# Popular Science Monthly/Volume 11/October 1877/The Modern Piano-Forte

 THE MODERN PIANO-FORTE.
By S. AUSTEN PEARCE, Mus. Doc, Oxon.[1]

MUSICAL instruments with manuals or key-boards, and fixed tones, occupy a most important position in the annals of modern art. All the greatest composers have been skilled performers on such instruments, and especially on the piano-forte. They are very greatly indebted to it; not that their works have been produced by its aid, or that it has been allowed to exercise a formative influence over their imaginings, but because of its companionship and sympathy. The creator of new musical forms, while engaged in his silent work—in the comparatively slow process of writing the individual parts for all the instruments employed in the orchestra—not only exercises the faculty of expression, but also the power to withhold. This power—this muscular strength of the brain, to grasp and retain whatever has been conceived, notwithstanding the perplexity as to means of expression, which commonly attends a crowd of ideas and feelings—is sometimes in danger of being overtaxed. On these occasions great relief is found by opening the piano-forte, and throwing off the piece at full speed on this plastic instrument. After realizing his ideals in this immediate and satisfactory manner, the composer returns refreshed to his patient labor—to the detailed record on paper of those emotions which fill him with such passionate energy. Or, should he wish merely to find relief in utterance—to commune with himself, and obtain recreation by driving temporarily from his thoughts the work in hand—then this comprehensive instrument, this miniature orchestra, enables him to extemporize elaborate contrapuntal forms, clashing cyclopean harmonies, or highly-involved melodic strains. The sounds thus evoked fall back on his delighted ear, exhibiting to him, in audible form, his psychologic condition. During these fleeting moments he thus beholds his subjective state, as clearly and definitely as in a mirror he would see, similarly reflected in visible form, the expression of his countenance.

But the piano-forte, by making domestic music at all times easily and immediately attainable, without the preliminary adjustments required for the harp or other stringed instruments, has become universally popular. Its literature is larger than that of any other, and whatever musical forms have found favor with the public are immediately adapted and rearranged for reproduction on it.

The piano-forte appears in four principal forms: as grand, square, upright, and curved, the latter being a newly-designed model, by Mr. J. W. Otto, of St. Louis, Missouri. The American grand piano-forte is, however, the greatest triumph of inventive genius and skill, aided by modern physical science; and this fact being acknowledged in all parts of the civilized world, foreign trade has been introduced to such an extent as to make the industry one of the largest in the United States. All the makers here daily strive for preeminence, and endeavor to surpass one another in the superior excellences of the smallest details, if not in the novelty and value, of their own respective inventions. No pains or expense are spared to obtain improvements, in the hope that these may, at least, lead to subsequent discoveries in the many untrodden paths of acoustical science. In this respect they resemble the old violin-makers of Italy, who also took a pardonable pride in their productions, which are the result of similar prolonged strivings.

The violin and the piano-forte, however, although in some respects similar, are in others widely different. The violin is endowed with perpetual youth. It even improves with age. The piano-forte does not. The violin is a mere shell of wood, modeled somewhat after a human shape, held together by glue, and strung with catgut; and although its various parts must be adjusted with great discrimination, and the bow with which it is excited be finely formed (having, for instance, a length of say twenty-nine and a quarter inches; weight of 900 grains; a diameter gradually decreasing, for twenty-three inches, from one-third to one-tenth of an inch, the curvature meanwhile increasing at an accelerating rate, to give a spring to the bow), yet this musical instrument, when compared with a piano-forte, appears as an extremely simple organism. It is more homogeneous, like all the other members of the numerous family of viols. The piano-forte, on the contrary, with its many kinds of wood, hard and soft, heavy and light; its many kinds of cloths and felts; of skins; with its masses of wrought and cast iron, steel, copper, brass, silver, lead, etc., is a more highly-complex production. It is heterogeneous, rather than homogeneous; and only by the most perfect coordination of all its parts does it retain an organization capable or worthy of preservation.

