## 2 Materials and Methods
### Frequency Measurement and Calculations for String Tension Force  
In stringed instruments, taut strings exert significant stress on the neck and soundboard of the instrument. Estimating the deformations that may be encountered due to the tension forces applied by the string is very important in terms of determining the design and material properties of the instrument [12]. The sound input to the body of a stringed instrument is provided when the string is plucked. The frequencies of the component modes of a string supported at both ends can be related to the length, tension, and mass per unit length of the string. Here, the tension forces can be calculated using the frequency and related material and geometrical features of the string. Frequency analysis (or spectral analysis) in string instruments refers to the process of determining the distribution of energy in the sound produced by the instrument across different frequency bands. This analysis provides a visual representation of the frequencies present in the sound and the strength or amplitude of each frequency. The frequency content of a sound can provide information about its timbre or tone colour and help in identifying and analysing different harmonic components. The spectral analysis can be performed using various techniques such as Fourier transforms or wavelet transforms, and the results can be displayed in a spectrogram. This information can be used to study the acoustics of string instruments, un derstand how different playing techniques affect the sound, and even in the development of new instruments or the improvement of existing ones [22; 23; 24]. In this study, the cura baglama was tuned with a digital tuner and frequency analysis was carried out for each string of the instrument with single plucking sound records via Adobe Audition (v 2022) audio processor software. Sound recording was realised with a 44,100 Hz sample rate, 16-bit bit depth, and mono channel recording using a Logic Pro X digital audio workstation system, including an SE Electronics Z3300A Multi-pattern Microphone and an Apollo Twin Duo MKII soundcard. A professional baglama performer (Dr. [PERSON]) generated identical single-plucking actions. A thermoplastic spectrum was used in plucking. The Shore-A scale (ASTM D2240 ISO/868) was utilised in the hardness measurements of the spectrum. The hardness measurement was repeated five times and the average scale was obtained as 83 \(\pm\) 2. Three repetitions of the plucking action were recorded for each of the strings, and then average values were calculated. The instrument adjusted to the tunings (end tune) of B2 (Si), C3 (Do), and D3 (Re) referenced to the tune of A4 (La) at 440 Hz, respectively. \"Playing end note or playing tuning or end tune\" is defined as the concluding note of a melody/musical phrase/composition or its modal progression, and within Turkish Folk Music, it encompasses various forms of determining  
Figure 1: Illustration of the sample cura baglama and the 3D modelling process. tonality and their corresponding sound characteristics. Turkish terminology refers to this particular definition as the \"karar\", \"eksen\", or \"durak\" sound [25; 26]. These tunings were set up since they force the limits of the string materials and are the preferred tones played by most performers in specific regional melodies. Subsequently, Equation (1) was employed for the string tension force calculations [27]. Additionally, cross-sectional stress magnitudes of the corresponding strings were calculated by using Equation (2) [28]:  
\[f_{n}=\left[\frac{n}{2L}\right]\sqrt{\frac{T}{\mu}} \tag{1}\]  
where \(n=1\), \(2\), \(3\), \(\ldots\); \(L\): Length of the string (m); \(T\): Tension force of the string (N); \(\mu\): mass per unit length of the string (kg m\({}^{-1}\)); and \(f\): Frequency of the string (Hz). When \(n=1\), Equation (1) provides the frequency of the lowest mode. This is the f0 of the string, which is also known as the \"first harmonic\". Thus, the first mode (\(f1\)) in Equation (1) is the \(f0\) of string vibration.