Influence of initial velocity of the hammer. Vertical axis - rebound deflection (d) of hammer in cm.; Horizontal axis - Distance (a) of impact from bridge in cm.
(W. H. George, "The Energy of the Struck String, Part II." Proc. Roy. Soc., 1927)
EDITOR MUSIC:
In the first place, Mr. Lang's position is not new but has been implicitly assumed by many, as by Lussy, and has been enunciated by Dr. Otto Klauwell in his "Musical Execution."
Dr. Klauwell says : The entire difficulty of execution (differentiated from technique) is reduced to a correct and appropriate conception of thesingle tones in regard to their duration and degree of power.
"To trace the finished execution of a piano-composition to the two external factors : Correct tempo, and rightly graduated fullness of tone, applied to the minutes sub-divisions of a composition."
This is the exact equivalent of Mr. Lang's "duration of tone and degree of power."
The net result of the "Symposium" of opinion upon the subject expressed by a half dozen and more celebrated teachers and pianists in America seems to be on the one hand, an acceptance of Mr. Lang's position unqualifiedly, or qualified only by the addition of the pedals to modify quality ; or, on the other hand, the re-assertion of the possibility of variation in quality of tone by the touch alone, by those who perceive a change in quality but who have only their perception, unsupported by argument to advance.
Mr. Foote's article adds the use of the pedals to thet resources of thepianist in the the variation of quality. That is a vital point to the player, but perhaps intentionally excluded from this discussion. The most tangible statement of the discussion and of its result is found in Mr. Kelso's article, where he says : "The theory advanced by some pianists that a clinging pressure on the key after it has been struck will bring out some hidden effect from the piano has not a scientific basis." This is, as I understand them, a fair statement of the position of all the writers. I am confident that the opposite is the fact, and that Mr. Kelso, in his statement, and his co-writers by implication, are entirely wrong.
It can be established beyond question that a certain touch for which the word "pressure" answers as a name not only does bring out a hidden effect from the piano, but that there is a know scientific basis for that effect. The word "pressure" related by its radical meaning to the word ex-press has been frequently used as decriptive of the touch used to produce the distinctively characteristic and melodic quality of the piano. Hummel says, in his Pianoforte School ; "The adagio requires expression and songdullness. The tones must by judicious pressure be made to sing." Klindworth's energetic English phrase by which to demand a melodic quality is : "Dig into the key." It is unnecessary to multiply examples of the statement of a touch principle which has long ago been discovered empirically and taught by the most eminent pedagogues. The following argument is the scientific proof of the verity of the perception which did empirically discover that principle.
The question is of the possible modification of quality of tone by touch alone. Difference in tonal quality has a very wide range, from the smaller difference between two equivalent voices singing the same tone, up to the greatest possible difference in any two instruments playing thesame tone. The quality of a tone is due to the proportion in which its overtones are present as component parts of thefundamental tone. Any device whatsoever which suppresses or reinforces any one or more of the overtones of a given fundamental must change the quality of that fundamental. This principle is clearly recognized in the very construction of the instrument. The seventh and ninth overtones (b flat and d of the fundamental C) are discordant to that fundamental. They are respectively produced by the vibration of one-seventh and one-ninth of the length of the C string. But it is an acoustic principle that the overtones normally produced by any division of the length of a string, will be suppressed if the string be struck by the hammer at the point of division. In consequence, the makers place the hammer in such a position that it strikes the string at just one-seventh or one-ninth of the string's entire length, and thus suppress the discordant overtones entirely. Here then, to begin with, is quality of piano tone changed and controlled by a purely mechanical device, based upon scientific principles! There is also another principle not recognized in the "Symposium," affecting the normal piano tone. It is an acoustic law that a fundamental tone dies away more rapidly than its overtones. In passage playing there is not time for the law to positively affect the quality of the tone for the better. But in slower playing, the meree continuation of the tone and the relatively faster diminuendo of thefundamental than its overtones, makes a positive difference in the quality of the tone.
As the distinctive quality of the tone of a given instrument depends upon the presence of certain more prominent overtones, it follows that whatever tone of that instrument which best exhibits its overtones, is the most characteristic tone thet instrument can produce. As a corollary, it may be noticed that so long as the piano had little sustaining power, passage-work with the simplest lyric effects was alone written for it ; but as its recent development has been chiefly in the direction of tone-sustaining power, composers have written in a new style, so as to utilize the new and most characteristic resources of the instrument. Passage-work must eventually be subordinated to this new capacity. Just here should enter the subject of Mr. Foote's article in the April number to which I refer, - and defer. And now, at last, to the gist of the matter.