The piano-fortes of Erard, so highly prized for their extreme refinement and susceptibility to slightest variations of touch, are extremely delicate; and while other Europeans have succeeded in making more robust instruments, it has been reserved for the Americans the ability to endow their productions with constitutions capable of resisting, to any remarkable extent, climatal influences. The degree of their success, with reference to longevity, is not yet fully proved; and the variations in this respect are so great that it would be even rash to form an estimate, as we shall presently see. It is only safe to say that a piano-forte is never better than when it first leaves the hands of its maker. Like a young, impressionable being, it may then be made to suit special tastes and requirements. The readiness and extent of response to touch can then be determined, and the tones may at once be made fuller, rounder, sweeter, harder, more brilliant and penetrating, or more sympathetic. It is vain to hope that they will be mellowed or otherwise improved with age or use.

For it is a common experience that piano-fortes differ greatly in the ability to retain their good qualities, even though subjected to the same conditions. It is also noteworthy that, although many instruments may be made precisely similar, and by the same workmen at the same season of the year, all other known things being also equal, they will differ in their characteristics, as children of the same family mysteriously differ from one another, although retaining many marked points of resemblance. It should, therefore, not cause surprise that among the 30,000 piano-fortes annually produced in the States some will be found so admirably balanced, so happily constituted, and adapted to endure great "wear and tear," as to survive mutilation, railway-accidents, extremes of heat and cold, dampness and dryness, and yet remain surprisingly vigorous and strong. Engineers and others acquainted with the conduct of iron—in suspension-bridges, for instance—which does not uniformly granulate, will not be surprised to learn that three strings struck uniformly with the same hammer may break at widely different periods, after losing their tenacity from the insidious nature of vibrations, and then from thermal changes rather than blows. But here we are not merely speaking of the strings, but of the piano-forte in its entirety—as consisting of a great number of mutually-depending parts, coöperating to a common end and the harmonious working of all.

To trace the gradual development of the piano-forte, from all its various archetypes, would occupy too much space. It is sufficient here to point out that virginals, spinets, clavichords, harpsichords, and various new forms of old types of similar instruments, were found incapable of further improvement. In the "struggle for existence" they failed to compete with the piano-forte, which, although at first far inferior, has finally survived them all. During the past fifty years, modern science has materially aided in enlarging its powers, especially in America; and it now claims our attention as the ultimate result of a long series of modifications superimposed on modifications which have led to what Mr. Herbert Spencer might designate as "an immense increase in the harmony between the organism and its environment."

European piano-fortes introduced by the early settlers here soon became useless. The dry land-winds of the interior, the moist sea breezes of the coasts, the violent and sudden thermal changes, could not be endured. A new species had to be produced, for this one failed to become acclimated. The problem to be solved in those days was by no means an easy one. It was as difficult to improve upon the then existing piano-forte as it is to increase the capabilities of those we possess now. But the indomitable perseverance of sturdy souls led them to face the difficulties resolutely, and devise "new internal relations" to meet "new external relations;" to bring about, as it were, a closer "correspondence between the organization and its environment." They learned that the "degree of life varied with the degree of correspondence;" that along with complexity of organization there goes an increase in the number, in the range, in the specialty, in the complexity of "adjustments of inner relations to outer relations," in what may perhaps be termed "the evolution of the piano-forte."

Their first, rather uncouth-looking instruments, with enormously large, solid wooden frames, appeared as an "unmixed breed," and therefore so far stable. They did not succumb so readily to the climate, and even presented peculiarities that attracted attention in Europe. The native woods of which they were made were found to be better adapted to the climate; polish was used even for the sound-boards, in preference to varnish, which evaporated, and other slight changes were adopted with great benefit. Yet still the requisite degree of strength could not be obtained from wood alone, and the comfortable classes using pile carpets, heavy curtains, soft cushions, and other warmth-retaining substances in their drawing-rooms, demanded a piano-forte that could make itself heard in the presence of so many deadeners of sound. Iron was then employed in combination with wood, but, the action of the two materials being by no means uniform under constantly-changing conditions, the desired equilibrium was not gained. In some instances the transverse swelling of the wood fractured the iron plates. Although this "mixed constitution" failed to meet the requirements then, the combination is now better understood.

