by pedals, one for each key, which put the organ in tune for its own scales. It could be played without the player knowing what sounds he used-he only needed to keep the organ in the right key. Gen. Thompson justly remarks that his system would have merits over ours, in compelling a musician to know what he is doing. But in the dark days of enharmonic science it may be excusable not to demand too much of the organists.

16. There are great difficulties which present themselves in admitting to a key-board the multitude of sounds required if several transpositions or signatures are to be played in. If the five series of sounds already described, § 12, are carried into the keys from nine flats to nine sharps-nineteen signatures-just one hundred notes to the octave are required! But an octave is limited in width by the span of the fingers. Six and a half inches is about the convenient average measure, and this is adopted by organ and piano-forte makers. If the notes we want are divided equally into this space each will get the hundredth part of it, or sixty-five thousandths of an inch. The pins of a barrel organ might play upon them, but with human fingers it is hardly possible.

17. But there is a fortunate circumstance in the relation of the sounds which comes to our aid. All are not wanted at the same time; when we are near the key of nine sharps there is no possibility of our requiring the notes of nine flats. These we may arrange therefore at a distance front or back, and place near by the related notes which may be required in connection with those already in use.

18. At least seven finger-keys should be in convenient relation to each other, and of sufficient size and position to allow of their being touched, and for the changes of fingers necessary in running scales and taking chords in different positions. Such a key-board I have endeavored to devise, the result of which may be seen from the following description and figures.*

19. The first point I took in the resolution of the problem was, the convenience of the broad white ivory keys of the common key-board, and the elevated black keys-the white especially affording room for shifting the fingers, and the raised keys making it easy to touch a narrow key, which it would be hard to do if all were in one level. The second: that the keynotes and the thirds, being of different classes, might be assigned to these two classes of finger-keys, naturally giving to the first class the more extended keys, or the white. So the octave ought to have its seven notes. Pieces of bristol board were cut to the width of the common white keys, or nearly an inch, and in length double that of the part in front of the black keys.

* At the time of writing (April, 1867) I have made application for a patent for this key-board.

With the same material I made elevated black keys of the width and height of those of the common key-board, and of the length of 2.7 inches, which were arranged in hopes of getting at least the diatonic scales, triple and double, which could be easily managed, and in a manner uniform for all keys.

20. This provisional key-board is not figured here, but may be understood by reference to figs. 1, 2 and 3, which contain also the additional series of sounds, IV and V, § 12. In fig. 1 let the black key, d, be moved to the left until its left edge coincides with the right edge of C, its back end as now being in contact with the front end of the white key D; let e, f#, and the two keys (F' and another not marked but really Eb') marked with vertical lines indicating their color, red, be moved in the same direction and distance as d, till they are in contact, respectively, with D and E. There is no room now for d# and d and their two companions by f#, but we have all the key-notes, thirds and perfect sevenths, and the advantage of greater width in the white keys, which are nearly an inch and a quarter wide (1.21 in., the black keys being 0:45). This key-board, although deficient in the minor mode, from the absence of the series IV and V, is still recommendable where economy is necessary, as all the music of the major key, including the beautiful chord of the seventh, can be played; except in cases where certain accidentals are introduced from the minor mode, as illustrated in the example from Rossini in § 8.

21. A portion of the complete enharmonic key-board is shown in perspective in fig. 1, in the natural size-the length of the keys being reduced to one-half by the perspective. The keys are of five different colors-represented here, the white and black by their natural colors, and the rest according to heraldic rules, viz., the red by vertical lines, the blue by horizontal, and the yellow by white stippled with black-and of as many different elevations. The following table represents this.

22. These keys all have vertical rectilinear motion so that a touch on any part of their surface produces always the same effect. This is attained-in one method-by attaching each to a pair of guiding rods, passing down through a couple of horizontal tables where they are secured to a piece which communi

AM. JOUR. SCI.-SECOND SERIES, VOL. XLIV, No. 130.-JULY, 1867.

cates in the usual manner with the valves or hammers.

It will be understood that the mechanical construction of the instrument beyond the key-board may be the same as usual, except that its number of pipes or strings must be multiplied.

23. As the assemblage of all the notes may confuse the eye at first sight, I have drawn on half scale the plan of the fingerkeys which in every signature-or commencing on any white key whatever-give the triple and double diatonic scales. The white keys are of the width of 0.993 in., the black keys having the width of 0.45.* The white keys on the common key-board are but 0.93, or the seventh of 6 inches. The plan in fig. 2 will enable a player to judge whether the scale can be executed. It is immediately intelligible even to a child, who, having learned the order in one key, knows it in every other. The keys are considered by their relations to each other, that is, as Do, Re, etc., and (to repeat it again), Do may be taken on any white key. The fingering in the triple diatonic scale is the same as in that of the natural key, and of others, on the common key-board, and the fingers easily reach the keys and change on Fa and Do as in the latter case. In the following scales the usual signs represent the thumb and four fingers; see fig. 2.

TRIPLE DIATONIC SCALE-Its fingering.

Do RE mi FA SOL la si

+

1

FA

1

2

3

+

Do

1

2

3

4 (or +)

1

2

FA 3

2 +
DOUBLE DIATONIC SCALE-Its fingering.
SOL la Se Do RE mi
+

The player is recommended to complete the octave, Fa to Fa, by copying the four lower keys, Do, Re, mi, Fa, figs. 2, 3, and placing the lower Do upon the upper one, or by conceiving that this has been done. This will show the double scale in its regular order.

24. I regret that the limits of these pages did not allow a larger portion of the key-board, and permit reference to it in the manner of taking the several chords in their various positions. But I think that those interested can extend the diagrams by the data given, and I shall, therefore, give the fingering for several chords, which being understood in one key will be the same in all transpositions.

The widths are established thus: first determine the width of the octave, and that of the black keys. Representing these respectively by O, and b, the width of the white key (W), is obtained thus: +=W. For the

O+b

key-board for major

Fig. 2.-A PORTION OF THE ENHARMONIC KEY-BOARD, SHOWING THE RELATIVE POSITION OF THE FINGER-KEYS WHICH GIVE THE TRIPLE AND DOUBLE DIATONIC SCALES IN EVERY KEY OR SIGNATURE, OR TAKING DO ON ANY WHITE KEY.-Scale of one-half. The white and black keys are represented in their natural colors; the red keys-perfect sevenths -by vertical lines; the blue keys-dominant thirds in the minor mode-by horizontal lines; the yellow keys-dominant sevenths in the minor mode-by white stippled with black.

Fig. 8.-SECTION THROUGH A B, OR THROUGH THE THIRD QUARTER OF ANY KEY-NOTE, EXPOSING ALL THE NOTES OF THAT KEY BOTH IN THE MAJOR AND MINOR MODES.

9:10

20:21 7:8