A Geometrical Method for Sound-Hole Size and Location Enhancement in Lute Family Musical Instruments: The Golden Method
- The method is described in an itemized flowchart form in chapter two.
- Two well-known instruments will be checked with this approach as case studies in order to show the effectiveness of the Golden Method.
- A new musical instrument will be developed using the proposed method and its damping capability would be compared with that of two well-known instruments to confirm the effectiveness of the golden method in optimizing the sound-hole size and location in lute family musical instruments from a damping point of view.
“Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.”
- The circular sound-hole has been assumed as the optimized shape for the lute family (based on the literature).
- The material and mechanical properties of the instrument are not discussed in this paper because of their dynamic-index nature. These parameters can be studied in a separate standalone research work.
- The main objective of the proposed method is to enhance the musical note keeping capability of the instrument for orchestral consideration.
- Plot the rectangle ABCD covering the instrument soundboard and tangent to it as shown in Figure 3a.
- Plot the golden rectangle and its logarithmic spiral from one side of the ABCD as shown in Figure 3b. Full details on how to plot such a golden rectangle and spiral are very straightforward and can be found in (Chang 2002, Hemenway 2005).
- Repeat step 2 from another side of the ABCD as shown in Figure 3c and draw another golden rectangle and logarithmic spiral that mirror those of step 2.
- Plot a circle C1 tangent over the 3 lines AB, BD, and CD as shown in Figure 4a.
- Plot the first golden circle C2 so that
- The vertical diameters and upper vertex of the two circles are common.
- The diameter ratio:
- Plot the second golden circle C3; this circle is drawn like C2 (but C3 should follow the above-mentioned conditions for C2) (Figure 4c).
- Now, if C3 touches the two golden spirals (Figure 5a), this can locate the precise location and size of the optimized sound-hole.
3. Experimental Evaluation
3.1. Case Study I: Delroba2
3.2. Case Study II: Eshghi3
3.3. Case Study III: Mahava4
4. Experimental Apparatus and Procedure
4.1. Data Acquisition System
4.2. Test Procedure
5. Results and Analysis
Conflicts of Interest
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Setar is a Persian member of lute family musical instruments.
Mean enchanting; one of the most famous Setar designs.
Means “related to love”; one of the most famous Setar designs.
Means “like the moos sound”.
|Maximum Amplitude (mV)||Maximum Amplitude Time (ms)||Damping Time (ms) §|
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Jafari, S.; Karbasbaf, M.M. A Geometrical Method for Sound-Hole Size and Location Enhancement in Lute Family Musical Instruments: The Golden Method. Arts 2017, 6, 20. https://doi.org/10.3390/arts6040020
Jafari S, Karbasbaf MM. A Geometrical Method for Sound-Hole Size and Location Enhancement in Lute Family Musical Instruments: The Golden Method. Arts. 2017; 6(4):20. https://doi.org/10.3390/arts6040020Chicago/Turabian Style
Jafari, Soheil, and Mohammad Mahdi Karbasbaf. 2017. "A Geometrical Method for Sound-Hole Size and Location Enhancement in Lute Family Musical Instruments: The Golden Method" Arts 6, no. 4: 20. https://doi.org/10.3390/arts6040020