The first intention of the application of iron—of the harp-shaped metallic ring—was not to enable the instrument to endure the constant strain of the strings. It was supposed that the metal would expand and contract uniformly with them, in the severe changes of this climate, and that in this manner the instrument would remain longer in tune, although the actual pitch might vary.

In 1837 the highly-skillful American maker, Mr. Jonas Chickering, conceived the bold idea of constructing a frame entirely of iron, and in the same year made his first square piano-forte in this way. In 1840 he produced the first grand piano-forte with an entire iron frame all in one casting. By this remarkable invention the piano-forte gained in truth an "iron constitution," competent to bear the atmospheric changes of this climate, and to it all subsequent successes are referred.

It was a great achievement to obtain a frame capable of resisting the enormous strain of the strings, but this advance imperatively led to innumerable variations being made in various details, for the attainment of an equilibrium, without which the promised gain could not have been fully realized. The softer tissues still remained of wood of various kinds, and other such essential materials. With the acquisition of an iron frame or vertebra equal to the tensile strain of thirty tons without danger of fractures, came the temptation to employ strings of greater thickness, with a tension of from eleven to sixteen tons. These strings, stretched as near as possible to the limit of elasticity, that they might give forth the most vigorous vibrations, required to be set in motion by blows from hammers specially adapted for the purpose. (Voices similarly strained on the highest notes within their compass also have the most brilliant quality, as for instance the "G" of Mr. Santley and the chest "C" of Tamberlik.) Then, again, the increased powers of the instrument made greater demands on the sound-board.

If we compare the vibrations of the violin, set up by the comparatively gentle friction of the bow, with those of a piano-forte sound-board, violently trembling in response to strong percussive accents, and the multitudinous and continuous vibrations of long, thick metallic strings, it is at once evident that they are of a more extraordinary nature. Great discrimination was used in the selection of the wood from the spruce-trees of the Northern forests; many experiments were made to discover which way the grain of the wood should be disposed, and. in what manner the sound-board should be compelled to receive and transmit impressions without fear of such derangements as should lead to a state of paralysis. To make it act most energetically the fibres were permanently compressed longitudinally, as in a vise, up to a certain point, similar to the strings, which, as we have just now seen, give forth tones of most satisfactory quality when stretched to the verge of breaking. There is a readily-found precise limit to this compression, after which the tones become hard and thin in quality. The sound-board is now also slightly curved, forced upward or made convex that it may resist the downward pressure of the bridge that holds the strings slightly elevated from their level, to secure a complete and intimate communion for the transmission of vibrations. It is clear that, if, from any cause, a sound-board should become concave, or loose at any of the sides, serious consequences would ensue. Considerations such as these sufficiently prove that the attainment of a perfect harmony among the parts, to resist successfully external influences, was no slight undertaking.

The American piano-forte has, however, attained a constitution that will endure dryness, cold, and even furnace-heat, but succumbs to excessive dampness. A good instrument, dried to the utmost, rapidly absorbs moisture. The well-fitted parts, having no room to swell, then become rigidly bound together, and thus the action is destroyed. It would therefore suffer if placed in a room having no sub-cellar, under which water-courses might be formed after rains. An inferior instrument made with damp materials and kept damp by judicious sprinkling, ostensibly to allay dust, might thus successfully compete with a good instrument during an ordinary public exhibition, although it would soon prove worthless.

Varnish is now used for sound-boards and cases, both here and in England.

