Davide Verotta



Harmonics & the Luminous Chord


The first sixteen harmonics of two different harmonics series starting from C2 and G2, respectively. If f is the frequency of the fundamental, the harmonic series is simply f, 2f, 3f, 4f, 5f, 6f ... . Octaves correspond to a geometric series: f, 2f, 4f, 8f, ...

As a curiosity a mapping of the first 14 elements of the Fibonacci series (0 1 1 2 3 5 8 13 21 34 55 89 144 233) in frequency domain picks only the elements of the luminous chord: C G (producing a sequence of perfect fifths and fourths), and B-flat D F-sharp (i.e. an augmented triad, spelled out in a sequence of augmented fifths/minor sixths),

The Luminous Chord


Fundamental frequency x (Fibonacci number +1), rounded to the nearest tempered tuning pitch.

No other pitch is picked by the series until the 15th to 17th terms, 377 610 987, pick another augmented triad G B D-sharp.

If 0 is omitted from the series, and the map is: Fundamental frequency x Fibonacci number, then the first 16 terms (1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987) pick the 12 tempered tones, with only C and G repeated.

Fundamental frequency x (Fibonacci number), rounded to the nearest tempered tuning pitch

Absolute frequencies are well above audible range, and for both mappings the rounding off to tempered pitch is quite promounced.