I am aware that some theorists may object to the method of assigning the same position to say B♭ and A♯, on the principle that B♭ is lower in pitch than A♯. However, if the matter is thoroughly looked into, we shall find that the system of portioning out the fingerboard with mathematical exactness, and giving to the various groups the names of positions, is really under the control of another system. This system, which is found to be the chief factor both in singing in tune, and in giving the stringed instrumentalist the power of playing in tune, for want of a more comprehensive title might be named "relative pitch." The student if sufficiently advanced may easily prove this to himself in the following manner.
Reverse the usual position of the instrument, that is, instead of having the fingerboard turned away, place the 'cello in such a position that the whole length of the fingerboard may be viewed from before. Now endeavour to point out the position of any given note, it will be found that an entirely wrong conception has been formed of the distance between the intervals, and it will be almost impossible to place the exact position, where any isolated note could be sounded exactly in tune. Perhaps more success will be experienced in placing the position of a few of the easier divisions of the string, like the harmonic at the half-string, but strange as it may appear, the attempts to point out the exact positions of notes even in the first position, will, in nearly every case, be complete failures. If the reader has had much experience in teaching the 'cello, and has become accustomed to judge the distance of notes by eye measurement, he must be considered an exception to the above. This proves to us then that the eye has, or should have, nothing to do with gauging the distances to be leaped, or stretched, for the various intervals. It is here that a wonderful faculty is found to exist in the trained violoncellist; this faculty is obtained by the wonderful connection between the fingers and arm movement, and the "ear," or more correctly, the brain. At first sight it appears very wonderful how any given interval between two sounds may be reduced down to measurement, and have its tonal character represented by a physical movement, but with long practice the movements of the arm and fingers become so perfectly under control, and work in such sympathy with the brain, that the act of conceiving the character of an interval, and its production, seems almost to be accomplished by the same brain action. This applies only to the production of one note in relation to another, or to the position of a note in relation to a fixed position, and not to isolated notes. How then is the 'cellist to establish the pitch, and decide the position of an isolated note, if in such a high position that no guide is given to the hand, such as is noticed in positions like the fourth? Although pursuing this subject has the appearance of leading us away from the chief matter of the present chapter, it is of such importance to the instrumentalist to know exactly how to obtain any isolated note, and as it is so much more easily explained at the present stage, it will be better to consider it straight away.
The brain must have some basis whereon to build up an expectation relative to any isolated sound. Thus, if a solitary note is represented on the music page, say E♭, the brain not having any fixed sound whereby to place the tonality of E♭, no expectation is raised as to its probable pitch; to bring this to practice. A pianist striking the one note E♭, on the piano, would feel quite satisfied with the pitch of the sound produced, whether the piano should happen to be tuned a quarter of a tone either below, or above concert pitch. This statement is open to challenge by the upholders of the theory of absolute pitch; I am well aware that a few musicians have this gift of absolute pitch, and perhaps a greater number still, from long practice with one fixed sound—like the singing master with his C tuning fork—are able to guess the pitch of that one sound with moderate success, but for a musician to have the pitch of all the range of sounds so thoroughly established, as to feel a sense of disappointment if an isolated note was sounded either slightly above, or below concert pitch, is almost an impossibility, if such an one does exist he must be considered an exception to the above. It may be accepted as the general rule, that until one note is heard, no expectation is raised as to any given note. The 'cellist, therefore, not having any fixed notes like the pianist, would be completely at sea, especially if a composition should commence on a note in rather an awkward position, say on the E♭ above the A half string. If an introduction in the accompaniment preceded, the 'cellist would be able to tell after the E♭ was sounded, whether he had happened to hit on the right position, but it would hardly be edifying to the audience to commence the note slightly out of tune, and shuffle to the correct pitch, after the accompanying chords were struck, nor would they appreciate a series of introductory grace notes leading to the required position.
It is here that the faculty of gauging the distance of a known interval, taking the required note by a leap from some equally well known position, is brought into force. If the 'cellist has just previously tuned his instrument, the sounds of the open strings will be still fresh in his mind, dispensing with A, D and G, the C being the nearest related to E♭ will be immediately seized upon, and a conception of the interval to be leaped (a minor third above the third octave), will be firmly established. After this the process is chiefly mechanical, the move may be made from any position the exact locality of which the student is thoroughly acquainted with, exactly as if leaping from a note in that position to the required E♭, as—
(The bow not to touch the strings until the E♭ is firmly stopped with the third finger, the grace notes merely show from which position the leap is made.)
The student should carry out this principle for all difficult leaps, and not seek for the position by gliding up, or down to it. However "to return to our sheep," this system of relative pitch affects the performance of flat and sharp keys in the following way, as an illustration the different manner in which B♭ and A♯ is treated, although both being in the back-shift, or half position, will be demonstrated.
In the first bar of Goltermann's Cantilena (Example 32), the first finger is on A♯ in the back position, the character of the accidental following the B♮ is such, that the musician seems almost compelled to sound this note as near the B as possible. It would irritate a musician with a well trained ear, to have anything but the smallest interval between the two notes, he will therefore quite unconsciously make the A♯ as "sharp" as possible, which conclusively proves that there is not any necessity for forming two positions for these enharmonic differences.