RE: [tuning] 22 tet guitar

Alison wrote,

>Having recently read Paul Erlich's excellent paper on 22 tet

Thanks!

>I have
>decided to refret a guitar.

Good idea -- I've found that my decatonic scales are extremely easy to play
on a 22-tET guitar.

>I have a question regarding the maths of
>this operation. The programme JI Calc gives the ratio 977/942 for 19
>tet, and the ratio 4233/4178 for 53 tet. I would be grateful if anyone
>could tell me how these are derived and how I could work out the ratio
>needed to generate 22 tet. I would like to make sure that the luthier
>and I agree on figures as the luthiers I know in Edinburgh rarely if
>ever do unconventional jobs. I would be extremely grateful for help on
>this point.

Alison, it's probably far better to give a luthier a full set of fret
positions in inches or centimeters, and a complex ratio-approximation for a
single step is next to useless. However, since you asked, 977/942 is an
approximation to 2^(1/19), 4233/4178 is an approximation to 2^(1/53), and an
approximations to 2^(1/22) of similar complexity is 1999/1937.

If you tell me the scale of your instrument (examples: Stratocaster = 25.5
inches, Les Paul = 24.75 inches), I can give you a full list of fret
positions that your luthier is likely to find infinitely preferable to a
single ratio.