The constitution of the English piano-forte enables it to bear the English climate, in which the humidity is more uniform. When brought here it breaks down. But even the American piano-forte can only to a certain extent bear the trials from climatal changes to which it is subjected, and for a very limited space of time in some parts of the States, as, for instance, the Rocky Mountains. If a good instrument, made with native woods, seasoned for two years in the open air, and kiln-dried for three months at 130° Fahr., be removed in winter, while the thermometer is at zero, and placed in a heated concert-room, the sudden rise in the temperature, causing dampness, would affect the glue as well as the wood-work. But when organic derangements are not caused, a host of minor ailments set in which impair and gradually destroy a piano-forte. The metals corrode, the strings break, the pins holding the wires relax their hold, and then turn round (in inferior instruments), the felt on the hammers becomes worn, the damper actions rattle, the various centres loosen, the hammers (that deliver the blow before the key is fully down, and then immediately retire from the string, to allow it to vibrate and take up such a position as to deliver a number of consecutive blows with rapidity) may act with irregularity, or without the requisite vigor, and moths may attack the felt and cloth. Although many of such ailments yield to treatment, yet they are unmistakable signs of general decay. In forming an estimate, however, of the longevity of a piano-forte, one should reflect on his growing insusceptibility to sensuous impressions, and not institute comparisons with newer instruments of greatly-enhanced capabilities. It is well also to point out that sometimes articles of furniture, free to vibrate, wall do so in sympathy with certain notes of the instrument, and thus make a supposed defect. Articles, such as a stiletto in a metal sheath, or a glass globe on a gasalier, are not readily detected in the act of responding.

On comparing piano-fortes by various makers it is well also to bear in mind the special peculiarities of each. The makers of the Erard piano desire to produce a brilliant, ringing effect, and do not destroy the numerous, tingling overtones which succeed the cessation of their primaries. Sensitive artists, who desire an achromatic quality, object to these, although they are intended to add a kind of harmonic halo or lustre to the general tone, which in a crowded drawing-room might appear dull and lifeless—wanting in radiance and animation. The Broadwood makers strive for the formation of a full, organ-like tone. The Collards are successful in obtaining flute-like and liquid tones, which in the treble are remarkably sweet and dulcet. The German piano-fortes are generally rough and unfinished in mechanical details when compared with the French, although the tones are stronger.

Yet neither bear comparison with those of America. These also, among themselves, present marked characteristics. One maker prides himself on the magnitude and power of his instruments, and their fitness to be employed with the orchestra in large halls; another on the delicacy and extreme purity of the tone, which he deems can only be attained from instruments intended for the drawing-room or halls of moderate size; a third may try to obtain a "traveling-power," which quality is so markedly deficient in many upright pianos and in free-reed organs, as compared with grand piano-fortes and pipe-organs, that always sound better when at some distance. Great attention is always paid to the material and form of the hammer, which is found to produce the best tone when covered with soft felt, made of the wool of the merino sheep. This Saxony wool is worked here by Germans. Great care is also paid to the spinning of the covered wires, and the consistency of all the others to avoid defects that would lead to beats, and deceive the tuner.

Much experience and practical skill are required in the designing of the scales, or elaborate balancing of. length, weight, thickness, material, and tension of the strings, to secure uniformity from bass to treble, while conforming to a given length of case, although the design may be planned in accordance with the mathematical theories of stretched strings. Then, again, the point where the blow is to be delivered is carefully chosen, that objectionable nodes may be destroyed. For the same reason wedge-like dampers are employed to check vibrations, and are made to act at a point where subsequent dissonant overtones may be rendered impossible. For the want of this last precaution, an otherwise valuable upright piano-forte, by a prominent firm in Germany, was pronounced a failure in London, some years ago. On striking any one of the bass notes, and then raising the key, after a short interval of silence, the harmonic seventh was generated; and this was no weak, vanishing tone, but a strong, continuous sound resembling that of a musical glass.

On studying the detailed accounts of new patents for improvements—real or imaginary—on comparing the statements of rival makers, or on being persistently contradicted by interested experts, one learns the difficulty of forming an opinion on points at issue, having reference to the advantages gained by alterations in the mode of constructing piano-fortes. It demands considerable special knowledge even to fully comprehend these points. One should carefully avoid expressing opinions that might tend to affect values, and be content with the reflection that the public at large is well enough informed to know that only. those firms possessing the requisite capital, intelligence, and experience, can produce an intrinsically valuable instrument. Cheaply-made piano-fortes are mostly sold to ignorant persons, living far from the great centres of civilization.

