Infinite Scales are musical illusions created to give the impression of an endlessly rising or falling harmonic momentum. As each note of the scale is played, a determination is made (by a random process) as to whether or not the pitch should be displaced by an octave (raised when descending the scale, lowered when ascending). The probability of such a leap occurring increases through the octave, ranging from highly unlikely at the start to almost certain by the end, and so the scale comes full circle and can begin again.
Multiple instruments playing the scale simultaneously - each with independently derived displacements - obscure the octave leaps and results in an aggregate pull in one direction. Denser textures more effectively distract from these wide gaps which can be further hidden by harmonizing the scale and substituting scale notes with harmony notes. Infinite Scales Descending (ISD) and Infinite Scales Ascending (ISA) use the chromatic scale with each note harmonized by a perfect fourth above and below. This quartal harmony is an attempt to avoid a competing pull of thirds. The trade-off with such substitutions is that the overall sense of pull is weakened. Other stochastic techniques are employed to carve these two short pieces from the vast initial possibility space.
The abrupt start and end of each piece joins together to form a seamless loop, endlessly rising or falling. Not all audio players are able to perform a nonstop repeat, so a short discontinuity may be heard. For example, Spotify's claim of “gapless playback” does not apply when repeating the same song and so a beat of silence is introduced, whereas iTunes is able to repeat the track flawlessly.
There is no traditional development or arrangement here; ISA and ISD are simply repetitions of the scale intended to demonstrate this new technique. Future works could use the effect to create periods of tension within a more varied piece.
The photo at the top shows an F Lydian scale (treble clef presumed) on a Möbius Strip, made for my daughter, Lydia. I also made a similar Dorian scale loop for my son, Dorian, and one based on a Dominant-Tonic progression for their sister, Vivian ( 'V I V I' in the standard Roman numeral notation). The same notes appear on both sides of the paper, though the pitch indicated depends on the orientation of the score, e.g. low f inverts to high e, g to d, etc. The use of eighth notes was an artistic choice; whole notes are actually more suitable as their symbol has, essentially, left-right symmetry.
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Click image to enlarge