The meantone hexachord

I found a unqiue 6-tone 9-limit chord/scale for the 31 et, which turns out to be a general feature of the standard septimal meantone temperament; this is the meantone in which both 81/80 *and* 126/125
(and hence 225/224 = (81/80)/(126/125)) are commas.

One mode of it is [0, 5, 10, 15, 21, 26] with steps 555655 in the 31 et, but it also has versions in 12, 19, 31, 43, 50 and 74. The 12-tone version is the whole-tone scale, and it would be interesting to see if Debussy or Griffes could be easily transported to, say, 50-et.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:

> One mode of it is [0, 5, 10, 15, 21, 26] with steps 555655 in the 31 et, but it also has versions in 12, 19, 31, 43, 50 and 74.

If someone wants to treat it as a chord rather than a scale, and would like to use them in succession, it should be noted that the structure of harmonic relationships is particularly simple. The meantone hexachord is a 6-tone MOS whose generator is the meantone, and a hexachord one meantone away will share five notes, two away four notes, and so forth. Hence movement by a major third (two meantones) is quite natural, and 7/5 (three meantones) and 7/4 (five meantones) also work.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> I found a unqiue 6-tone 9-limit chord/scale for the 31 et, which
>turns out to be a general feature of the standard septimal meantone
>temperament; this is the meantone in which both 81/80 *and* 126/125
> (and hence 225/224 = (81/80)/(126/125)) are commas.
>
> One mode of it is [0, 5, 10, 15, 21, 26] with steps 555655 in the
>31 et, but it also has versions in 12, 19, 31, 43, 50 and 74. The 12-
>tone version is the whole-tone scale, and it would be interesting to
>see if Debussy or Griffes could be easily transported to, say, 50-et.

Gene, there's something quite similar in 22-tET. The chord/scale
434434 has all 15 intervals as approximate 9-limit consonances.