Danny, can you elaborate on your temperament suggestions based on sine and

Danny, can you elaborate on your temperament suggestions based on sine and
cosine functions? A step by step demonstration would be most helpful.

SNIP

> A long time ago I proposed, either here or on tuning-math, a couple of
> temperaments using sine and cosine functions.
>
> One of them is a classic 12-tone WT centered on re/D using the formula T
> = -sin (pi * n / 12) / 2 * (531441 / 524288), where n is the number of
> fifths away from the central note, integer range -6 to +6, and T is the
> frequency ratio which is multiplied into the note to be tempered (so find
> the base-2 logarithm and multiply by 1200 for pitch value in cents). Also,
> I'm using radians for angles; replace pi with 180° if you'd rather think
> in terms of degrees.
>
> The other is 41-tone, and the formula is T = (1 - cos (pi * n /
> 41)) / 2 * (2^65 / 3^41). This time, the range of n can either
> be 0 to +41, -20 to +20 or even -41 to 0 if you prefer.

SNIP