ty and naturalness, and was later sanctioned by
acoustical law; the interval of a perfect fifth having one of the
simplest ratios (2-3), and being familiar to people as the first
overtone (after the octave) struck off by any sounding body--such as a
bell or an organ pipe. The Venetian composers, notably Willaert, had
also quite fully developed this principle of Tonic, Dominant and
Subdominant harmony in order to give homogeneity to their antiphonal
choruses. Even to-day these tonal centres are still used; for they are
elemental, like the primitive colors of the spectroscope. But
modulation, in the modern sense of a free shifting of the centre of
gravity to _any one_ of the twelve semitones of our chromatic scale,
was not developed and accepted until after the acoustical reforms of
Rameau, and the system of tuning keyed instruments embodied in that
work called the _Well-tempered Clavichord_ of Sebastian Bach. Both
these men published their discoveries about the year 1720.

[Footnote 25: In counting the measures of a phrase always consider the
first _complete_ measure,--_never_ a partial measure--as _one_.]

As we have just used the term _modal_, and since many Folk-songs in
the old modes sound peculiar or even wrong (hence the preposterous
emendations of modern editors!) because our ears can listen only in
terms of the fixed major and minor scales, a few words of explanation
concerning the nature of the medieval modes should here be given.
Their essential peculiarity is the freer relationship of tones and
semitones than is found in the definite pattern of our modern scales.
It is of great importance that the music-lover should train himself to
think naturally in these modes; for there has been a significant
return to their freedom and variety on the part of such modern
composers as Brahms, Tchaikowsky, Dvo[vr]ak, d'Indy, Debussy and
others, and some of their most individual effects are gained through
the introduction of modal types of expression. The following modes are
those most commonly employed in the formation of Folk-songs.

[Music: DORIAN]

[Music: PHRYGIAN]

[Music: LYDIAN]

[Music: MIXOLYDIAN]

[Music: AEOLIAN]

[Music: IONIAN]

The Dorian mode, at the outset, is identical with our modern minor
scale; its peculiarity lies in the _semitone_ between the 6th and 7th
degrees and the _whole_ tone between the 7th and 8th. An excellent
example of a modern adaptation of this mode may be found in Guilmant's