Re: Classical minor tonality as an example for xenharmonic tonalitie

I thought I'd mention that the major mode, harmonic major, melodic major and 3 types of minor scale are all instances of what Alexander John Ellis called the "principal trichordals" of the "duodene." The "duodene" is one of the most compact and harmonious 5-limit JI 12-tone tunings: 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1. The "trichordals" may be thought of as the 8 scales constructed from either major or minor triads on the roots 1/1, 4/3 and 3/2. The other two are 1/1 9/8 5/4 4/3 3/2 5/3 9/5 2/1 and 1/1 9/8 6/5 4/3 3/2 5/3 9/5 2/1.

These 8 scales are part of the set of 52 7-tone harmonic scales. Harmonic scales are those in which every note is part of a major or minor triad and all the triads are connected by common tones.

A number of these have been found by Graham Breed and Gene Ward Smith. Kraig Grady has made a most useful and cleaer plot of these scales on the triangular lattice.

--John

Hi John;
Here is a copy of the chart you mentioned
http://anaphoria.com/Chalmersharmheptatonics.jpg
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--- In tuning@yahoogroups.com, "John H. Chalmers" <JHCHALMERS@...> wrote:

> These 8 scales are part of the set of 52 7-tone harmonic scales.
> Harmonic scales are those in which every note is part of a major or
> minor triad and all the triads are connected by common tones.
>
> A number of these have been found by Graham Breed and Gene Ward Smith.
> Kraig Grady has made a most useful and cleaer plot of these scales on
> the triangular lattice.

Not to mention there's this:
http://xenharmonic.wikispaces.com/The+Marveldene
and this:
http://xenharmonic.wikispaces.com/thirteendene