# On the Correlation of Symbols' Vibrational Behavior and Manufacturing Processes
## 5 Conclusions  
This study explored the potential use of the CFDAC and the spectral correlation index in the cymbal manufacturing process. The proposed methodology highlights the influence of the manufacturing processes of forming, hammering, and finishing to the vibrational behavior of the cymbals and demonstrates the capability of the correlation criterion to monitor, identify, and visualize the vibrational state of any cymbal compared to a pristine one. Very small deviations in the criterion were observed for the blank cymbals, produced by the same manufacturer, using the same material and machining processes. Common materials and shapes were recognized and reflected in the computed values when comparing the hammered cymbals to a finished commercial cymbal. The CFDAC allows for a clear distinction between blanks and semi-finished cymbals, and since hammering cannot be easily visually detected, the proposed methodology offers a monitoring diagnostic tool capable of identifying the vibroacoustic state of a cymbal. The SCI values allow for the evaluation of the vibrational state of the cymbals and indicate if additional processes are required to lead the vibrational characteristics of the cymbal to a different state relative to a pristine reference. Additionally, the SCI was employed to evaluate the similarity of the FRFs within the same cymbal.  
A qualitative representation of the cymbals' vibrational state was easily recognized, enabling a novel methodology for manufacturers and musicians to emerge. This offers a potential control tool for various stages of cymbal manufacturing. Moreover, in the context of automated cymbal measurements, this method offers a practical approach for use on production lines. A proposal for future research involves applying this method during the hammering process in incremental steps, enabling the tracking of changes in a cymbal's vibrational response after a predefined number of hammer hits. Additionally, extending this study to examine the behavior of non-finished cymbals in subsequent manufacturing stages will further enhance the knowledge and capability for sound emission prediction studies.  
Figure 13: SCI calculated by using the CFDACs of the originally measured FRF matrix and the CFDACs after shifting the rows of the matrix.  
**Author Contributions:** Conceptualization, S.B., E.K., and V.D.; methodology, S.B., Y.O., M.B., N.A.P., and E.K.; investigation, S.B., E.K., and V.D.; writing--original draft preparation, S.B., E.K., and V.D.; writing--review and editing, S.B., E.K., and V.D.; supervision, V.D. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available within the article.  
**Acknowledgments:** This research was funded by the Hellenic Mediterranean University, within the project <<Recording and metrological analysis of the vibro-acoustic characteristics of musical instruments for the investigation of alternative and low-cost materials and geometries with relevant sound characteristics>>.  
**Conflicts of Interest:** The authors declare no conflicts of interest.