Musical Offerings ⦁ 2024 ⦁ Volume 15 ⦁ Number 1 31 be lower in pitch, therefore also bringing down the standardized pitch of string instruments during the Renaissance or Baroque time period. This further confirms the reason for a tuning note of “A” being 415 to 420 hertz as opposed to 440 hertz. The tension of the strings plays a role in the intonation of a violin, as does the material of which the strings are made. The type of string also varies depending on the model of instrument, the time in which the string is being produced, and the pitch of the string. Strings during the Baroque period were made of gut, which is the intestine of animals such as cattle. There were also strings that were overspun metal enclosing a gut string. Overspun strings rose to popularity around 1660. These strings were primarily used for the lowest string (G) of the violin and were a thin metal spun around a gut core.22 The proportion of the string thickness in relation to each other is also significant in the history of the violin’s tuning. Seventeenth- and eighteenth-century writers concluded that “relative thickness of strings should be in proportion to their relative pitches and tension should be equal from string to string.”23 Violinist Giuseppe Tartini came to the conclusion that the most effective tension for violin strings tuned to A=420 hertz is 63 pounds. This is the amount of weight from the strings that is placed on the violin when the strings are tuned to their exact pitches. During Tartini’s experiment in 1734, the standard pitch was 420 hertz. Using Mersenne’s Law ( =� 2 2 ), the diameters of gut strings during this experiment can be calculated. Marin Mersenne was a mathematician living in the late 1500s and early 1600s who took an interest in the diameters of strings on the violin and how they related to the frequency of the string. In this equation, D is the diameter in meters of the string, T is the tension of the string in newtons, F is the frequency in hertz, L is the length of the string in meters, and is the density of the gut in kilograms per cubic meter. This equation calculated a diameter of 2.14 mm for the G string, 1.43 mm for the D string, 0.95 mm for the A string, and 0.64 mm for the E string.24 Mersenne’s Law renders the conclusion that there is a relationship between a string’s diameter and its frequency.25 These proportions of diameters for the strings were the most effective for the best tone for the 22 Pollens, 123. 23 Pollens, 124. 24 Pollens, 126. 25 Pollens, 124–125.
RkJQdWJsaXNoZXIy MTM4ODY=