class Spiral =
{
    class Note {
        constructor(index) {
            this.pos = get_note_pos(i);
        }
        // blabla
    }

    constructor() {
        this.z1_radius = math.pow( .3 , 1/this.notes );  // <-- radius of innermost note
        this.z1 = math.complex({ r:this.z1_radius, phi:τ/12 });

        // Find ∂ s.t. spiral * (1+∂)^+1 and spiral * (1+∂)^-1 meet as single amonite-groove
        // i.e. outside edge 1 rev in = inside edge
        //    z^12 * (1+∂) = 1/(1+∂) (12 hops => back to real numberline)
        //    z^12 = (1+∂)^-2
        //    1+∂ = z^12 ^ -1/2 = z^-6
        this.amonite_∂ = math.pow( this.z1_radius, -6 ) - 1;

        // equation of spiral: z(ϕ) = z1^(wϕ)
        // with w chosen s.t. z(τ/12) = z1^1 = z1
        // i.e. z1^(w.τ/12) = z1^1, so w.τ/12=1, so w=12/τ
        // so: z(ϕ) = z1^(ϕ.12/τ)
        // length of spine for button 0
        // ∫z^(wϕ) dϕ  over [-τ/24, +τ/24] (with w s.t. ϕ=τ/12 gives wϕ=1 i.e. w=12/τ)
        // i.e. at angle τ/12, we want z^1
        this.arc_0 = (root_r - 1/root_r) * τ / ( 12 * Math.log(r) );

        this.notes = new Array(88);
        for( i=0; i<this.notes.length; i++ )
            this.notes[i] = new Note(i);


    }
}