Hi Hudson,
On Friday 10 February 2006 2:28 pm, Hudson Lacerda wrote:
> Hi Aaron,
>
> Aaron Krister Johnson escreveu:
> > On Wednesday 08 February 2006 6:28 pm, Hudson Lacerda wrote:
> >>For an equal tempered scale, one can:
> >>
> >>- Define the tuning for the base pitches C D E F G A B (pitches C and c
> >>are equivalent mod N, but N doesn't have to be the 2/1 octave);
> >>
> >>- Define the number of steps included in a whole tone (C to D); the
> >>number of steps involved in a specific accidental can be represented by
> >>its ratio numerator.
> >
> > Hi Hudson,
> >
> > The above assumes a regular meantone-type ET (or EDO as they are
> > sometimes called). Sometimes, as in a non-meantone ET like 22-tet or
> > 53-tet, there are two sizes of major 2nd--one for the 9/8 approximation,
> > the other, a smaller major 2nd, representing 10/9.
> >
> > So, the above only works for temperaments that temper out the 81/80
> > syntonic comma (i.e. meantone-family temperaments)
> >
> > Best,
> > Aaron.
>
> Fortunately, I think not. I can agree with that it works *better* for
> meantone-like temperaments. If one uses the suggested notations provided
> by the program scala, there is no such a limitation, although some
> pitches are rather roughly approximated (e.g. E vs. E\ in E22).
>
> For 22-ET using E22 notation, a whole tone is always 4 steps:
>
> 0: 1/1 C unison, perfect prime
> 1: 54.545 cents C/ Db
> 2: 109.091 cents C#\ Db/
> 3: 163.636 cents C# D\
> 4: 218.182 cents D
> 5: 272.727 cents D/ Eb
> 6: 327.273 cents D#\ Eb/
> 7: 381.818 cents D# E\
> 8: 436.364 cents E
> 9: 490.909 cents F
> 10: 545.455 cents F/ Gb
> 11: 600.000 cents F#\ Gb/
> 12: 654.545 cents F# G\
> 13: 709.091 cents G
> 14: 763.636 cents G/ Ab
> 15: 818.182 cents G#\ Ab/
> 16: 872.727 cents G# A\
> 17: 927.273 cents A
> 18: 981.818 cents A/ Bb
> 19: 1036.364 cents A#\ Bb/
> 20: 1090.909 cents A# B\
> 21: 1145.455 cents B
> 22: 2/1 C octave
Good point--but the question is, how would abcm2ps handle E\? What would the
accidental look like?
BTW, it would be nice to implement a version of abcm2ps that could do the full
gamut of 31-equal accidentals....
Cheers,
Aaron.
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