Abstract
Some say that pianists are human and quote the case of Harry Truman.
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Change history
18 July 2020
The inadvertently published equations have been corrected as mentioned below.
Notes
- 1.
Chris Robinson (private communication) noted that one reason the early pins tended to move upward was that they were not threaded. Hence, the early tuning keys had a hammer head on them to permit driving the pins back down—thus the origin of the term “tuning hammer” which persists to the present day.
- 2.
The above description, of course, assumes that the strings are only vibrating in the vertical plane. As Weinreich (1977) noted, if the top of the hammer is not perfectly horizontal, the strings may also be excited to vibrate in the horizontal plane, in which case there is much smaller coupling (e.g., ≈10 dB less) to the bridge. Hence, a longer-lived component with very much smaller energy may also be excited through that mechanism with poorly voiced hammers.
- 3.
Chris Robinson (private communication) noted that some piano tuners deliberately keep the unison strings slightly out of tune to preserve the decay time of the instrument. [The necessary detuning at middle C would only be about 0.5 cents. WRB]
- 4.
Taub (2002, p. 34) points out that one can also obtain a slight crescendo by depressing the normal right-hand pedal after the notes are struck, but that, of course, is a very different effect than the one discussed in the text. Taub (p. 47) also suggests obtaining a “crisp fp” by depressing the keys rapidly to create the forte, immediately releasing them and then depressing them again immediately so that the dampers rise quickly allowing the strings to vibrate further at decreased amplitude. That is really the inverse of the crescendo effect discussed in the text (which perhaps should be designated pf.)
- 5.
The ones I’ve heard personally sounded as if the strings were actually struck by “steins” (i.e., rocks).
- 6.
The pedal mania reached a climax in the instruments built by Conrad Graf in Vienna during the early 1800s, some having as many as six or seven pedals. Usually, two would split up the dampers between bass and treble. According to Taub (2002, p. 42), Beethoven only mentioned that device once (in the score for the Sonata, Opus 53) and said not to use it. Some pedals were designated “bassoon stops” and pushed a tissue-paper-like structure onto the strings. Another, the “Janizary stop,” would thump the sound board with a leather glove and in some cases ring a bell for use in “Turkish marches.” There is currently a multi-pedal Graf instrument in Ferdinand Schubert’s apartment in Vienna, but the composer himself was too poor to afford any piano. Franz spent his last days in his brother’s apartment. (See Neumayr 1994, p. 407).
- 7.
Taub 2002. (See, especially, Chapter 7, “The Myth of the Authentic Pianoforte.”)
- 8.
Karl Reichardt in his Vertraute Briefe of February 7, 1809 (see Thayer and Forbes 1973, p. 461.) It is not clear how this request fits in with the octave glissandos Beethoven wrote in the Waldstein Sonata and the C-Major Piano Concerto. I know one pianist who spent many weeks pricking her fifth fingers just to develop calluses sufficient to permit playing those glissandos on a modern Steinway. Artur Schnabel and Rudolph Serkin would discretely lick their little fingers to ease the slide. Rosen (2002) suggests adding lubricant to the vertical pins at the front of the keys. Teflon sprayed on the hammer-shank knuckles also helps.
- 9.
The New York Times, May 14, 2000, p. AR 37. But according to The New York Times, June 15, 2003, p. NJ 9, Mr. Taub may have changed his mind.
- 10.
The agraffe also serves another beneficial purpose that is not generally appreciated: the strain on the string is usually largest at that point, where there is a bend in the wire. Consequently, when a string breaks under the high tension in a modern piano, it is usually at the player’s end of the instrument and the whip action of the loose wire goes toward the back of the piano rather than hitting the player in the face. (One piano maker left a short piece of a thick bass string imbedded in a beam in the ceiling of his shop as a grim reminder of the danger inherent when a string breaks.)
- 11.
- 12.
Thomas Jefferson was probably the first American to purchase a piano. According to Ripin (1980, p. 702), during the Spring of 1771 Jefferson asked Thomas Adams in England to purchase a piano instead of the clavichord he had originally ordered for his fiancée. Alas, he sold it to a captured and paroled Hessian general in 1779 for £100 (Salgo 2000, p. 10, footnote.) The first piano made in colonial American was by John Behrent (alias Johann Behrend) in Philadelphia in 1775. (Dolge 1911, p. 49, and Brookes 2002, p. 4).