It will be found interesting to notice some of the facts learned by those who have conducted experiments in the hope of improving the piano-forte, for many of these are somewhat peculiar, and contrary to general anticipation. Thus: Chladni's figures are not formed by sand strewed on the sounding-board; nor does the sand travel from the point where the shocks or impulses are imparted to this vibrating body, but collects at this very point, namely, close to the bridge. Again, no difficulty is experienced by "interference," when two or three strings tuned in perfect unison vibrate side by side; nor from overstringing the bass wires. The fitting together of trough and crest of sound-waves—the coincidence of the "swing" and the "swang," which cancels both, and forms the hyperbolic curve of silence on the outer broad side of each prong of a tuning-fork, is a phenomenon that does not appear in any portion of the scale. Nor does that which is termed "sympathy," that occurs when two organ-pipes stand too near each other, require consideration from the designer of a piano-forte. The addition of a second string, far from destroying the vibrations of the first, or even interfering with them, more than doubles the power of the tone. A single string gives forth a comparatively insignificant and feeble note. When three strings are used, the third does not add half as much again, a fourth string adds still less in proportion, and, judging from the quality of the tone produced, seems to require an entirely new design.

In the final adjustments of the piano-forte by men of extremely keen sensibilities, certain defects, limitations, and peculiarities of the human ear, have been discovered that are noteworthy. The Greek architects well knew that long horizontal lines, if straight, would not appear to be straight when viewed from below, and therefore in the Parthenon they executed exceedingly delicate curves. Their columns were not exactly cylindrical, and many similar and most subtile deviations from geometrical truth were employed that remain as evidences of their consummate skill. In music, also, certain nuances—deviations from rigid accuracy or mathematical truth—are constantly made by which the powers of true artists are manifested. These minute shades of difference—these slight variations or modifications of quality of tone, power of tone, pitch, speed, etc.—when not exaggerated, but determined with an art-concealing art, are found to be true to Nature, and find their justification, not as exceptions to general rules, but as exemplifications of the highest principles. The refined perceptions of piano-forte finishers have led them to the fact that the highest notes of the instrument should be tuned slightly sharper than perfect, or each note will appear to be flat, when compared with the octave below. If these notes are tuned perfectly, and proved to be so by various tests, there still remain a secret dissatisfaction and consciousness of a certain dullness, which detracts so much from the good effect of the instrument as to lead some persons to suppose it to be one of inferior quality. The expedient, therefore, of slightly raising the pitch of about seventeen of the highest notes (when the piano-forte is extended to high C) is adopted, by which the instruments gain greatly in brilliancy, briskness, sprightliness, or whatever term may fitly denote the reverse of flatness and insipidity. Octaves tuned in the middle of the key-board are frequently deemed perfect when too small, and some few students of tuning are prone to accept as true, octaves that are too large in this region of the scale.

But by far the most extraordinary fact, with reference to the final adjustment of the piano-forte, is the general acceptation of its particular "temperament" for all instruments having twelve notes to each octave. Whatever other temperament may be chosen for such instruments, only one simple, natural diatonic scale can be properly rendered. With this arrangement, called the "equal temperament," not a single chord is correctly tuned. No intervals are made absolutely perfect, but the ear has gradually been led to be content with them, when they approximate the truth in conformity with this particular system. By the equal distribution of the many kinds of apotomes, found on calculating intervals from the scale given by Nature's super-harmonics, they are subsequently practically disregarded—treated as non-existent—and thus elaborate modulatory harmonies are rendered comparatively easy to construct; and the human ear being less able to detect imperfections in dissonances than in consonances, composers have gradually employed, with increasing freedom, dissonances of the most unusual and startling kind. It would not be strictly true to say that modern writers have neglected the sweet, cloying style—abounding in pleasant-sounding phrases—because the absolute perfection of these ready-made, dissonant harmonies is more readily overlooked. The influences that have determined the course of modern art can only be perceived from a psychologic point of view. We may, however, safely say that modern composers have not been deterred, but rather assisted, if not actually emboldened, by their enharmonic intervals being made freely interchangeable, their far-fetched harmonies easily found and little scrutinized; and point out that the dynamic power of discords increases their present value as artistic materials, now that fugal and similar forms, compelling progress, are more rarely used.

