Many Viewpoints for Many Sounding Points: Approaching Francklin's Quartet

See Ivan Galamian , Principles of Violin Playing and Teaching (Englewood Cliffs, N.J.: Prentice Hall Inc., 1962), 58.

Given space constraints, I must presume an elementary knowledge of the overtone series. The term “partial” is here used to avoid the common confusion about numbering overtones/harmonics (the fundamental pitch is the first partial). For an introductory discussion of the overtone series and the terminology associated with it, see John Backus , Acoustical Foundations of Music, 2nd ed. (New York: Norton, 1977).

Raman Chandrasekhara Venkata , On the Mechanical Theory of the Vibrations of Bowed Strings and of Musical Instruments of the Violin Family with Experimental Verification of the Results: Part I, Bulletin 15 (Calcutta: Indian Association for the Cultivation of Science, 1918), 7. This extremely rare text has generously been made available online by the Digital Repository of the Raman Research Institute. <http://dspace.rri.res.in/>

Raman's research (1918) suggests that the isolation of up to the eighth partial with the bow may be of practicality for the violinist (as the individual isolation of higher nodes becomes impossible considering the bow hair's width) (54).

Backus , Acoustical Foundations oof Music, 62.

Carl Flesch , The Art of Violin Playing, Vol. 1, trans. Eric Rosenblith (New York: Carl Fischer, 2000), 77.

Werner Bachmann , The Origins of Bowing, trans. Norma Deane (London: Oxford University Press, 1969), 139.

Cornelia Fales , “The Paradox of Timbre,” Ethnomusicology 46/1 (2002): 56.

David Rycroft , “Friction Chordophones in South-Eastern Africa,” The Galpin Society Journal 19 (April, 1966): 95.

Generally, those sounding points not on a partial's node (lower in the overtone series) can handle more bow weight and therefore be played quite loudly.

On the issue of categorization, see Bo Lawergren , “A New and A Rediscovered Type of Motion of the Bowed Violin String or How Bowing Position Affects the Shape and the Sound of the String,” Catgut Acoustical Society Newsletter 3 (November 1978): 8–13.

John Schelleng , “The Bowed String and the Player,” Journal of the Acoustical Society of America 53/1 (1973): 31.

In addition to Lawergren, see Anders Askenfelt , “Measurement of the Bowing Parameters in Violin Playing. II: Bow-bridge Distance, Dynamic Range, and Limits of Bow Force,” Journal of the Acoustical Society of America 86/2 (August 1989): 503–516.

McIntyre M.E. , and Woodhouse J. , “A Parametric Study of the Bowed String: The Violinist's Menagerie,” Journal of the Catgut Acoustical Society 42 (November 1984): 18–21.

Stewart Dickson , “On Electronic Strings in Live Performance: The Design and Construction of an Electroacoustic Monochord,” Perspectives of New Music 20/½ (Autumn, 1981- Summer, 1982): 623–639.

For those unacquainted with this odd piece (in which Benjamin Franklin's name is even misspelled on the primary source), see

Benjamin Franklin , Quatuor pour trois violins et violoncelle, ed. Guillaume de Van (Paris: O. Lieutier, 1946).

Grenander M.E. , “Reflections on the String Quartet(s) Attributed to Franklin,” American Quarterly 27/1 (March, 1975): 73–87.

Marrocco W. Thomas , “The String Quartet Attributed to Benjamin Franklin,” Proceedings of the American Philosophical Society 116/6 (December, 1972): 477–485.

David Blum , Casals and the Art of Interpretation (Berkeley: University of California Press, 1980), 15.

Benjamin Franklin , “String Quartet,” Kohon String Quartet, The Unknown String Quartet (New Jersey: Vox Box SVBX 5301). Due to limitations of space only the first movement is pictured; however, it is representative of the entire performance.

Menuhin Yehudi , and Primrose William , Violin & Viola (New York: Schirmer Books, 1976), 84.

For an introduction to spectrographic analysis, see Robert Cogan , New Images of Musical Sound (Cambridge: Harvard University Press, 1984). The American String Teachers Association, by the way, was among the first to disseminate such analysis as applied to music. See Frederick Polnauer and Morton Marks, Senso-Motor Study and its Application to Violin Playing (Urbana: American String Teachers Association, 1964).

Gerhard Mantel , Cello Technique: Principles and Forms of Movement, trans. Barbara H. Thiem (Bloomington: Indiana, 1975), 129.

Jeffrey Pulver , “Violin Methods Old and New,” Proceedings of the Musical Association 50th Session (1923-1924): 117.

Franz Kneisel , Principles of Bowing and Phrasing: Hints to Serious Violin Students (New York: Carl Fischer, 1925), 23–24.

On the notion of “de-territorialization,” see Deleuze Gilles , and Guattari Félix , “Of the Refrain,” in A Thousand Plateaus, trans. Brian Massumi (Minneapolis: University of Minnesota Press, 1987), 310–350. It is assuredly all too easy to project one's own desires onto another's creation. Yet the mystery surrounding this piece spurs vast speculation. In fact, it is equally plausible to interpret Francklin's Quartet as an unprecedented attempt at invariance in string sound color. But invariance would ultimately be subsumed in a reactionary consideration of all varied sounding points. Such an interpretation, therefore, would be superfluous for the pedagogue.

Heller George N. , “To Sweeten Their Senses: Music, Education, and Benjamin Franklin,” Music Educators Journal 73/5 (January, 1987): 24.

Robert Fludd (1547-1637) is most often credited with the discovery of blood's circulation. He is also known for his controversies with Johannes Kepler, and for his alleged Rosicrucianist beliefs.

Fludd Robert , Mundana De Musica , in Utriusque cosmi maioris scilicet et minoris metaphysica, physica atqve technica historia, in duo volumina secundum cosmi differentiam diuisa (Oppenhemii: ære Johan-Theodori de Bry, typis Hieronymi Galleri, 1617).

As called for by Raman, On the Mechanical Theory of the Vibrations of the Bowed Strings, 2.

This experiment but expands the parameters set forth by Galamian in his Principles of Violin Playing and Teaching, 58–61.

For a discussion of the higher partials’ nodes (in between the bridge and the fingerboard), see Emile Leipp , The Violin; History, Aesthetics, Manufacture, and Acoustics, trans. Hildegard W. Parry (Toronto: University of Toronto Press, 1969), 100.

Ammann Peter J. , “The Musical Theory and Philosophy of Robert Fludd,” Journal of the Warburg and Courtauld Institutes 30 (1967): 224.

For the present discussion, this term denotes the excitation of the string's exact midpoint. Again, this sonority is otherwise nameless under the general classification sul tasto.

As Lawergren (1978) has demonstrated: “It is actually not the length between the bridge and the bow, B, that is relevant [to the spectrum of partials] but rather the relative length, i.e. B/L (where L is the total length of the vibrating part of the string)” (9).