"Would I care to discuss any special feature of violin technic? I might say something anent double harmonics--a subject too often taught in a mechanical way, and one I have always taken special pains to make absolutely plain to my own pupils--for every violinist should be able to play double 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]:
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:
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:
"Beginning with the lower of these two notes, the C, we find that it cannot not be taken as a natural harmonic
because natural harmonics on the open strings run as follows: G, B, D on the G string; D, F♯, A on the D string; A, C♯, E on the A string; and E, G♯, 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--
we have a choice of the two _possible_ combinations remaining, with the fingering indicated:
"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 harmonics. In other words, they try to produce the harmonics _immediately_, instead of first making sure that both fingers are on the right spot before they loosen one finger on the string. For instance in the following: [Illustration: Musical Notation] first play [Illustration: Musical Notation] and then [Illustration: Musical Notation] then loosen the fourth finger, and play [Illustration: Musical Notation]