The temperament of the piano-forte led directly to the entire remodeling of the "king of instruments," the church-organ; but yet, not without considerable strife. During the first three-quarters of the present century this particular form of temperament was a matter that greatly exercised mathematicians, organ-builders, musical purists, clergymen, and organists, in England, and has only now become generally adopted in that country. The solid and highly-compound tones of the organ, sustained with equal energy, caused the imperfections of the concords to be markedly apparent. They could not be ignored, as when occurring with the evanescent tone of a piano-forte. The super-harmonics, or summation-tones, disagreeing with each other, developed, in common with difference-tones, a mass of attendant dissonances, which even the employment of a double foundation (sixteen-feet manual stops) and powerful pedal-organ, etc., could barely hide.

The music of the Church was then as calm and free from passion as the sculptures of Phidias; no exciting dissonances held the listener spellbound until they were resolved. The organ-builders, accordingly, produced instruments that were solemn, sedate, serious and grave, forcible and powerful, without betraying passion or the flutterings of private, personal emotion. To use this temperament would be to destroy these features, which the piano-forte-makers did not desire to retain. They sought brilliancy and contrast for secular requirements, and were at once manifestly gainers by the system; while the organ-builders were compelled to reflect very seriously on matters of ritual and their own reputations.

To make this clear: Let the length of a stretched string be represented by unity, and 12 or 64128 the octave. Now, three major-thirds are less than an octave; for 45 ${\displaystyle \times }$ 45 ${\displaystyle \times }$ 45 ${\displaystyle =}$ 64125. Again, let 12 or 6481296 represent the octave, and it will be seen that four minor-thirds are greater than an octave; for 56 ${\displaystyle \times }$ 56 ${\displaystyle \times }$ 56 ${\displaystyle \times }$ 56 ${\displaystyle =}$ 6251296.

The contraction of the minor-thirds, therefore, by one-fourth of the ratio 625 to 648, caused a further depression of the significant note in the minor-chord, by which it became more gloomy and depressed; and the expansion of the eloquent major-third by one-third of the diesis, or ratio of 125 to 128, caused the expression of joy in the major-chord to be exaggerated or intensified, or even over-excited, when compared with the peaceful, contented, restful character of the pure harmony.

These violent contrasts affected the quality of the tones, not individually, but when heard in combination. The general character of the tone-tint was thus greatly modified.

That the ear is much more sensitive to imperfections of intervals with simpler ratios is proved by the uneasiness experienced while a violinist tunes his strings to the interval of a fifth (23). Twelve such fifths exceed the octave by an interval having the ratio of 524.288 to 531.444. Each successive fifth must, therefore, be contracted one-twelfth of this interval (or diaschisma), that the series may be bounded by a perfect octave; and in this manner the tonal system of keys, which is in reality a slowly-ascending infinite spiral, practically takes the form of a circle. This fact must be borne in mind if one would satisfactorily account for many laws of art. The ideal purity which enraptures the creative artist is never realized; for all performances are marked by the imperfections attending human efforts.

That a general compromise, or sacrifice of truth to convenience, must be made in instruments having twelve fixed tones to the octave, will be seen by a comparison of three most closely-related diatonic scales, and their respective proportions:

 G. 240 A. 213⅓ B. 192 C. 180 D. 160 E. 144 F-sharp. 128 G. 120 C. 360 D. 320 E. 288 F. 270 G. 240 A. 216 B. 192 C. 180 D. 160 E. 144 F. 135 G. 120 F. 540 G. 480 A. 432 B-flat. 405 C. 360 D. 324 E. 288 F. 270 G. 240 A. 216 B-flat. 202½ C. 180 D. 162 E. 144 F. 135 G. 120

It is clear to the meanest comprehension that the sound "D," the second note of the scale of "C," differs from "D," the sixth note of the scale of "F;" and also that the sound "A," the sixth note of the scale of "C," differs from "A," the second sound of the scale of "G;" and similarly, in the ratio of 80 to 81.[2] It is evident that any 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.

