Mountain Dulcimer Picture in Mathematics Magazine
General mountain dulcimer or music discussions
Thank you for this very interesting discussion.
Excited by the question,I took some measurements on the melody string of one of my dulcimers with an acoustic spectrometer. I successively plucked the string at different points along the VSL, starting in the middle (fret 7) and gradually moving toward the bridge.
The measurements showed that all the notes emitted had exactly the same scale of overtones (I measured up to the 27th...).Qualitatively speaking, none of the resulting sounds was purer than any other, wherever the string was plucked.
The only visible difference between all these sounds was the energy associated with each individual wave. I read somewhere in this thread that the octave (second overtone) might be responsible for the mellowness of the note obtained in the middle of the string, but this overtone was actually almost nonexistent at this plucking point, where odd overtones #3, #5, and #7 dominated the vibrational energy. The octave only appeared when moving toward the bridge, around frets 11-12, and disappeared again toward the bridge.
Near the bridge, too, the vibrational energy was distributed between overtones #3 to #8 with higher frequencies, in keeping with the brightness of the resulting sound, and its slightly acidic character, given that the higher overtones become a bit dissonant (this is quite noticeable for #7).
If that helps...