A 540/539 tempered chord

Pondering Minerva[12], I was led to consider the chord 1-7/6-7/5-18/11. The interval from 7/5 to 18/11 is 90/77, which is 540/539 sharper than 7/6. Tempering by 540/539 leads to a chord which is a sort of unidecimal diminished seventh of sorts: 7/6-6/5-7/6-11/9, closing out at an octave. If you add 225/224 to the comma mix, you get unidecimal marvel temperament, with 1-5/4-14/9 tempering to a 5/4-5/4-9/7 triad. If you have 7/6-7/5-7/6-18/11 chords in the octave classes equal to some value mod four, and 5/4-5/4-9/7 equal to some value mod three, you get various twelve note scales, which might be interesting. I plan to find the twelve-note hobbit for unidecimal marvel and see if that has any of these chords.

This 7/6-6/5-7/5-11/9 chord has, of course each interval one apart as an 11-limit consonance. Two apart gives 7/5, 7/5, 10/7, 10/7, and three apart of course inverts one apart. So it's all consonances, and ones pretty close to just, since tempering out 540/539 leads to a very accurate tuning.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>I plan to find the twelve-note hobbit for unidecimal marvel and see if that has any of these chords.

It turns out that if you tune both to 72et, a very reasonable choice, unidecimal marvel12 and prodigy12 become the same scale. This scale has three 7/6-6/5-7/6-11/9 quasi-diminished chords and two 5/4-5/4-9/7 augemented chords among its other talents.