harmonics out of a clear understanding of how to form them.

"There are only two kinds of harmonics: natural and artificial. Natural
harmonics may be formed on the major triad of each open string, using
the open string as the tonic. As, for example, on the G string [and Mr.
Sametini set down the following illustration]:

[Illustration: Musical Notation]

Then there are four kinds of artificial harmonics, only three of which
are used: harmonics on the major third (1); harmonics on the perfect
fourth (2); harmonics on the perfect fifth (3); and harmonics--never
used--on the octave:

[Illustration: Musical Notation]

Where does the harmonic sound in each case? Two octaves and a third
higher (1); two octaves higher (2); one octave and a fifth higher (3)
respectively, than the pressed-down note. If the harmonic on the octave
(4) were played, it would sound just an octave higher than the
pressed-down note.

"Now say we wished to combine different double harmonics. The whole
principle is made clear if we take, let us say, the first double-stop in
the scale of C major in thirds as an example:

[Illustration: Musical Notation]

"Beginning with the lower of these two notes, the C, we find that it
cannot not be taken as a natural harmonic

[Illustration: Musical Notation]

because natural harmonics on the open strings run as follows: G, B, D on
the G string; D, F{~MUSIC SHARP SIGN~}, A on the D string; A, C{~MUSIC SHARP SIGN~}, E on the A string; and
E, G{~MUSIC SHARP SIGN~}, B on the E string. There are three ways of taking the C before
mentioned as an artificial harmonic. The E may be taken in the following
manner:

Nat. harmonic Artificial harmonic
[Illustration: Musical Notation] [Illustration: Musical Notation]

Now we have to combine the C and E as well as we are able. Rejecting
the following combinations as _impossible_--any violinist will see why--

[Illustration: Musical Notation]

we have a choice of the two _possible_ combinations remaining, with the
fingering indicated:

[Illustration: Musical Notation]

"With regard to the _actual execution_ of these harmonics, I advise all
students to try and play them with every bit as much expressive feeling
as ordinary notes. My experience has been that pupils do not pay nearly
enough attention to the intonation of