Basic consonant meantone pentads and hexads

A pentad can be considered either as a scale or a chord. As a scale,
it has the nice property that if the pentad is consonant, so are all
of its chords. The same, of course, is true for hexads, etc. This
gets nice, as we've seen before, if we go to the 11-limit and look at
7-note scales. But here is what we have in a span of 10 for the 9-
limit.

Consonant (9-limit) meantone pentads

1: [0, 1, 2, 3, 4]
9: [0, 2, 3, 4, 6]
50: [0, 2, 4, 6, 8]
128: [0, 1, 2, 4, 10]
141: [0, 2, 4, 6, 10]
166: [0, 2, 4, 8, 10]
173: [0, 2, 6, 8, 10]
175: [0, 4, 6, 8, 10]
209: [0, 6, 8, 9, 10]

Consonant (9-limit) meantone hexands

61: [0, 2, 4, 6, 8, 10]

--- In tuning-math@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:

> Consonant (9-limit) meantone pentads
>
> 1: [0, 1, 2, 3, 4]
> 9: [0, 2, 3, 4, 6]
> 50: [0, 2, 4, 6, 8]
> 128: [0, 1, 2, 4, 10]
> 141: [0, 2, 4, 6, 10]
> 166: [0, 2, 4, 8, 10]
> 173: [0, 2, 6, 8, 10]
> 175: [0, 4, 6, 8, 10]
> 209: [0, 6, 8, 9, 10]
>
>
> Consonant (9-limit) meantone hexands
>
> 61: [0, 2, 4, 6, 8, 10]

Of these chords/scales, three are strictly proper when tuned to 31-et:

1: [0, 1, 2, 3, 4]
128: [0, 1, 2, 4, 10]
209: [0, 6, 8, 9, 10]

The first, of course, is the standard meantone pentatonic scale. The
other two are inversely related, and are best known as chords rather
than scales, being the otonal and utonal complete ninth chords. In
their JI version, they appear as the 7-limit 5-note dwarf (otonal)
and as a scale called "minor_5" in the Scala directory (utonal.)