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

[Hans Aberg]

On 25 Sep 2009, at 13:13, Stefan Thomas wrote:

> How many cents are an alteration of 10/1023?

I made some Haskell functions that compute these; I use Hugs <http://haskell.org/hugs/ 
>, but perhaps somebody can translate it to Scheme code.

For example, for E12276, LilyPond scale degree 4 (note G relative C),  
and interval ratio 3/2 (Just perfect fifth), the LilyPond alteration  
ratio with offset in cents is:
  LilyPond> lyalt (12276) 4 (3/2)
  (10 % 1023,-3.33477112590685e-05)
Rational number ratios are written with % in Haskell, so this is  
10/1023, and the second component is -3.33477112590685e-05 cents -  
approximation is a bit lower than 3/2.

If one wants to know which ET is used, compute the pitch as a fraction  
of an octave:
  LilyPond> lyp 4 (10/1023)
  7181 % 12276
As this is fraction of an octave, the denominator gives the ET: E12276.

  Hans

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