Acoustical measurements of a rabab reconstructed after a pictorial source from the 14th century

Instrument: rabab 
Pictorial source: Francesc Comes, Madonna and Child with angel musicians, around 1394, Gold and tempera on wood, Pollença (Mallorca), Museu de Pollença 
Instrument maker: Thilo Hirsch 
Year of manufacture: 2022 
Location: Basel, property of the ensemble arcimboldo

Dimensions: 
Total length: 579 mm 
Max. Body width: 112 mm 
Body depth: approx. 95 mm 

Vibrating string lengths: 
d-string: 500 mm 
G-string: 497 mm

Materials: 
Body: cherry 
Pegbox: cherry 
Fingerboard: serviceberry 
Bars: spruce 
Nut/String attachment button: bone 
Bridge: boxwood 
Top: goatskin

The main aim of this research was to measure the acoustic effects of the different sound holes. To do this, the instrument was first measured with the upper rosette and the two holes in the body closed, then with both rosettes and the body holes open, and finally only with the body holes closed.

Acoustical measurements: Alexander Mayer, mdw - University of Music and Performing Arts Vienna, Department of Music Acoustics – Wiener Klangstil (IWK), 25.9.2023

Force: Impact hammer exciting at the bass side of the bridge 
ACC: Acceleration measured on the same side, close to the impact point. 
Average is the average of all measurements (to be used in the analysis).

Photos of the setup: Thilo Hirsch

Folder comes_rosette_o_loecher_zu 
Files: comes_rolz_1 to 6 (Description: upper rosette closed with wooden sheet, body-holes closed)

Folder comes_rosette_oO_loecher_offen 
Files: comes_roo_lo_1 to 6 (Description: rosette open , body-holes open)

Folder comes_rosette_oO_loecher_zu 
Files: comes_roo_lz_1 to 6 (Description: rosette open , body-holes closed)          

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How to read VIA-Files:

Line 1 to 9: Header, Line 8 holds the number of values

Data is organized as followed: 1st col: Frequency [Hz], 2nd col: Magnitude [as Factor not dB!], 3rd col: Phase [rad], 4th col:  Real part [as Factor not dB!], 5th col: Imaginary part [as Factor not dB!]. So only first 3 columns are needed!

To get dB Value: Amplitude[dB] = 20 log [Magnitude]

Usually the Magnitude was calculated as response/reference (input) in the frequency domain. As for measuring the mechanical admittance the sensor is most likely an accelerometer (capturing the response in m/s2 of the object of interest) and the reference an impact hammer capturing the input force in Newton. As the mechanical admittance is defined as v/F (speed over force) the acceleration signal has to be integrated. The here captured signals are integrated in the frequency domain, what means the magnitude is divided by the corresponding frequency value in s-1. Values coded like: 3.30750000000000E+1 -> 3.3075 * 10 -> 33.075