- 13.
See Dolge (1911) pp. 97–106; also, the Renner web site at www.rennerusa.com.
- 14.
Piano craftsman Christopher Robinson always does a spectrum analysis of the tone quality produced by a new hammer before gluing it onto the shank. He found that the spectrum often differed significantly when the hammer was rotated 180∘ about its long dimension. They are clearly not quite symmetric.
- 15.
See Giordano and Winans (2000) and the numerous references given in that paper. They determined the compression by integrating the measured time-dependent acceleration twice: the first integral gives the velocity and the second gives the compression as a function of time. The maximum compression occurs when the velocity goes to zero.
- 16.
The sound of an 1881 Erard with straight stringing is preserved on a digital CD recording by Madeleine Forte (2002).
- 17.
The Edward Ballade is one of the few “programmatic” pieces by Brahms and is based on one of the Scottish tales in Herder’s “Stimmen der Völker.” After anxiously calling for her son and being reassured that he was merely playing in the barn, Edward’s mother discovers that he has slaughtered his father.
- 18.
A similar thing happened during a concert by pianist Christopher O’Riley. While looking down at the wreckage, a cellist overheard him exclaim, “I hate it when it does that!” Some composers actually wrote a “crashing piano” into the musical score. For example, the sound of a crashing piano in E major is contained at the end of the Beatles recording of Sgt. Pepper’s Lonely Hearts Club Band. (EMI Stereo SMAS X-2-2653, NEM Enterprises Ltd., 1967, Side. 2.)
- 19.
The piano in question was a large rosewood, late-1860s-vintage Steinway grand, similar-looking to that shown at the left in Fig. 4.16. It had 85 keys, parallel stringing, and did not have a one-piece cast iron frame.
- 20.
This fact was obscured by a color photograph published by The New York Times (Thursday, November 22, 2001, The Arts, p. E1) showing an 1871 Streicher piano similar to the one Brahms owned that seemed to have a third pedal. Investigation showed that the “third pedal” in the photograph was actually the shadow of one of the two real pedals on the instrument. Someone had cut the piano out of its background in the photograph and thought that the shadow was a third pedal. The same piano is shown in the photograph taken by the author in Fig. 4.18.
- 21.
As with the earlier French harpsichord builders, the Viennese piano builders were inter-related. For example, Nanette Streicher, who with her husband Andreas Streicher tried to incorporate Beethoven’s suggestions in pianos built by their company, was the sister of André Stein. Her son, Johann Baptist Streicher (1796–1871) provided Brahms with his 1868 piano, similar to the 1871 instrument shown in Fig. 4.17. But by then, Johann’s son Emil had taken over the Streicher firm (which was finally dissolved in 1896).
- 22.
J. B. Hayes (1982) concluded that the optimum shape for a piano bridge was a catenary curve But just why he thought that remains a mystery. The common form of the catenary is given by the equation
$$\displaystyle \begin{aligned} y \propto [\cosh(kx) - 1] = \frac{1}{2}[\exp(+kx) + \exp(-kx) -2] \end{aligned} $$where k is an adjustable constant. [See Synge and Griffith (1949), pages 99–104.]
- 23.
The Steinway Company feels such data constitute “proprietary information.” Of course, they are available to anyone with a Steinway piano and a tape measure. Measuring the lengths of string terminating under the capo d’astro bar is the trickiest part, but can be done easily by slipping narrow strips of paper along the strings to the end points under the bar.
- 24.
It is said that Steinway made a special piano with a narrower octave span for the legendary pianist Joseph Hoffman because his hands were so small.
- 25.
The absolute sound levels at maximum from a concert grand can exceed the limits recommended by OSHA for prolonged exposure by a significant factor and may well cause deafness.
- 26.
Hanon (1900), exercise No. 35. Several professional pianists have told me that the first thing they have had to teach their students is to forget what Hanon had taught them.
- 27.
