Absolute trueness;
2. Temperate trueness;
3. Passional trueness.
Absolute trueness is that adopted by theorists, who divide the gamut
into five notes and two semi-notes; the note into nine commas, or shades
of tone; the chromatic semi-tone into five, and the diatonic semi-tone
into four.
Thus from C to C# they count five shades of tone; whereas from C to Db
they count but four. Likewise, from D to Db they count five shades of
tone, and from D to C# but four.
[Illustration: Absolute scale]
The difference of a comma between the D flat and the C sharp, seemingly
a very slight difference, is, nevertheless, most important in singing,
as we shall see later on. But performers, to simplify our musical
system, have divided this comma into two, making synonymous notes of D
flat and C sharp; that is to say, notes having the same sound. The note
is, therefore, practically divided into two semitones of four commas and
a half. This is what is known as moderation or temperate trueness.
[Illustration: Temperate scale]
Temperate trueness is defective from many points of view. This is the
universal opinion, but we are forced to accept this method by the
absolute impossibility of any improvement, especially with the key-board
instruments now in vogue; and it must be accepted until some new
invention shall revolutionize the piano by modulating its tones, a
transformation which would give that instrument not only the musical
design, but also the color and warmth which it now lacks.
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