Preset group · Fibonacci · frequencies

Fibonacci in hertz. The sequence, low to high.

The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21… and each number is the sum of the two before it. Leonardo of Pisa brought it to Europe in 1202, in the Liber Abaci, with a problem about rabbits; in India it was known centuries earlier, in the meter of Sanskrit poetry.

The tradition sees it in the spirals of the sunflower and the pine cone. This group listens to it: eight numbers from the sequence used as frequencies, as they are.

Open the group in the appThe presets
01How it's madeFibonacci · frequencies

The formulas and the figures in the code.

Each preset is a Fibonacci number, F(n), in hertz: 89, 144, 233, 377, 610, 987, 1597 and 2584 Hz. That's 8 pure tones, with no ratio. Each is the sum of the two before it in the sequence (89 + 144 = 233), and between two neighbors the ratio is already close to φ.

They all carry the Golden Spiral layer, at 40%.

02The presetsFibonacci · frequencies

One line per preset.

  • 89 Hz

    89 Hz

    89 Hz, the lowest in the group: few lines, very clear.

    Physical figure (4, 0) · Symbolic layer: Golden Spiral

  • 144 Hz

    144 Hz

    144 Hz, twelve times twelve.

    Physical figure (4, 2) · Symbolic layer: Golden Spiral

  • 233 Hz

    233 Hz

    233 Hz, almost exactly A#3.

    Physical figure (6, 2) · Symbolic layer: Golden Spiral

  • 377 Hz

    377 Hz

    377 Hz, in the middle octave.

    Physical figure (8, 2) · Symbolic layer: Golden Spiral

  • 610 Hz

    610 Hz

    610 Hz, the Succulent's frequency in Nature.

    Physical figure (10, 4) + (10, 2) · Symbolic layer: Golden Spiral

  • 987 Hz

    987 Hz

    987 Hz, almost exactly B5.

    Physical figure (12, 6) · Symbolic layer: Golden Spiral

  • 1597 Hz

    1597 Hz

    1597 Hz, already very high: a fine web.

    Physical figure (16, 6) · Symbolic layer: Golden Spiral

  • 2584 Hz

    2584 Hz

    2584 Hz, the last one before the top of the range.

    Physical figure (18, 12) · Symbolic layer: Golden Spiral

Tab. 01 · Plate figure calculated by the app's core (cym.core.js) for each frequency: a square plate driven at the center, f = 5.5·(n² + m²) Hz. Two modes = the plate answers with both.

03What you seeFibonacci · frequencies

The physical figure and the symbolic layer.

It's the group that covers the most of the plate: from 89 Hz, mode (4, 0), to 2584 Hz, mode (18, 12), almost at the top of the range (2600 Hz). Watching all eight in a row is watching the plate fill with lines.

The Golden Spiral on top is a symbolic layer: a drawing from the tradition, not calculated from the sound.

04QuestionsFibonacci · frequencies

What people ask about this group.

Q1What is the Fibonacci sequence?

A series where each number is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… Leonardo of Pisa made it known in Europe in 1202.

Q2Why these eight?

They're the numbers in the sequence that fit in the app's range, from 89 to 2584 Hz. That way you hear the whole series, low to high.

Q3What about the ratio between two tones?

That's in the Fibonacci · ratios group: there two tones play together at 3:2, 5:3, 8:5… all the way to φ.

The other groups.