Playable Nodes on Strings

The following documents are supplementary materials to the article “Farey Sequences Map Playable Nodes on a String” by Thomas Nicholson and Marc Sabat, published in TEMPO, completed under the supervision of Marc Sabat during the summer of 2020 by Idin Samimi Mofakham.

These charts aim to ease understanding and practical application of the abovementioned article for composers and performers unfamiliar with the mathematical process of finding the natural harmonic nodes by themselves but who wish to use this concept as inspiration for their artistic works. The documents consist of the playable natural harmonic nodes of the entire string instrument family (violin, viola, cello, and contrabass).

As it is fully explained in Nicholson/Sabat’s article, the strings’ thickness and rigidity and the pressure applied to them will each cause distortion of the higher partials of the strings,  slightly raising (‘stretching’) the actual frequencies of (some) higher partial. Therefore, we have chosen a lower limit for partials on the lower strings and higher limits for the higher strings.

The Playable Nodes on Strings documents are notated in the Helmholtz-Ellis JI Pitch Notation (HEJI) and two staves. The lower one shows the natural harmonic node’s place as if played as stopped pitches and the upper staves show the result of the touching node.

Playable Nodes on Violin 
Playable Nodes on Viola
Playable Nodes on Cello
Playable Nodes on Contrabass

Idin Samimi Mofakham
Oslo – November 2020