In the English translation of Bombet's "Life of Haydn" a list of the keys is given with their acknowledged characteristics appended. Thus: "D-flat major. Awfully dark. In this remote key Haydn and Beethoven have written their sublimest thoughts. They never enter it but for tragic purposes." Again "A-flat major. The most lovely of the tribe. Unassuming, gentle, soft, delicate, and tender, having none of the pertness of A in sharps. Every author has been sensible of the charm of this key, and has reserved it for the expression of his most refined sentiments." And so on. Now, it was never supposed that the peculiarities of the keys could be confused with the peculiarities of the old modes, such as Dorian, Phrygian, etc., which led Dryden to say, "Softly sweet in Lydian measure;" for all these modes were designedly, mathematically, and markedly, dissimilar. But it was generally supposed that the "unequal temperament," which favored some keys at the expense of others, led to the various, otherwise unaccountable, characteristics. These, however, have remained, singularly enough, with the "equal temperament," by which system all the keys are equal—i.e., the ratios of their intervals are precisely similar.

This peculiarity of the key is not to be confounded with other, accountable differences: such as induce composers to write in flat keys for military bands to attain the greatest brilliancy, and in sharp keys for orchestras for the same end. In these cases the greater number of open notes (more naturally and simply formed tones), and other such known facts, lead to a clear understanding on this point. But in the piano-forte no such considerations can be made to account for the subtile phenomenon. It was once supposed that the absolute pitch employed was the cause of the difference; but since the time of Haydn the pitch in all countries has risen to such an extent that the scale of A-flat characterized above has become virtually the scale of A-natural, with which it was there compared; but no corresponding variation of opinion respecting it has been recorded. Ladies still commonly express a decided preference for flat keys, and probably for this reason fashionable drawing-room music is generally cast in four or five flats—although these keys may be also chosen partly because, according to the conformation of the hand and the disposition of the ivory keys, the chords with flats are more easily and readily controlled, especially when distributed in the arpeggio style, and have to be played with great speed, freedom, and facility. But the various attempts made to account satisfactorily for key-character on the piano-forte have hitherto only demonstrated that reason and understanding are incapable of fathoming and explaining the matter.

The piano-forte of the present day is, as we have seen, the result of many contributions. Posterity alone can pronounce judgment upon it, and show in what it is deficient; for who shall say what the "piano-forte of the future" will be? We ourselves complacently regard our age and its works, while anticipating the constant progress of the human race and its increasing ability to "reveal itself in tones."

1. Lecturer on Harmony and the Science of Music, at the General Theological Seminary, New York; Musical Director of Columbia College Glee-Club, etc.
2. The relative speeds of the vibrations of each note of the diatonic scale are here given for the convenience of persons accustomed to calculate by their aid.
 264 297 830 352 396 440 495 528

The true diatonic scale may be represented in various ways, which may occasionally prove useful in measuring intervals, although the divisions are not exactly correct. Such as—

 ASCENDING SCALE. 1. The Periphery of a Circle. 2. 53 Degrees. 3. 301 Degrees. 4. 730 Degrees. 5. In Mean Semitones. C. 33° 31" 11’ 10 56 136 1.1173 B. 61﻿10﻿22﻿ 27 153 372 2.0391 A. 54﻿43﻿16﻿ 16 92 222 1.8240 G. 61﻿10﻿11﻿ 27 153 372 2.0391 F. 33﻿31﻿11﻿ 10 56 136 1.1173 E. 54﻿43﻿16﻿ 16 92 222 1.8240 D. 61﻿10﻿22﻿ 27 153 372 2.0391 C. . . . . . . . . . . . . . . . . . . . . . . . . . .

But the logarithms of the ratios of the intervals are most generally used. The logarithmic or equiangular spiral best illustrates to the eye the return of the octave, the curve

being so drawn that a complete revolution halves the distance from the pole. It is also valuable for other properties besides this geometric periodicity, representing a continuously-rising tone.