To make the figures above, digital recordings were made of the transient ringing of single strings for selected notes following a mf to f
key strike (only the center string of three-string notes, and the upper string for two-string notes were utilized, the other strings were muted with rubber mutes). Recordings were usually made with a portable handheld Tascam
DR-1 recorder with either the internal mic (20-20,000 Hz) or an external Audio Technica AT822 mic (30-20,000 Hz response).
Digital (wav) files were imported into GoldWave
to remove silent sections before the transient, and zero filled to 22 seconds if needed (giving 1 million points per file). The two channels were matched and normalized, then the file was saved as a monaural file in text format. The files were imported into Mathematica
for Fourier transformation and analysis. Digital resolution of the frequency files were defined by 1/AT where AT is the length of the transient (e.g. 0.045 Hz for a 22 sec transient). (Thanks to my son Christopher for writing a very efficient routine in Mathematica for extracting the overtone frequencies.)