Partials and Overtones

It is helpful to have a look at the number and range of the partials for various piano notes (strings). Recordings of the single (central) strings of the 8 A's of a Steinway B were made with a digital recorder. That of A0 is shown here, with an acquisition time of 11 sec and a sampling frequency of 44.1 kHz (485,100 data points).


A0 transient
Fourier transformation of the recording provides a distribution of the partials for each A (see methods below). Over 40 overtones can be observed for A0, while only 2 (the fundamental and the first overtone) is observable for A6, and only the fundamental can be reliably defined for A7 (frequencies are in Hz). The variation of intensities of the overtones is what gives each piano its characteristic color.


A0 overtones (0.1 Hz resolution)
|


A1 overtones
|


A2 overtones
|


A3 overtones
|


A4 overtones
|


A5 overtones
|


A6 overtones
|


A7 overtones
Recording:
Digital recordings are 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 are utilized, the other strings are muted with rubber mutes). Recordings are 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).

Signal processing:
Digital (wav) files are imported into GoldWave sound editor to remove silent sections before the transient, and truncate the recording at a reasonable file length (e.g. 10 sec for bass notes, 4-7 sec for tenor to treble, and 2.5 sec for the highest notes). The two channels were matched and maximized, 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. 0.1 Hz for the bass, 0.2 Hz for the mid-section, and 0.4 Hz for the high treble). (Thanks to my son Christopher for writing a very efficient routine in Mathematica for extracting the overtone frequencies.)