The capo d’astro bar is of great practical value when the bridge is properly adjusted, but it also contributes to what one piano technician described to me as “Steinway Disease.” The problem occurs when the sound board sags, pulling down the bridge with it. Under this condition, the geometry is such that when the returning pulse from the bridge (which is peaked downward) reaches the capo d’astro bar, it can pull the string down off the bar, producing a sound much like overload distortion in a “Hi-Fi” set. (The phenomenon is similar to the returning pulse in a clavichord pulling the string up off the tangent.) Cure usually involves raising the bridge, hence restringing the instrument.
- 28.
The moment of inertia about an axis a distance r away for a point mass M goes as Mr2, whereas the balancing torque goes as Mr. Hence, putting a larger mass closer to the balance point can speed up the response of the action.
- 29.
See, Malcolm W. Brown, “With Ivory in Short Supply, Pianists Tickle the Polymers,” The New York Times, May 25,1993; p. C1.
- 30.
See, “A Humid Recital Stirs Bangkok” in the Washington Post, July 23, 1967. This hilarious review describes a concert in which the pianist became so exasperated with sticking keys and other problems with a concert grand that he grabbed a fire axe and started to smash the piano to pieces. Although masterfully written by Kenneth Langbell for the English Language Bangkok Post under the title “Wild Night at The Erawan” on May 27, 1967 and made available to the Washington Post by Martin Bernheimer of The Los Angeles Times. The story is, alas, just humorous fiction according to the Web service, Urban Legends.
- 31.
This frictional loss can be extremely important. For example, it can increase the weight necessary to push down middle C from about 52 g (standard) to more than 70 g. For comparison, Horowitz had his Steinway adjusted so that a weight of only 35 g was needed. (That decrease in required force increases the ease of playing fast passages enormously; however, it also makes controlling the loudness of successive notes harder.)
- 32.
Blüthner probably couldn’t think of a good German word for it. Aliquot is Latin for “some” or “several.” In Italian, ali’quota comes from the French and means “quota” or “share.” According to the O.E.D., the English word “aliquot” means “a part contained in the whole an integral number of times.” In German, “aliquot part” becomes ohne Rest aufgehende Teil.
- 33.
One version of the Bösendorfer Imperial (the Bösendorfer 290 SE System) came complete with a computer that registered the impulse given the hammers optically at a rate of about 800 samples per second. Together with solenoids connected to each note, the system provided a kind of “High Tech” player piano with expression on which mistakes could be edited with the computer. In a demonstration of the system, pianist Charles Rosen said that the playback provided an exact mirror of his touch and dynamic expression. (Audio, January 1986, pp. 20,21.)
- 34.
Jon Paroles, The New York Times, January 4, 2001, p. 7.
- 35.
James Barron, “Why Today’s Piano is Much Like Yesterday’s and Last Century’s,” The New York Times, July 19, 2003, p.A11.
- 36.
One piano technician commented to me after hearing it, “It’s too bad they didn’t voice the piano first!”
- 37.
See A. Tomasini, “Not Even Practice Gets a 2-Lid Piano into Carnegie,” New York Times, December 8, 1997, p. 1.
- 38.
Christopher Robinson (private communication.)
- 39.
Young (1957), p. 3–102, Table 3b-2.
- 40.
See Feynman et al. (1963) Vol. 2, Chapter 38, for an explanatory discussion of elasticity in solids.
- 41.
See Trent and Stone (1957), 2–70.
- 42.
According to Hayes (1982), piano strings are normally tightened so much that bringing the string up another whole step, or a frequency increase of 1.122—hence, a tension increase of 1.26 would break the string.
- 43.
Young (1957, p. 3–101) provided a table of mass per unit length for steel and gut strings of different diameter.
- 44.
The quadratic equation is T 2 − (A 2 − 2B)T + B 2 = 0.
- 45.
A table of string diameters for nearly every model piano currently made is given in Travis (1982), Part II.
- 46.
That may explain why Babe Ruth threw his upright piano into Willis Pond near Boston in 1918. (See The New York Times, 9/30/2002, p. A17 and 11/5/2002, p. WK 5.)
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Bennett Jr., W.R. (2018). The Struck String. In: Morrison, A. (eds) The Science of Musical Sound. Springer, Cham. https://doi.org/10.1007/978-3-319-92796-1_4
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