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Melody "Hänschen klein"

"Hänschen klein" is a very simple monophonic melody well known to all (German) children. For programming, the diatonic tuning was employed. In the pulse sequence, for each individual tone interval (prime, second, third etc.) the exact frequency difference between the carrier signal and the resonance line in the spectrum (acetone in CDCl3) is calculated by the pulse program. The merit of this method is that the song may be played in any arbitrary tune. The drawback is that we are restricted to using the diatonic tuning. Employment of the tempered tuning would imply real numbers (e.g., 12th-root(2)) instead of arithmetic integer expressions (e.g., 5/3) for frequency calculation. This feature is not yet implemented in the current version of the pulse programmer (JEOL PEDL version 2.0).

An interesting feature is seen in the Fourier-transformed spectrum of the "Hänschen klein" summed up FID. According to the five different tones in the song there are five distinct signals (the upper right one is the prime, the lower left one is the fifth). The integral of the individual signals reflects the abundance of the tones in the song.

Remarkably, the prime is the least abundant tone whereas the fifth is the most abundant one. I checked some further simple children songs for the occurence of tones - in most cases the fifth is the major abundant tone. Any plausible explanation by psychologists would be highly welcome!

Melody "Hänschen klein", FID

Melody "Hänschen klein", spectrum

Melody "Hänschen klein", .aiff

Melody "Hänschen klein", .wav

Melody "Hänschen klein", pulse program

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April 28, 1997