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
