[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.
[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.
[50] Two tones are said to be "enharmonic" when, although written differently, they sound the same on an instrument of fixed temperament like the pianoforte, or organ, e.g., D-sharp and E-flat, E and F-flat. A violin, however, can make a distinction between such notes and often does.
[51] This assertion holds for most of our Western European music; though in Hungarian and Scotch music we find a natural fondness for phrases of three measures, and the Croatians are known for their phrases of five measures so often used by both Haydn and Schubert. But it is true that we tend to think in groups which are some multiple of 2, i.e., either 4, 8, 12 or 16 measures.
[52] Always count the first complete measure as one.
[53] The two phrases are often designated Thesis and Antithesis.
[54] In listening to a clock it is impossible to think of the ticks singly, or otherwise than in groups of two: an accented beat and an unaccented; although the beats are of equal strength and duration. This principle of dual balance is derived from the rhythmic pulsation of the human heart and, as we shall see, runs through all music.
[55] Whenever this book is used in class, the teacher can easily explain, on the pianoforte and by charts, the different cadential effects. For those who have sufficient harmonic insight Chapter XIV in Foote and Spalding's Modern Harmony is worth consulting.
[56] See also the strikingly original cadences in Debussy's L'Isle joyeuse.
[57] Another interesting eight-measure sentence may be found at the beginning of the slow movement of Beethoven's Eighth Sonata, in which every section differs from any one of the others; in the opening sentence of the first movement of the Tenth Sonata—noticeable for the indefiniteness of the cadences until the final close is reached in measure 8, and in the first sentence of the Allegretto of the Sixth Sonata which is one long sweep, with only the faintest indications of subdivision.