : C-F#-C-Db-G,etc. ; or,C-Ffl-C-B-F,etc.; or,C-F#-G-Db-D, these modulations should be carefully studied at the pianoforte. i. 2. 3- 4- 5-6. LESSON LTV. MODULATION IN GENERAL KEY RELATION. The modulations already given have not included changes of keybetween different modes, excepting the immediate relations of a giventonic. But since the modulating chords (the dominant and dimin- 22 *74 HARMONY. ished seventh) may be

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. Harmony : a course of study . C-F#(Gb)-C. Db-G-Db. D-Ab-D. Eb-A-Eb. E-Bb-E. F-B-F. These may be combined in turn with the modulations upward anddownward a semitone, viz : C-F#-C-Db-G,etc. ; or,C-Ffl-C-B-F,etc.; or,C-F#-G-Db-D, these modulations should be carefully studied at the pianoforte. i. 2. 3- 4- 5-6. LESSON LTV. MODULATION IN GENERAL KEY RELATION. The modulations already given have not included changes of keybetween different modes, excepting the immediate relations of a giventonic. But since the modulating chords (the dominant and dimin- 22 *74 HARMONY. ished seventh) may be preceded by and resolved to both major andminor tonics, the modulations already given are sufficient to cover allchanges of key. In the modulations between sharp and flat keysmany enharmonic changes occur, the diminished seventh chord beingoften so changed for the sake of convenience. As keys are relatedin proportion to the number of tones in common between them, thedifference in the number of accidentals in the signature of an

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