Interval as perspective

Using equal tempered chromaticism as the simplest means of auralising a concept, the familiar Doppler Effect alters the frequency of a singular PC depending on the position of the listener relative to a moving sound source, their auditory perspective; all sound and light is ostensibly “moving” perceptually, with expansion described by the notions of Red Shift, and Octave Shift. Taking the concept of visual perspective (where the size and shape of an observed object varies depending on the relative position of the observer) as a metaphor for sound, a C Major triad may be rendered as follows (figi).


Removing the starting (static) triad leaves the expanded & contracted centrally symmetrical tetrachord/scale B (2) C# (5) F# (2) G#. Transposing this scale up (and down) a major third produces the 12 tone row: B C# F# G# | G A D E | Eb F Bb C.

Set i B C# F# G#
Set ii G A D E
Set iii Eb F Bb C

This can be expressed in various ways:

(figure ii – as informed by the concept of M.C.Esher’s  [Penrose] stairs)

PDF score – figure iii

(figure iii – as informed by the Sheppard – Risset scale/glissando

 (figure iv – romanticized gestures)

 (figure v – simple serial rendition )