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Symmetrical Non-Equal Divisions of the Octave?

🔗Bill Flavell <bill_flavell@email.com>

3/4/2006 11:34:00 AM

That would be my designation for the class/species
of bi-directional just intonation tunings I'm interested
in designing/exploring.

Has this class/species been enumerated/defined in
alternative tuning history yet?

Thanks. :)

Bill Flavell

🔗Keenan Pepper <keenanpepper@gmail.com>

3/4/2006 3:35:12 PM

On 3/4/06, Bill Flavell <bill_flavell@email.com> wrote:
>
> That would be my designation for the class/species
> of bi-directional just intonation tunings I'm interested
> in designing/exploring.
>
> Has this class/species been enumerated/defined in
> alternative tuning history yet?

I would say _most_ of the tunings discussed on this list have
inversional symmetry. Any collection of contiguous notes from a linear
temperament, such as a MOS, has inversional symmetry, and many JI
constructions like tonality diamonds and hexanies have inversional
symmetry. Asymmetry is the exception, not the rule.

Keenan

🔗Bill Flavell <bill_flavell@email.com>

3/4/2006 3:41:29 PM

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> I would say _most_ of the tunings discussed on this list have
> inversional symmetry. Any collection of contiguous notes from a linear
> temperament, such as a MOS,

What is MOS?

> has inversional symmetry, and many JI
> constructions like tonality diamonds and hexanies have inversional
> symmetry. Asymmetry is the exception, not the rule.

Very interesting, Keenan! :) Thanks for that info! :)

Bill Flavell

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

3/4/2006 4:33:27 PM

--- In tuning@yahoogroups.com, "Bill Flavell" <bill_flavell@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> >
> > I would say _most_ of the tunings discussed on this list have
> > inversional symmetry. Any collection of contiguous notes from a linear
> > temperament, such as a MOS,
>
> What is MOS?

You can often find definitions for tuning list jargon on the Tonalsoft
encyclopedia site.

http://tonalsoft.com/enc/m/mos.aspx

🔗Bill Flavell <bill_flavell@email.com>

3/4/2006 4:50:42 PM

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...> wrote:
>
> You can often find definitions for tuning list jargon on the Tonalsoft
> encyclopedia site.
>
> http://tonalsoft.com/enc/m/mos.aspx

Thank you very much, Keenan! :) I'll archive that URL! :)

Bill Flavell