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

[Stefan Thomas]

Dear Community,
I've already defined some microtonal pitchnames
But, unfortunately I have problems with the correct spacing.
Especially I don't understand why the distance between the barline and the cis is better if it is a whole note but not, if it is a quartenote.
Here the snippet:
\version "2.13.3"

\include "stefansMikrotoene.ly"
\relative c' {
  
c co coo cih cis cis cis cis
c4 co coo cih cis 1
}

2009/9/25 Hans Aberg <address@hidden>

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

stefansMikrotoene.ly
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