Rankin guitar tuning

Brian Carlson wrote:

> I live in Denver and play a 19 tone steel
> string acoustic guitar and another with the frets spaced at the following
> ratios - 21/20 9/8 7/6 6/5 5/4 21/16 4/3 7/5 35/24 3/2 14/9
> 8/5 5/3 7/4 9/5 15/8 and 35/18. Mark Rankin worked out these ratios
> to include the 7 limit ratios and also keep the frets spaced far enough
> apart to be playable.

Brian only listed 18 tones, I'm guessing that the one that got left out
was a 35/32 between the 21/20 and 9/8. If that's the case, the only
irregularity in the resulting scale comes from the 21/16, which
introduces a wide 21/20 and narrow 64/63. If it were replaced by a
35/27 you'd get a scale composed entirely of only three steps (36/35,
28/27, 25/24).

This scale and its ilk are very similar to the 19-tone Mandelbaum I
also have on a (Tom Stone interchangeable fingerboard) guitar:

1/1 25/24 15/14 9/8 7/6 6/5 5/4 9/7 4/3 7/5 36/35 3/2 14/9 8/5 5/3 7/4
9/5 15/8 27/14 2/1

which consists only of those three steps mentioned. Like Mark's
scale it extends the same set of 5-limit ratios with 7's, except that
the 7's are distributed more or less evenly between otonal and utonal
ratios.

Ken Wauchope

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