DE concordant chain scales

There are scales which can be constructed from chains of two types of
concordances, ordered in a DE manner. Examples are Meantone[5], which
can be taken as the reduction to an octave of four fifths followed by
a minor third, and Ennealimmal[45], which can be constructed as the
reduction to an octave of a DE chain of major thirds and fourths.

For every scale step of Ennealimmal[45], there is either another a
major third above or one a fourth above, but not both. The scale is
completely contructable as a chain of thirds/fourths. The pentatonic
scale is similar.

Does this ring any bells? Has this been discussed or studied before?

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

It occurs to me that I should call these concordant cycle scales.
Also, it would be reasonable to add scales with more than one cycle.
For instance, Meantone[12] has three cycles of diminished seventh
chords, so that above any note there is always either a minor third or
a subminor third (or augmented second, if you prefer.) Of course given
a MOS looking at it as a cycle scale depends heavily on what the set
of allowed concordances are.

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

Miracle[21] = Blackjack also has a concordance circle of 7/6 and 6/5
intervals, but it isn't based on diminished seventh chords since
126/125 is not a comma of miracle. Instead, it is based on |10 5 8
-13>, which tells us that 13 7/6's and 8 6/5's could complete a circle
of concordances for Blackjack, which in fact they do.

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

> There are scales which can be constructed from chains of two types of
> concordances, ordered in a DE manner. Examples are Meantone[5], which
> can be taken as the reduction to an octave of four fifths followed by
> a minor third, and Ennealimmal[45], which can be constructed as the
> reduction to an octave of a DE chain of major thirds and fourths.
>
> For every scale step of Ennealimmal[45], there is either another a
> major third above or one a fourth above, but not both. The scale is
> completely contructable as a chain of thirds/fourths. The pentatonic
> scale is similar.
>
> Does this ring any bells?

Other than the part about concordance, this reminds me of aspects of
both Erv Wilson's work and some academic stuff I've read.

The octatonic scale (Dimipent[8]) can be constructed by alternating
fourths and major thirds.