Re: Microtonal Helmholtz-Ellis notation in Lilypond: fine-tuning

[Hans Aberg]

On 25 Sep 2009, at 14:44, Graham Breed wrote:

> > what I don't understand:
> > How many cents are an alteration of 10/1023?
>
> It's a fraction of 200 cents.  So 200 * 10/1023 = 2000/1023 =  
> 1.955... cents, which looks like a schisma.

From my computations, it corresponds choosing an approximation in  
E12276 (tonestep 7181) of the interval ratio (3/2) which gives an  
accuracy of -3.33477112590685e-05 cents. How did you choose this?

It might be more natural to choose from the series of successive  
continued fraction convergents of log2(3/2):
  0/1, 1/1, 1/2, 3/5, 7/12, 24/41, 31/53, 179/306, 389/665,  
9126/15601, ...
Or E12, E41, E53, E306, E665, E15601, ...

E665 is less acurate that your choice, but within 0.000113647342336876  
cents; E15601 is better: -2.01904306607048e-06 cents. E306 is good,  
too: -0.00578344833810363 cents.

  Hans