Sounds based on the golden ratio.


This is a script for norns and a midi input device. The timbre of the sound is based on the golden ratio, and the scale is also based on the golden ratio.

The 12 notes per phitave go like so:

  • A: 1
  • A#: 1 + phi^-6
  • B: 1 + phi^-5
  • C: 1 + phi^-4
  • C#: 1 + phi^-4 + phi^-6
  • D: 1 + phi^-3
  • D#: 1 + phi^-3 + phi^-5
  • E: 1 + phi^-2
  • F: 1 + phi^-2 + phi^-6
  • F#: 1 + phi^-2 + phi^-5
  • G: 1 + phi^-2 + phi^-4
  • G#: 1 + phi^-2 + phi^-4 + phi^-6

I have highlighted the “minor pentatonic analog” which is I think my favorite scale in here. The scale is made by using “phitaves” instead of octaves, and then subdividing each “phitave” into proportions themseves based on the golden ratio, and then subdividing those, etc. With the additive synth timbre I have chosen (where the partials are phi-ratios away, exponentially), the phitaves are so close to the same timbre that the whole scale has a bit of a shepherd-tone aspect.

There’s also an FM tone; in this tone the modulator is related to the carrier by a ratio of phi^n, but the actual partials of the sound will be distributed in multiples of phi rather than powers of phi like the additive tone. This feels very different, but I feel like it’s still suited to the phi-based scale.

This is a little scriptlet I just spent a couple hours on this morning. I think it is cute.


Norns, a MIDI input device of some kind.




Connect midi keeb or seq.

Select it in params.




this is so brilliant!!!

this part is total genius! love the forms within forms.

I may borrow this term :slight_smile: norns is built for scriptlets.


Sounds interesting, will check this out tonight!

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