If a ball be thrown against a wall and caught in the hand on its rebound, the force of the stroke against the hand will be a measure of the speed with which theball travels though the air. That speed, from the wall back to the hand will be in direct ratio to the speed from the hand to the wall. If the speed be changed from the wall to the hand, it must have been changed from the hand to the wall. If a greater speed exist, a greater force will be felt from the impact of the ball against the hand, but as the speed is equal both ways, a greater force must have been felt by the wall, and the rebound from the wall must have been quicker. Or to say it scientifically, its moment of contact with the wall must have been shorter. Just so with the piano hammer. The quicker the motion of the hammer up, the quicker its rebound and the shorter the instant of its contact with the string : and inversely. I risk prosiness to make that point clear. Dr. Helmholtz has discovered that the longer the instant of contact of the hammer with the strings, the more are the overtones excited and the fundamental supressed. This instant must obviously be very short in any case, but a complete vibration of a string is a very short time, and a small proporiton of that small time can alone be used to modify its character. If the hammer remained in contact with the string any appreciable time, it would stop the tone itself had started. Dr. Helmholtz' principle as verified with his usual accuracy is this : A hammer properly constructed can be placed against a string by a piano key movement so as to remain in contact with that string for an instant equal to one half the vibrational number of the first overtone of such string, except on the higher strings, where the instance of contact is equal to half the vibrational number of the fundamental tone.
If the one-lines "a" have 435 vibrations a second, its first overtone, - the two-lines a, - will have 870 vibrations per second ; one complete vibration of that overtone requiring one eight-hundred-and-seventieth of a second to complete itself. That one complete vibration is the protoype of successive vibrations of the same string. Anything which modifies that first vibration will modify the form of the vibrations through the entire tone. The pressure touch can modify the blow of the hammer so that it lies agianst this "a" string one seventeen-hundred-and-fortieth of a second. That instant of time, inappreciable by ordinary methods of observation, is yet one-fourth of the time of the first vibration of the tone, which vibration determines the character of its successors, and thus of the entire tone. This infinitesmal amount of time is yet large enough to become a stumbling-block to the contributors to the "Symposium." They have evidently mislaid some of thier fundamental acoustic knowledge or they would have remembered that a vibration is a very small thing, and may be affected by a very small cause, in itself too slight to discover itself to such very exoteric logic. Furthermore, the measured instant of time, varying with every tone of the key-board, during which it is necessary that the hammer lie against the string, is not the measure of the time of the necessary touch pressure upon the key. If it were, any of use who have implicit confidence in the possiblities of touch consciousness would shrink from the task of discriminating a pressure of one seventeen-hundred-and-fortieth of a second on "a" from one thirty-four-hundred-and-eightieth of a second upon its octave, and proportionally throughout the chromatic scale!
But touch consciousness applied to each key requires that the mind shall recognize the touch as a perception. That recognition requires the same time for every key and is dependent upon the rate at which the sensory nerves carry the sensatiion (pressure, in this case) to the brain, and its rapidity of perception of that sensation. In melodic playing, a pressure upon the key long enough to be recognized by the mind as pressure is necesary, and at the instant of recognition, may be relaxed. If the pressure be continued it can do no harm, but can do no further good. The condition arises just there. The first thing is to secure the recognition of the pressure-sensation. The natural exaggeration of the time of the pressure, even throughout the tone length, may have been used to exaggerate the sensation and facilitate its recognition of pressure. Only the intitial instant of that pressure can affect the tone, but a continuation to the point of certain recognition of the sensation can effect the player. The essence of the error in the subject Mr. Lang seriously proposes, and Mr. Sherwood and the others seriously discuss, is the confusion of thetime in which a vibration of a string may be affected, and the time in which the mental consciousness of a player may be affected. The former time is imperceptible ; the latter time may be as long as the player chooses. Mr. Lang's logic is to the effect that a stroke of lightning could not have torn a tree in pieces because it was not in contact with it long enough to be seen there, or as it would take a buzz-saw to rip it.
The method of touch necessary to secure that result is in all points as if the attempt were made to produce the tone by laying the hammer against the string without a stroke, - not really a possibility. The energetic pressure of the finger upon the key, with power originating in the forearm, without striking at the key surface at all, is a bald description of the method,. Such touch, empirically used by many, is the means by which, - according to no less an authority than Dr. Helmholtz, - the overtones of every piano tone can be excited at the expense of the normal fundamental. But as the relative prominence of overtones determines the quality of a tone, so this touch method does change the quality of the tone by developign overtones. Quod erat demonstrandum.
A most important corollary : more important than any other possible argument to prove the artistic capacity of the piano, is this : If the change of quality produced by one given method, empirically discovered long ago, is dependent upon a principle so obscure as to have escaped the analysis of such trained pianists and acute thinkers as constitute this Symposium, it will be well not the reject the testimony of our ear in relation to any other quality of tone we hear, or think we hear, merely because our crude analysis does not verifuy our perception.
Influence of initial velocity of the hammer. Vertical axis - rebound deflection (d) of hammer in cm.; Horizontal axis - Distance (a) of impact from bridge in cm.
(W. H. George, "The Energy of the Struck String, Part II." Proc. Roy. Soc., 1927)