note, say "D" on the piano-forte, which has to do duty for all the various kinds of "D," as well as those of "C double-sharp" and "E double-flat," must be so attuned as to form a happy mean between them.
If, then, in the extremely simple case given above, drawn from the triune system of scales and chords, exemplified in the most insignificant compositions, one may be led to doubt and difficulty, it is easy to understand that violinists and others prefer to follow blind rules, leading them to make, for instance, all notes with sharps, higher than their enharmonic equivalents in flats, and vice versa, in elaborate compositions, that would involve calculations of extreme complexity; or, in such cases, to follow their own subjective feelings rather than seek justification by mathematical proofs, especially when performing alone their own parts, and thus not called upon to act in conformity with others. In such cases, notes depressed, and having a downward tendency, are more depressed; and notes raised, which are aspiring, are made more elevated. The interval C: G flat would therefore be contracted, and that of C: F sharp enlarged in the following (frequently-heard) expressions:
| G-flat | F. | F-sharp | G. | |
| C | D-flat | and | C | B. |
The "C" in the first progression is also virtually a raised note, and the "C" in the second a depressed note, as may be seen by reference to the scales indicated by the terminating chords. The laws which musicians obey, consciously or unconsciously, in the ordinary routine of composition and performance, are very fascinating, and will ere long be systematized.
The three scales given above prove that the chord of A-minor, formed with two notes from the chord of C, differs in altitude from the chord of A-minor formed from the chord of the parallel A-major, by depressing the third; and also that the minor-third from the second to the fourth note of a scale is smaller than the remaining minor thirds. These facts seem to have escaped the attention of all writers on harmony, who bewilder students with elaborate arguments respecting the so-called "chord of the added sixth," that undermine their own theories.
Having now drawn attention to the use of the piano-forte, its evolution, longevity, ailments, etc., and compared it with the violin with reference to its vitality; having also shown some of the singular facts that are the common experience of piano-forte makers and tuners respecting the human ear, and the system of temperament, which has not been a hinderance to the course of modern art—let us now consider that remarkable phenomenon, the "peculiarity of the key," which remains, or is acknowledged to remain, by most candid persons, even now that equal temperament is universal, and that the pitch has been gradually raised.
