Re: Diatonic circle of major/minor thirds in terms of Rameau/Riemann

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

> > By this I mean the following cycle in the diatonic scale:
> > C==>E==>G==>B==>D==>F==>A==>C
>
> > Does this have some recognized name?
>
> C==>E==>G is called the "Tonic" of C-major

This kind of misses the point, which was that in the diatonic scale,
we can get the whole scale as a circle of thirds. This is related to
the way we can get it as a chain of whole tones and semitones; instead
of "llsllls" the pattern now is "lslssls". That in this case the
circle consists of thirds, and that triads appear in it, is not
something we can generally expect in similar cases. For the pentatonic
scale, the corresponding circle would be CGADFC, with fifths and a
minor sixth (or equivalently, we could use fourths and a major third.)
The pattern now would be "lllsl", as opposed to "slssl" for the step
sizes. I'm trying to find if this has a name in the diatonic case
which could be used to concoct a more general name.

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

> For the pentatonic
> scale, the corresponding circle would be CGADFC

CGDAFC, with pattern "sssls".

Chalmers referred to this as a tritriadic scale.
If you start with the F you alternate L and s.
lslsls.
if you start the pentatonic on F you don't have a minor 6th except as the disjunction back to C

>>> > By this I mean the following cycle in the diatonic scale:
>>> > C==>E==>G==>B==>D==>F==>A==>C
>> >>
>> > >
>>> > Does this have some recognized name?
>> >>
>> >> C==>E==>G is called the "Tonic" of C-major
> >

This kind of misses the point, which was that in the diatonic scale,
we can get the whole scale as a circle of thirds. This is related to
the way we can get it as a chain of whole tones and semitones; instead of "llsllls" the pattern now is "lslssls". That in this case the
circle consists of thirds, and that triads appear in it, is not
something we can generally expect in similar cases. For the pentatonic
scale, the corresponding circle would be CGADFC, with fifths and a
minor sixth (or equivalently, we could use fourths and a major third.)
The pattern now would be "lllsl", as opposed to "slssl" for the step
sizes. I'm trying to find if this has a name in the diatonic case
which could be used to concoct a more general name.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
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