The harmony of the IIIds and 3ds in any of the foregoing systems for the changeable scale is so much finer than it can possibly be in the common Douzeave, that it seems highly desirable that this scale should be introduced into general use. But the increased bulk and expense attendant on the introduction of so many new pipes or strings, together with the trouble occasioned to the performer, in rectifying the scale for music in the different keys, have hitherto prevented its becoming generally adopted. To multiply the number of finger keys would render execution on the instrument extremely difficult; and the apparatus necessary for transferring the action of the same key from one string or set of pipes to another, besides being complicated and expensive, requires such exactness that it must be continually liable to get out of order. This latter expedient, however, has been deemed the only practicable one, and has been carried into effect, under different forms, by Dr. Smith, Mr. Hawkes, M. Loeschman, and others. But Dr. Smith's plan (which is confined to stringed instruments) requires only one of the unisons to be used at once; while those of the two latter nearly double the whole number of strings or pipes. It deserves an experiment, among the makers of imperfect instruments, whether a changeable scale cannot be rendered practicable, at least on the piano forte,[26] without increasing the number of strings, and at the same time allowing both the unisons to be used together--either by an apparatus for slightly increasing the tension of the strings, or by one which shall intercept the vibrations of such a part of the string, at its extremity, as shall elevate its tone, by the diesis of the system of temperament adopted. Were only 4 degrees to the octave, furnishing the instrument with 5 sharps and 4 flats, thus rendered changeable, there is little music which could not be correctly executed upon it. _Scholium_ 3. In the same general manner, may be found the best system of intervals, for a scale confined to a less number of degrees than that of the complete Enharmonic scale. In such an investigation, the numbers in Table IV. expressing the frequency of all such adjacent degrees as have but one sound in the given scale, must be united; and the temperaments _m_, _n_, &c. of the theorem, when belonging to concords whose terminating degrees are united to those adjacent, must be taken, not what they were in the complete scale, but what they become, considering them as terminated by the substituted adjacent degree.