related—though in varying degrees of closeness; and in modern
music, no matter how complex the modulations often sound,
we may be sure that the composer plans them as carefully as
the painter adjusts his color-scheme. For definite acoustical[48]
and harmonic reasons, however, the keys most closely related to
a given tonal centre are those situated a perfect fifth above—
the Dominant; a perfect fifth below—the Subdominant; and the
Relative Minor, the key-note of which is a minor third below,
e.g., A minor in relation to C major, C minor to E-flat ma-
jor. The relative minors of the Dominant and Subdominant
also bear a close relationship to a given tonic; and into these
fivekeys is made a large majority of the modulations in any
piece of music.[49]
[Music:
Subdominant Tonic Dominant
Relative Relative Relative
Minor Minor Minor]
[Footnote 46: As for example the famous one of Chopin.]
[Footnote 47: Even great composers have at times made this
mistake,e.g., Mendelssohn in the first movement of theScotch
Symphony, where the interminable length of the portion in A
minor (of all keys!) is simply deadening in its effect. Compare
also thePrelude to the Rheingold; where, however—for dramatic
purposes—to depict the world as “without form and void” Wag-
ner remains in the key of E-flat major for some 150 measures!]
[Footnote 48: It is left to the teacher to explain, by the ratios
found in the overtones of the Harmonic Series, the validity of
this statement.]
[Footnote 49: Some modern theorists,e.g., Calvacoressi (see
the New Music Review for September, 1909) have thought that
the dominant relationship was “overworked.” It is true that
the great charm of modern music is its freedom and boldness
in modulation; but the dominant keys can never be entirely
abandoned, for the relationship between them and a tonic is as
elemental as that between the colors of the spectroscope.]
Beginning with Beethoven, a modulation into what are known
as themediantkeys became frequent; and is, in fact, a favorite