How to Create Dramatic Tension within a Xenotonal Environment:
A Proposal for a Polar Bohlen-Pierce Harmonic System (2020)
For most musicians and musicologists, it is taken for granted that tonality goes hand in hand with the 12-ED2 scale, i.e., the musical scale formed by the equal division of the second harmonic into twelve parts. Besides, the macrotonal and non-octave-repeating Bohlen-Pierce scale seems not to share any common points with the conventional dodecaphonic octave-repeating one. However, both of them are built from the same material: the harmonic series. Indeed, whereas the latter is based upon the complete spectrum of the harmonic series, the former is only based upon the odd partials comprised within it. Would applying the basic tonal behaviours to this scale then produce a dramatic tension-release polarity effect similar to the one produced by tonality? The Bohlen-Pierce scale has, above all, hitherto been perceived as having modal qualities and yet no potential for dramatic tension. The present research aims to envisage the possibility of a polar harmonic system for this scale by first defining the BP major, minor, and diminished triads via the principles of harmony along with the hierarchization of sonance values and respecifying 12-ED2 tonal functionality to then correlate diatonic functions between both scales. Although it has been highlighted that a total equivalence between a tonal system based upon an even number and another based upon a prime one is impossible, it has nevertheless been demonstrated that a coherent polar harmonic system could be designed for the Bohlen-Pierce scale. Thenceforth, the results imply that the principles of tonality are not restricted to operating exclusively with the dodecaphonic octave-repeating scale.